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Diverse implicit structures of fluids are discovered lately, providing opportunities to study the physics of fluids applying network analysis. Although considerable works devote to identifying informative network structures of fluids, we have limited understanding about the information these networks convey about fluids. To analyze how fluid mechanics is embodied in network topology or vice versa, we reveal a set of fluid-network relations that quantify the interactions between fundamental fluid properties (e.g., kinetic energy and enstrophy decay laws) and defining network characteristics (e.g., spatial self-similarity, scale-invariance, and control scaling). By analyzing spatial self-similarity in classic and generalized contexts, we first assess the self-similarity of vortical interactions in fluid flows. Deviations from self-similarity in networks exhibit power-law scaling behaviors with respect to fluid properties, suggesting the diversity among vortex as essential to self-similar fluid flows. Then, the same paradigm is adopted to investigate scale-invariance using renormalization groups, which reveals that the breaking extents of scale-invariance in networks, similar to those of spatial self-similarity, also scale with fluid properties in power-law manners. Furthermore, we define a control problem on networks to study the propagation of perturbations through vortical interactions over different ranges. The minimum cost of controlling vortical networks exponentially scales with range diameters (i.e., control distances), whose growth rates experiences temporal decays. We show that this temporal decay speed is fully determined by fluid properties in power-law scaling behaviours. In summary, these fluid-network relations enable a deeper understanding of implicit fluid structures and their interactions with fluid dynamics.

We consider how to target evolution conditioned on atypical measurement outcomes in monitored quantum circuits, i.e., the post-selection problem. We show that for a simple class of measurement schemes, post-selected light-cone dynamical correlation functions can be obtained efficiently from the averaged correlations of a different unitary circuit. This connects rare measurement outcomes in one circuit to typical outcomes in another one. We derive conditions for the existence of this rare-to-typical mapping in brickwork quantum circuits made of XYZ gates. We illustrate these general results with a model system that exhibits a dynamical crossover (a smoothed dynamical transition) in event statistics, and discuss extensions to more general dynamical correlations.

The theory of stochastic thermodynamics has revealed many useful fluctuation relations, with the thermodynamic uncertainty relation (TUR) being a theorem of major interest. When many nonequilibrium currents interact with each other, a naive application of the TUR to an individual current can result in an apparent violation of the TUR bound. Here, we explore how such an apparent violation can be used to put a lower bound on the strength of correlations as well as the number of interacting currents in collective dynamics. Our proposed protocol allows for the inference of hidden correlations in experiment, for example when a team of molecular motors pulls on the same cargo but only one or a subset of them is fluorescently tagged. By solving analytically and numerically several models of many-body nonequilibrium dynamics, we ascertain under which conditions this strategy can be applied and the inferred bound on correlations becomes tight.

We investigate the dynamics of phase oscillators in the fully disordered Kuramoto model with couplings of defined asymmetry. The mean-field dynamics is reduced to a self-consistent stochastic single-oscillator problem which we analyze perturbatively and by numerical simulations. We elucidate the influence of the asymmetry on the correlation and response function of the system as well as on the distribution of the order parameter. The so-called volcano transition is shown to be robust with respect to a small degree of coupling asymmetry but to disappear when the antisymmetry in the couplings outweighs the symmetry.

We point out an inconsistency in the theoretical treatment of Bosetti and collaborators (Crystal Growth & Design, 2021, 22.1: 87-97), and then proceed to prove that for monomers interacting by two-body potentials, the presence of an infinite, flat, attractive crystal surface may not induce an increased propensity for cluster formation (that is, secondary nucleation) of the type envisioned by these authors., Comment: 6 typeset pages (achemso class), 1 double-panel figure, rejected by Crystal Growth \& Design

We consider a class of non-integrable 2D Ising models obtained by perturbing the nearest-neighbor model via a weak, finite range potential which preserves translation and spin-flip symmetry, and we study its critical theory in the half-plane. We prove that the leading order long-distance behavior of the correlation functions for spins on the boundary is the same as for the nearest-neighbor model, up to an analytic multiplicative renormalization constant. In particular, the scaling limit is the Pfaffian of an explicit matrix. The proof is based on an exact representation of the generating function of correlations in terms of a Grassmann integral and on a multiscale analysis thereof, generalizing previous results to include observables located on the boundary., Comment: 59 pages, 9 figures

We study the Heisenberg $S=1/2$ chain with random ferro- and antiferromagnetic couplings, using quantum Monte Carlo simulations at ultra-low temperatures, converging to the ground state. Finite-size scaling of correlation functions and excitation gaps demonstrate an exotic critical state in qualitative agreement with previous strong-disorder renormalization group calculations, but with scaling exponents depending on the coupling distribution. We find dual scaling regimes of the transverse correlations versus the distance, with an $L$ independent form $C(r)=r^{-\mu}$ for $r \ll L$ and $C(r,L)=L^{-\eta}f(r/L)$ for $r/L > 0$, where $\mu > \eta$ and the scaling function is delivered by our analysis. These results are at variance with previous spin-wave and density-matrix renormalization group calculations, thus highlighting the power of unbiased quantum Monte Carlo simulations., Comment: 8 pages, 10 figures

A system with a one-form global symmetry at finite temperature can be viewed as a dissipative fluid of string-like objects. In this work, we classify and construct the most general effective field theories for hydrodynamics of such string fluids, in a probe limit where the one-form charge density is decoupled from the energy-momentum tensor. We show that at leading order in the derivative expansion, there are two distinct types of diffusive transport in a string fluid depending on the discrete spacetime symmetries present in it. One particular application of interest is magnetohydrodynamics (MHD), where the effective field theories describe the diffusion of magnetic field lines. Due to the distinction between the effective field theories for different discrete symmetries, we show that the MHD of a fluid with charge conjugation symmetry is qualitatively different from that of a neutron star, which we previously discussed in arXiv:2207.01636. The explicit effective actions that we write down can be used to obtain the dispersion relations $\omega(k)$ up to cubic order in momenta for each of the different discrete symmetry choices. As another application of this formalism, we show that when the one-form symmetry is spontaneously broken, the effective action reduces to the Maxwell theory. This confirms the interpretation of the photon as a Goldstone boson arising from the spontaneous breaking of a one-form symmetry., Comment: 39 pages, 6 figures

The energy surplus resulting from radiative forcing causes warming of the Earth system. This initial warming drives a myriad of changes including in sea surface temperatures (SSTs), leading to different radiative feedbacks. The relationship between the radiative feedbacks and the pattern of SST changes is referred to as the "pattern effect". The current approach to study the pattern effect relies on diagnosing the response of atmosphere-only models to perturbations in the SST boundary condition. Here, we argue that the fluctuation-dissipation relation (FDR), together with coarse-graining procedures, is a computationally cheap and theoretically grounded alternative to model experiments. We introduce a protocol to study the pattern effect and present its application in a state-of-the-art coupled climate model. By focusing on the coupled dynamics, we unveil the role of the slow ocean component in setting the pattern effect. We present a new "sensitivity map", representing a first, qualitative prediction of the response of the average top-of-the-atmosphere (TOA) radiative flux to perturbations in the SST field. We find negative sensitivity throughout the tropics, in contrast to the current understanding of a positive-negative dipole of sensitivity in the tropical Pacific. Considering only the shortest time scales, the response is dominated by the fast atmospheric variability and we recover results in qualitative agreement with the literature. Therefore, the difference between our results and previous studies, largely comes from including the atmosphere-ocean coupling. The framework offers a conceptually novel perspective on the pattern effect: feedbacks in the coupled system are encoded in a temporally and spatially dependent response operator, rather than time-independent maps as for previous studies.

We investigate the dynamics of multipartite entanglement after quenches from initial states which generate multiplets of quasiparticle excitations beyond the usual pair structure. We focus on the dynamics of tripartite entanglement through the lens of the Markov gap -- a computable quantity that signals irreducible tripartite entanglement when positive. In the XX spin chain, we show that the Markov gap is positive at intermediate times, implying the presence of tripartite entanglement. After a time delay, the Markov gap increases and then decays at longer times, thus exhibiting an entanglement barrier. We argue that those qualitative features are consistent with an interpretation of the spreading of tripartite entanglement by triplets of tripartite-entangled quasiparticles., Comment: 3+3 pages, 3+2 figures

A percolation model inspired by crossword puzzle games is introduced. A game proceeds by solving words, which are segments of sites in a two-dimensional lattice. As test case, the \emph{iid} variant allows for independently occupying sites with letters, only the percolation criterion depends on the existence of solved words. For the \emph{game} variant, inspired by real crossword puzzles, it becomes more likely to solve crossing words which share sites with the already solved words. In this way avalanches of solved words may occur. Both model variants exhibit a percolation transition as function of the a-priori site or word solving probability, respectively. The \emph{iid} variant is in the universality class of standard two-dimensional percolation. The \emph{game} variant exhibits a non-universal critical exponent $\nu$ of the correlation length. The actual value of $\nu$ depends on the function which controls how much solved words accelerate the solved of crossing words., Comment: 6 pages, 7 figures

We investigate $\phi^{2n+1}$ deformations of the generalized free theory in the $\epsilon$ expansion, where the canonical kinetic term is generalized to a higher-derivative version. For $n=1$, we use the conformal multiplet recombination method to determine the leading anomalous dimensions of the fundamental scalar operator $\phi$ and the bilinear composite operators $\mathcal J$. Then we extend the $n=1$ analysis to the Potts model with $S_{N+1}$ symmetry and its higher-derivative generalization, in which $\phi$ is promoted to an $N$-component field. We further examine the Chew-Frautschi plots and their $N$ dependence. However, for each integer $n>1$, the leading anomalous dimensions of $\phi$ and $ \mathcal{J}$ are not fully determined and contain one unconstrained constant, which in the canonical cases can be fixed by the results from the traditional diagrammatic method. In all cases, we verify that the multiplet-recombination results are consistent with crossing symmetry using the analytic bootstrap methods., Comment: 41 pages, 14 figures

Many natural and human-made complex systems feature group interactions that adapt over time in response to their dynamic states. However, most of the existing adaptive network models fall short of capturing these group dynamics, as they focus solely on pairwise interactions. In this study, we employ adaptive higher-order networks to describe these systems by proposing a general framework incorporating both adaptivity and group interactions. We demonstrate that global synchronization can exist in those complex structures, and we provide the necessary conditions for the emergence of a stable synchronous state. Additionally, we analyzed some relevant settings, and we showed that the necessary condition is strongly related to the master stability equation, allowing to separate the dynamical and structural properties. We illustrate our theoretical findings through examples involving adaptive higher-order networks of coupled generalized Kuramoto oscillators with phase lag. We also show that the interplay of group interactions and adaptive connectivity results in the formation of stability regions that can induce transitions between synchronization and desynchronization

2D nonlinear sigma models with Hermitian symmetric target admit a theta-term, which couples the field theory to the topological charge of its instanton gas. At the special coupling theta = pi, by what is nowadays attributed to a coupling-constant anomaly of Lieb-Schultz-Mattis type, such models have a degenerate ground state. Yet, the details of their non-trivial infrared limit have remained open in general. Here we suggest that non-perturbative renormalization group flow into the strong-coupling regime induces strong fluctuations of the theta-parameter, with the consequence that the instanton density is suppressed, the target-space topology effectively altered, and the target-space metric driven off reality and into geometrostasis. Assuming this heuristic scenario and combining it with a Cauchy process of target-space deformation, we present a detailed argument that the O(3) nonlinear sigma model at theta = pi, known to be the effective field theory for critical antiferromagnetic quantum spin chains with large half-integer spin, renormalizes to the conformal field theory of a U(1) boson compactified at a special radius with SU(2) symmetry. A closely related scenario applies to Pruisken's nonlinear sigma model for the integer quantum Hall transition., Comment: 14 pages, 2 figures

The asymptotic correspondence between the probability mass function of the $q$-deformed multinomial distribution and the $q$-generalised Kullback-Leibler divergence, also known as Tsallis relative entropy, is established. The probability mass function is generalised using the $q$-deformed algebra developed within the framework of nonextensive statistics, leading to the emergence of a family of divergence measures in the asymptotic limit as the system size increases. The coefficients in the asymptotic expansion yield Tsallis relative entropy as the leading-order term when $q$ is interpreted as an entropic parameter. Furthermore, higher-order expansion coefficients naturally introduce new divergence measures, extending Tsallis relative entropy through a one-parameter generalisation. Some fundamental properties of these extended divergences are also explored., Comment: 8 pages

This article reviews recent progress in understanding the physics of many-body localisation (MBL) in disordered and interacting quantum many-body systems, from the perspective of ergodicity breaking on the associated Fock space. This approach to MBL is underpinned by mapping the dynamics of the many-body system onto that of a fictitious single particle on the high-dimensional, correlated and disordered Fock-space graph; yet, as we elaborate, the problem is fundamentally different from that of conventional Anderson localisation on high-dimensional or hierarchical graphs. We discuss in detail the nature of eigenstate correlations on the Fock space, both static and dynamic, and in the ergodic and many-body localised phases as well as in the vicinity of the MBL transition. The latter in turn sheds light on the nature of the transition, and motivates a scaling theory for it in terms of Fock-space based quantities. We also illustrate how these quantities can be concretely connected to real-space observables. An overview is given of several analytical and numerical techniques which have proven important in developing a comprehensive picture. Finally, we comment on some open questions in the field of MBL where the Fock-space approach is likely to prove insightful., Comment: 32 pages, 19 figures, Invited review article for J. Phys.: Condens. Matter

The search for quantum algorithms to tackle classical combinatorial optimization problems has long been one of the most attractive yet challenging research topics in quantum computing. In this context, variational quantum algorithms (VQA) are a promising family of hybrid quantum-classical methods tailored to cope with the limited capability of near-term quantum hardware. However, their effectiveness is hampered by the complexity of the classical parameter optimization which is prone to getting stuck either in local minima or in flat regions of the cost-function landscape. The clever design of efficient optimization methods is therefore of fundamental importance for fully leveraging the potential of VQAs. In this work, we approach parameter optimization as a sequential decision-making problem and tackle it with an adaptation of Monte Carlo Tree Search (MCTS), a common artificial intelligence technique designed for efficiently exploring complex decision graphs. We show that leveraging regular parameter patterns deeply affects the decision-tree structure and allows for a flexible and noise-resilient optimization strategy suitable for near-term quantum devices. Our results shed further light on the interplay between artificial intelligence and quantum information and provide a valuable addition to the toolkit of variational quantum circuits., Comment: 10+5 pages, 7+5 figures

Out-of-time-ordered-correlators (OTOCs) have been suggested as a means to diagnose chaotic behavior in quantum mechanical systems. Recently, it was found that OTOCs display exponential growth for the inverted quantum harmonic oscillator, mirroring the fact that this system is classically and quantum mechanically unstable. In this work, I study OTOCs for the inverted anharmonic (pure quartic) oscillator in quantum mechanics, finding only oscillatory behavior despite the classically unstable nature of the system. For higher temperature, OTOCs seem to exhibit saturation consistent with a value of $-2 \langle x^2 \rangle_T \langle p^2 \rangle_T$ at late times. I provide analytic evidence from the spectral zeta-function and the WKB method as well as direct numerical solutions of the Schr\"odinger equation that the inverted quartic oscillator possesses a real and positive energy eigenspectrum, and normalizable wave-functions., Comment: 20 pages, 4 figures

The mode-coupling theory (MCT) of the glass transition ranks among the most successful first-principles kinetic theories to describe glassy dynamics. However, MCT does not fully account for crucial aspects of the dynamics near the glass transition. To facilitate improving the theory, we critically test the approximations inherent in MCT for a supercooled mixture using Brownian dynamics simulations. Although each MCT approximation significantly impacts the predicted dynamics, our findings show that long-time cancellations of errors occur due to static and dynamic approximations of four-point correlation functions, with the validity of these approximations remaining relatively constant across different temperatures. Notably, the MCT form of the memory functional maintains remarkably high accuracy even in the supercooled regime when evaluated with the intermediate scattering function from simulations. The primary discrepancies between theoretical predictions and experimental results arise from the self-consistent nature of the MCT equations, which amplify minor errors in the memory kernel. This suggests that minor corrections to the memory functional could substantially enhance the theory's predictive accuracy.

We explore how the disorder impacts the current fluctuations in the symmetric simple exclusion process (SSEP) within a heterogeneous environment. First, we analyze the SSEP with a defect site under the periodic boundary conditions. We derive the exact expression for the second moment of the current and observe deviations from that of the homogeneous system. Notably, the second moment of the current shows asymmetric density dependence around a density of 1/2 and surpassing that of the homogeneous system in the low-density region. Furthermore, based on the finding from the SSEP with a defect site, we present an approximate derivation of the second moment of the current in the SSEP on a quenched random energy landscape using a partial-mean-field approach. The second moment of the current is heavily influenced by the energy landscape, revealing unique effects arising from the interplay between the heterogeneous environment and the many-body system. Our findings provide valuable insights that can be applied to control current fluctuations in systems involving the interactions of many particles, such as biological transport., Comment: 9 pages, 3 figures

We show that randomness in quadratic Hamiltonians for multimode bosonic systems results in certain information scrambling diagnostics, mirroring those seen in chaotic systems. Specifically, considering initial Gaussian states, we observe the disappearance of the memory effect in entanglement dynamics and the negative value of tripartite mutual information. However, in contrast to chaotic systems, we find that the spectral form factor exhibits a non-linear ramp and the out-of-time-ordered correlators display a power law growth. These results show that information scrambling, associated with randomness, is a distinct feature from quantum chaos. Moreover, our results provide insight into the dynamics of Gaussian states of continuous-variable systems that are useful and available resources for quantum information processing., Comment: 8+4 pages, 4+2 figures

Finding optimal control strategies to suppress quantum thermalization for arbitrarily initial states, the so-called quantum nonergodicity control, is important for quantum information science and technologies. Previous control methods largely relied on theoretical model of the target quantum system, but invertible model approximations and inaccuracies can lead to control failures. We develop a model-free and deep-reinforcement learning (DRL) framework for quantum nonergodicity control. It is a machine-learning method with the unique focus on balancing exploration and exploitation strategies to maximize the cumulative rewards so as to preserve the initial memory in the time-dependent nonergodic metrics over a long stretch of time. We use the paradigmatic one-dimensional tilted Fermi-Hubbard system to demonstrate that the DRL agent can efficiently learn the quantum many-body system solely through the interactions with the environment. The optimal policy obtained by the DRL provides broader control scenarios for managing nonergodicity in the phase diagram as compared to, e.g., the specific protocol for Wannier-Stark localization. The continuous control protocols and observations are experimentally feasible. The model-free nature of DRL and its versatile search space for control functions render promising nonergodicity control in more complex quantum many-body systems., Comment: 19 pages, 8 figures

We study operator dynamics in Brownian quantum many-body models with $q$-local interactions. The operator dynamics are characterized by the time-dependent size distribution, for which we derive an exact master equation in both the Brownian Majorana Sachdev-Ye-Kitaev (SYK) model and the spin model for general $q$. This equation can be solved numerically for large systems. Additionally, we obtain the analytical size distribution in the large $N$ limit for arbitrary initial conditions and $q$. The distributions for both models take the same form, related to the $\chi$-squared distribution by a change of variable, and strongly depend on the initial condition. For small initial sizes, the operator dynamics are characterized by a broad distribution that narrows as the initial size increases. When the initial operator size is below $q-2$ for the Majorana model or $q-1$ for the spin model, the distribution diverges in the small size limit at all times. The mean size of all operators, which can be directly measured by the out-of-time ordered correlator, grows exponentially during the early time. In the late time regime, the mean size for a single Majorana or Pauli operator for all $q$ decays exponentially as $t e^{-t}$, much slower than all other operators, which decay as $e^{-t}$. At finite $N$, the size distribution exhibits modulo-dependent branching within a symmetry sector for the $q \geq 8$ Majorana model and the $q \geq 4$ spin model. Our results reveal universal features of operator dynamics in $q$-local quantum many-body systems., Comment: 31 pages, 7 figures

A spin-1/2 Heisenberg model with a chirality-chirality interaction (CCI) on a two-leg ladder offers a minimal setup to study an interplay between spin and chirality degrees of freedom. This model is potentially relevant to understanding the effects of a four-spin ring exchange and a phonon-mediated interaction on a ladder. By applying the Abelian bosonization and two types of spin-chirality duality, we derive a rich phase diagram of this model that includes previously unexplored cases of a ferromagnetic rung exchange $J_\perp<0$ or a negative CCI $K_{\rm ch}<0$. The phase diagram consists of the rung singlet (RS) phase, the Haldane phase, and three non-magnetic ordered phases. Furthermore, the RS and Haldane phases consist of several regions with different dominant correlations in terms of spin, dimer, or chirality. We perform numerical simulations to confirm the predicted phase structure and critical properties., Comment: 16 pages, 13 figures. arXiv admin note: text overlap with arXiv:2311.07053

Formulating order metrics that sensitively quantify the degree of order/disorder in many-particle systems in $d$-dimensional Euclidean space $\mathbb{R}^d$ across length scales is an outstanding challenge in physics, chemistry, and materials science. Since an infinite set of $n$-particle correlation functions is required to fully characterize a system, one must settle for a reduced set of structural information, in practice. We initiate a program to use the number variance $\sigma_N^2(R)$ associated with a spherical sampling window of radius $R$ (which encodes pair correlations) and an integral measure derived from it $\Sigma_N(R_i,R_j)$ that depends on two specified radial distances $R_i$ and $R_j$. Across the first three space dimensions ($d = 1,2,3$), we find these metrics can sensitively describe and categorize the degree of order/disorder of 41 different models of antihyperuniform, nonhyperuniform, disordered hyperuniform, and ordered hyperuniform many-particle systems at a specified length scale $R$. Using our local variance metrics, we demonstrate the importance of assessing order/disorder with respect to a specific value of $R$. These order metrics could also aid in the inverse design of structures with prescribed scale-specific degrees of order/disorder that yield desired physical properties. In future work, it would be fruitful to explore the use of higher-order moments [S. Torquato et al., Phys. Rev. X, 11, 021028 (2021)] to devise even more sensitive order metrics., Comment: 19 pages, 8 figures

We investigate the critical behavior of the Kinetic Ising model with non-reciprocal nearest neighbors interactions. A finite-size scaling study suggests that the model belongs to the Ising universality class. We characterize the off-equilibrium behavior of the model by measuring the entropy production rate and by studying the coarsening dynamics, which shows a super-diffusive relaxation. A coarse-grained equation of motion is in compelling agreement with the numerical findings. A one-loop renormalization group calculation shows that the model belongs to the Model A universality class.

Nodal loop semimetals are topological materials with drumhead surface states characterized by reduced kinetic energy. If the Fermi energy of such a system is near these nondispersive states interaction among charge carriers substantially impacts their electronic structure. The emergence of magnetism in these surface states is one of the possible consequences. Ca3P2 an already synthesized material possesses a remarkably large nodal loop which is situated exactly at the Fermi level of the bulk system. In the present work, we investigate how surface magnetism is impacted by surface reconstruction and lattice termination in finite slabs in this material. We show that a slight deviation from the stoichiometric occupation of Ca sites results in the stabilization of magnetic patterns.

We apply the hybrid Projectionless Dynamic Theory (hybrid PDT) formulation of the Elastically Collective Nonlinear Langevin Equation (ECNLE) activated dynamics approach to study dense fluids of sticky spheres with short range attractions. Of special interest is the problem of non-monotonic evolution with attraction strength of the elastic modulus ("re-entrancy") at high packing fractions far beyond the ideal mode coupling theory (MCT) nonergodicity boundary. The dynamic force constraints explicitly treat the bare attractive forces that drive transient physical bond formation, while a projection approximation is employed for the singular hard-sphere potential. The resultant interference between repulsive and attractive forces contribution to the dynamic vertex results in the prediction of localization length and elastic modulus re-entrancy, qualitatively consistent with experiments. The non-monotonic evolution of the alpha time predicted by ECNLE theory with the hybrid PDT approach is explored in depth as a function of packing fraction, attraction strength, and range. Isochronal dynamic arrest boundaries based on activated relaxation display the classic non-monotonic glass melting form. Comparisons of these results with the corresponding predictions of ideal MCT and the ECNLE and NLE activated theories based on projection reveal large qualitative differences. The consequences of stochastic trajectory fluctuations on intra-cage single particle dynamics with variable attraction strengths are also studied. Large dynamical heterogeneity effects in attractive glasses are properly captured. These include a rapidly increasing non-Gaussian parameter with packing fraction and a non-monotonic evolution with attraction strength, in accord with recent simulations. Extension of the microscopic theoretical approach to treat double yielding in attractive glass nonlinear rheology is possible., Comment: Accepted in Softmatter

This extended article presents a thermomechanical approach for calculating the stress tensor from the thermodynamic potential of ionic fluids. Our technique, which is based on the invariance of the thermodynamic potential with respect to spatial transformations of shear and rotation, offers an alternative to the general covariant approach recently developed by two of us. We apply this technique in both pure mean field theories of ionic fluids and in a theory that includes thermal fluctuations of the electrostatic potential, using variational field theory. We also apply the thermomechanical approach to fluid models described by vector order parameters, such as liquid dielectrics, and obtained for this case a general expression for the stress tensor. Additionally, we discuss specific issues related to the calculation of disjoining pressure in ionic fluids confined in nanoscale slit-like pores with conductive or dielectric walls., Comment: Submitted to Journal of Statistical Mechanics: Theory and Experiment

We consider random walks in the form of nearest-neighbor hopping on Erdos-Renyi random graphs of finite fixed mean degree c as the number of vertices N tends to infinity. In this regime, using statistical field theory methods, we develop an analytic theory of the first return time probability distribution. The problem turns out closely related to finding the spectrum of the normalized graph Laplacian that controls the continuum time version of the nearest-neighbor-hopping random walk. In the infinite graph limit, where loops are highly improbable, the returns operate in a manner qualitatively similar to c-regular trees, and the expressions for probabilities resemble those on random c-regular graphs. Because the vertex degrees are not exactly constant, however, the way c enters the formulas differs from the dependence on the graph degree of first return probabilities on random regular graphs.

In this study, we analyzed urn models by solving the discrete-time master equation using an expansion in moments. This approach is a viable alternative to conventional methods, such as system-size expansion, allowing for the determination of analytical expressions for the mean and variance in an exact form and thus valid for any system size. In particular, this approach was used to study Bernoulli-Laplace and Ehrenfest urns, for which analytic expressions describing their evolution were found. This approach and the results will contribute to a more comprehensive understanding of stochastic systems and statistical physics for small-sized systems, where the thermodynamic limit cannot be assumed., Comment: 6 pages, 5 figures

Imaginary-time path integral (PI) is a rigorous tool to treat nuclear quantum effects in static properties. However, with its high computational demand, it is crucial to devise precise estimators. We introduce generalized PI estimators for the energy and heat capacity that utilize coordinate mapping. While it can reduce to the standard thermodynamic and centroid virial (CVir) estimators, the formulation can also take advantage of harmonic character of quantum oscillators and crystals to construct a coordinate mapping. This yields harmonically mapped averaging (HMA) estimators, with mappings that decouple (HMAc) or couple (HMAq) the centroid and internal modes. The HMAq is constructed with normal mode coordinates (HMAq-NM) with quadratic scaling of cost or harmonic oscillator staging (HMAq-SG) coordinates with linear scaling. The estimator performance is examined for a 1D anharmonic oscillator and a 3D Lennard-Jones crystal using path integral molecular dynamics (PIMD) simulation. The HMA estimators consistently provide more precise estimates compared to CVir, with the best performance obtained by HMAq-NM, followed by HMAq-SG, and then HMAc. We also examine the effect of anharmonicity (for AO), intrinsic quantumness, and Trotter number. The HMA formulation introduced assumes the availability of forces and Hessian matrix; however, an equally efficient finite difference alternative is possible when these derivatives are inaccessible. The remarkable improvement in precision offered by HMAq estimators provides a framework for efficient PI simulation of more challenging systems, such as those based on \textit{ab initio} calculations.

We study a class of many body chaotic models related to the Brownian Sachdev-Ye-Kitaev model. An emergent symmetry maps the quantum dynamics into a classical stochastic process. Thus we are able to study many dynamical properties at finite N on an arbitrary graph structure. A comprehensive study of operator size growth with or without spatial locality is presented. We will show universal behaviors emerge at large N limit, and compare them with field theory method. We also design simple stochastic processes as an intuitive way of thinking about many-body chaotic behaviors. Other properties including entanglement growth and other variants of this solvable models are discussed., Comment: 16pages + appendix

Control landscape phase transitions (CLPTs) occur as abrupt changes in the cost function landscape upon varying a control parameter, and can be revealed by non-analytic points in statistical order parameters. A prime example are quantum speed limits (QSL) which mark the onset of controllability as the protocol duration is increased. Here we lay the foundations of an analytical theory for CLPTs by developing Dyson, Magnus, and cumulant expansions for the cost function that capture the behavior of CLPTs with a controlled precision. Using linear and quadratic stability analysis, we reveal that CLPTs can be associated with different types of instabilities of the optimal protocol. This allows us to explicitly relate CLPTs to critical structural rearrangements in the extrema of the control landscape: utilizing path integral methods from statistical field theory, we trace back the critical scaling of the order parameter at the QSL to the topological and geometric properties of the set of optimal protocols, such as the number of connected components and its dimensionality. We verify our predictions by introducing a numerical sampling algorithm designed to explore this optimal set via a homotopic stochastic update rule. We apply this new toolbox explicitly to analyze CLPTs in the single- and two-qubit control problems whose landscapes are analytically tractable, and compare the landscapes for bang-bang and continuous protocols. Our work provides the first steps towards a systematic theory of CLPTs and paves the way for utilizing statistical field theory techniques for generic complex control landscapes., Comment: 38 pages, 24 figures

We explore the phenomena of prethermalization in a many-body classical system of rotors under aperiodic drives characterised by waiting time distribution (WTD), where the waiting time is defined as the time between two consecutive kicks. We consider here two types of aperiodic drives: random and quasi-periodic. We observe a short-lived pseudo-thermal regime with algebraic suppression of heating for the random drive where WTD has an infinite tail, as observed for Poisson and binomial kick sequences. On the other hand, quasi-periodic drive characterised by a WTD with a sharp cut-off, observed for Thue-Morse sequence of kick, leads to prethermal region where heating is exponentially suppressed. The kinetic energy growth is analyzed using an average surprise associated with WTD quantifying the randomness of drive. In all of the aperiodic drives we obtain the chaotic heating regime for late time, however, the diffusion constant gets renormalized by the average surprise of WTD in comparison to the periodic case., Comment: 12 pages, 12 figures

Metastable phases, in general, are unstable to nucleating droplets of the order defining the global free energy minima. However, whether such a droplet grows or shrinks relies on a competition between the surface tension and bulk energy density. We study the role of coupling a topological fermionic field to a scalar field undergoing such nucleation processes. We find that existence of non-trivial fermionic boundary modes on the nucleating droplets leads to substantial quantum corrections to the surface tension thereby modifying the size of the critical nucleus beyond which unrestricted droplet growth happens. To illustrate the phenomena we devise a minimal model of fermions in a Chern insulating system coupled to a classical Ising field in two spatial dimensions. Using a combination of analytic and numerical methods we conclusively show that topological phases can lead to characteristic quantum surface tension. Apart from material systems, our work has implications on the interplay of physics of statistical classical fields and quantum topological order., Comment: 6+2 pages, 4+2 Figures

Multifractal analysis is a powerful tool for characterizing the localization properties of wave functions. Despite its utility, this tool has been predominantly applied to disordered Hermitian systems. Multifractal statistics associated with the non-Hermitian skin effect remain largely unexplored. Here, we demonstrate that the tree geometry induces multifractal statistics for the single-particle skin states on the Cayley tree. This sharply contrasts with the absence of multifractal properties for conventional single-particle skin effects in crystalline lattices. Our work uncovers the unique feature of the skin effect on the Cayley tree and provides a novel mechanism for inducing multifractality in open quantum systems without disorder., Comment: 19 pages, 7 figures

The structure, thermodynamics and slow activated dynamics of the equilibrated metastable regime of glass-forming fluids remains a poorly understood problem of high theoretical and experimental interest. We apply a highly accurate microscopic equilibrium liquid state integral equation theory that has not been previously explored in the deeply metastable regime, in conjunction with na\"ive mode coupling theory of particle localization, to study in a unified manner the structural correlations, thermodynamic properties, and dynamic elastic shear modulus in deeply metastable hard sphere fluids. New and distinctive behaviors are predicted including divergent inverse critical power laws for the contact value of the pair correlation function, pressure, and inverse dimensionless compressibility, and a splitting of the second peak and large suppression of interstitial configurations of the pair correlation function. The dynamic elastic modulus is predicted to exhibit two distinct exponential growth regimes with packing fraction that have strongly different slopes. These new thermodynamic, structural, and elastic modulus results are consistent with simulations and experiments. Perhaps most unexpectedly, connections between the amplitude of long wavelength density fluctuations, dimensionless compressibility, local structure, and the dynamic elastic shear modulus are discovered. These connections are more broadly relevant to understand the slow activated relaxation and mechanical response of colloidal suspensions in the ultra-dense metastable region and deeply supercooled thermal liquids in equilibrium., Comment: Accepted in Phys. Rev. E

We study the dynamics of a single spin coupled to a bosonic bath at zero temperature driven by a ramp of the bias field. A single spin coupled to a bosonic sub-Ohmic bath exhibits a quantum phase transition at a certain strength of spin-boson coupling. When the bias field is ramped from a large value to zero at this critical coupling strength, the system initialized at the ground state ends up with a finite magnetization due to the critical slowing down near the transition. On the basis of the pulse-impulse approximation, we derive a scaling law between the residual magnetization and the ramp speed. The obtained scaling relation is examined using a numerical simulation based on the tensor network. The data are in favor of the scaling law to hold. We discuss the demonstration of our theoretical results by means of quantum simulation using the quantum annealer., Comment: 15 pages, 5 figures

The power and expressivity of deep classical neural networks can be attributed to non-linear input-output relations. Such non-linearities are at the heart of many computational tasks, such as data classification and pattern recognition. Quantum neural networks, on the other hand, are necessarily linear as they process information via unitary operations. Here we show that effective non-linearities can be implemented in these platforms by exploiting the relationship between information processing and many-body quantum dynamics. The crucial point is that quantum many-body systems can show emergent collective behavior in the vicinity of phase transitions, which leads to an effectively non-linear dynamics in the thermodynamic limit. In the context of quantum neural networks, which are necessarily finite, this translates into metastability with transient non-ergodic behavior. By using a quantum neural network whose architecture is inspired by dissipative many-body quantum spin models, we show that this mechanism indeed allows to realize non-linear data classification, despite the underlying dynamics being local and linear. Our proof-of-principle study may pave the way for the systematic construction of quantum neural networks with emergent non-linear properties., Comment: 19 pages, 6 figures

Based on the tensor tree network with the Born machine framework, we propose a general method for constructing a generative model by expressing the target distribution function as the quantum wave function amplitude represented by a tensor tree. The key idea is dynamically optimizing the tree structure that minimizes the bond mutual information. The proposed method offers enhanced performance and uncovers hidden relational structures in the target data. We illustrate potential practical applications with four examples: (i) random patterns, (ii) QMNIST hand-written digits, (iii) Bayesian networks, and (iv) the stock price fluctuation pattern in S&P500. In (i) and (ii), strongly correlated variables were concentrated near the center of the network; in (iii), the causality pattern was identified; and, in (iv), a structure corresponding to the eleven sectors emerged., Comment: 9 pages, 3 figures

We investigate the evaporation of trace amounts of helium solvated in liquid water using molecular dynamics simulations and theory. Consistent with experimental observations, we find a super-Maxwellian distribution of kinetic energies of evaporated helium. This excess of kinetic energy over typical thermal expectations is explained by an effective continuum theory of evaporation based on a Fokker-Planck equation, parameterized molecularly by a potential of mean force and position-dependent friction. Using this description, we find that helium evaporation is strongly influenced by the friction near the interface, which is anomalously small near the Gibbs dividing surface due to the ability of the liquid-vapor interface to deform around the gas particle. Our reduced description provides a mechanistic interpretation of trace gas evaporation as the motion of an underdamped particle in a potential subject to a viscous environment that varies rapidly across the air-water interface. From it we predict the temperature dependence of the excess kinetic energy of evaporation, which is yet to be measured., Comment: 6 pages, 3 figures

We argue for the existence of a universal phase diagram of $k$-local quantum chains subject to the conservation of a total charge and its dipole moment, which exhibits "freezing" transitions between strongly and weakly Hilbert space fragmented phases as charge filling $\nu$ is varied. We show that these continuous phase transitions occur at a critical charge filling of $\nu_c=(k-2)^{-1}$ independently of the on-site Hilbert space dimension $d$. To this end, we analytically prove that for any $d$, any state for $\nu<\nu_c$ hosts a finite density of sites belonging to "blockages": local regions across which transport of charge and dipole moment cannot occur. We prove that this implies strong fragmentation of typical symmetry sectors into Krylov sectors that each form an exponentially-vanishing fraction of the total sector. By studying the distribution of blockages we analytically characterise how typical states are subdivided into dynamically-disconnected local "active bubbles", and prove that typical states at these charge fillings exhibit area-law entanglement scaling, with rare "inverse quantum many-body scar" states featuring non-area-law scaling. We then numerically show that for $\nu>\nu_c$ and arbitrary $d$, typical symmetry sectors are weakly fragmented, with their dominant Krylov sectors constituted of states that are free of blockages. We also study the critical scaling of the dimensions of various Krylov sectors at $\nu=\nu_c$, as well as investigate the properties of certain special case models for which no phase transitions occur., Comment: 43 pages, 11 figures, 2 tables

In the tensor network approach to statistical physics, properties of the critical point of a 2D lattice model are encoded by a four-legged tensor which is a fixed point of an RG map. The traditional way to find the fixed point tensor consists in iterating the RG map after having tuned the temperature to criticality. Here we develop a different and more direct technique, which solves the fixed point equation via the Newton method. This is challenging due to the existence of marginal deformations -- linear transformations of the coordinate frame, which parametrize a two-dimensional family of fixed points. We address this challenge by including a 90 degree rotation into the RG map. This flips the sign of the problematic marginal eigenvalues, rendering the fixed point isolated and accessible via the Newton method. We demonstrate the power of this technique via explicit computations for the 2D Ising model. Using the Gilt-TNR algorithm at bond dimension $\chi=30$, we find the fixed point tensor with $10^{-9}$ accuracy, much higher than what was previously achieved., Comment: 32+20 pages, 15 figures, 4 tables

We theoretically study the open quantum system dynamics (in the Trotterized limit) of integrable quantum circuits in the presence of onsite dephasing noise with a spin-$\frac{1}{2}$ impurity interacting at the edge. Using a combination of Bethe Ansatz (BA) and exact diagonalization (ED), we study the dynamics of both the bulk and the impurity for the XXX (Heisenberg) and the XX qubit chains in the presence and absence of bulk noise. In the absence of noise, we show that the impurity exhibits two distinct phases, the bound mode phase where the impurity keeps oscillating in time, and the Kondo phase where it decays with Kondo time $t_K$. Turning on the bulk dephasing noise, we find for the two models that in the long time limit in both regimes the quantum Zeno effect takes place where the dynamics of the impurity magnetization slows down as the noise strength $\gamma$ increases. The impurity magnetization in the bound mode regime shows the opposite effect, decaying faster as the noise strength increases for short times ($t \ll 1/\gamma$). We show that the bulk KPZ dynamics of the XXX model is converted to diffusive dynamics as in the XX case studied before by V. Alba, driving both systems to the Zeno effect for the impurity in the long time limit.

Chaos makes isolated systems of many interacting particles quickly thermalize and forget about their past. Here, we show that quantum mechanics hinders chaos in many-body systems: although the quantum eigenstates are thermal and strongly entangled, exponentially many of them are scarred, that is, have an enlarged weight along underlying classical unstable periodic orbits. Scarring makes the system more likely to be found on an orbit it was initialized on, retaining a memory of its past and thus weakly breaking ergodicity, even at long times and despite the system being fully thermal. We demonstrate the ubiquity of quantum scarring in many-body systems by considering a large family of spin models, including some of the most popular ones from condensed matter physics. Our findings, at hand for modern quantum simulators, prove structure in spite of chaos in many-body quantum systems., Comment: 5 pages, 3 figures

In lattice models with quadratic finite-range Hermitian Hamiltonians, the inherently non-Hermitian transfer matrix (TM) governs the band dispersion. The van Hove singularities (VHSs) are special points in the band dispersion where the density of states (DOS) diverge. Considering a lattice chain with hopping of a finite range $n$, we find a direct fundamental connection between VHSs and exceptional points (EPs) of TM, both of arbitrary order. In particular, we show that VHSs are EPs of TM of the same order, thereby connecting two different types of critical points usually studied in widely different branches of physics. Consequently, several properties of band dispersion and VHSs can be analyzed in terms of spectral properties of TM. We further provide a general prescription to generate any order EP of the TM and therefore corresponding VHS. For a given range of hopping $n$, our analysis provides restrictions on allowed orders of EPs of TM. Finally, we exemplify all our results for the case $n=3$.

The Quantum-Monte-Carlo technique known as the Stochastic Series Expansion (SSE) relies on a crucial no-branching condition: the SSE sampling is carried out in the computational basis, and the no-branching assumption ensures that superpositions of basis-states do not appear when operators are applied. Without this proviso, the number of complex amplitudes would grow exponentially with the number of qubits and would eventually overwhelm the memory and processing power of a classical computer. However, the action of Clifford group elements on stabilizer states can be very efficiently described without resorting to an amplitude description. We explore how stabilizer states allow an extension of the SSE technique, and we give an example of a toy model that can be studied in this way., Comment: 8 pages, 2 figures

Isolated quantum systems follow the reversible unitary evolution; if we focus on the dynamics of local states and observables, they exhibit the irreversible relaxation behaviors. Here we study the local relaxation process in an isolated chain consisting of \emph{N} three level systems. Though the entropy of the full many body state keeps a constant, it turns out the total correlation of this system approximately exhibits a monotonically increasing behavior. More importantly, a variation analysis shows that, the total correlation entropy would achieve its theoretical maximum when each site stays in a generalized one-body Boltzmann state, which is not solely determined by the energy but also depends on the spin value of each onsite level. It turns out such a theoretical correlation maximum is highly coincident with the result obtained from the exact time dependent evolution. In this sense, the total correlation entropy well serves as an indicator for the dynamical irreversibility of the nonequilibrium relaxation in this isolated system., Comment: 7 pages, 4 figures, comments are welcome

State-of-the-art quantum simulators permit local temporal control of interactions and midcircuit readout. These capabilities open the way towards the exploration of intriguing nonequilibrium phenomena. We illustrate this with a kinetically constrained many-body quantum system that has a natural implementation on Rydberg quantum simulators. The evolution proceeds in discrete time and is generated by repeatedly entangling the system with an auxiliary environment that is monitored and reset after each time-step. Despite featuring an uncorrelated infinite-temperature average stationary state, the dynamics displays coexistence of fast and slow space-time regions in stochastic realizations of the system state. The time-record of measurement outcomes on the environment serves as natural probe for such dynamical heterogeneity, which we characterize using tools from large deviation theory. Our work establishes the large deviation framework for discrete-time open quantum many-body systems as a means to characterize complex dynamics and collective phenomena in quantum processors and simulators., Comment: 8+6 pages, 3+2 figures, comments welcome