Search

We investigate the magnetic quantum phase-transitions in bulk correlated metals at the level of dynamical mean-field theory. To this end, we focus on the Hubbard model on a simple cubic lattice as a function of temperature and electronic density, determining the different regimes of its magnetic transition - classical, quantum critical, and quantum disordered - as well as the corresponding critical exponents. Our numerical results, together with supporting mean-field derivations, demonstrate how the presence of Kohn-anomalies on the underlying Fermi surface does not only drive the quantum critical behavior above the quantum critical point, but shapes the whole phase diagram around it. Finally, after outlining the impact of different Fermi surface geometries on quantum criticality, we discuss to what extent spatial correlations beyond dynamical mean-field might modify our findings., Comment: 7 pages (including references), 3 figures

We show how the stability conditions for a system of interacting fermions that conventionally involve variations of thermodynamic potentials can be rewritten in terms of one- and two-particle correlators. We illustrate the applicability of this alternative formulation in a multi-orbital model of strongly correlated electrons at finite temperatures, inspecting the lowest eigenvalues of the generalized local charge susceptibility in proximity of the phase-separation region. Additionally to the conventional unstable branches, we address unstable solutions possessing a positive, rather than negative compressibility. Our stability conditions require no derivative of free energy functions with conceptual and practical advantages for actual calculations and offer a clear-cut criterion for analyzing the thermodynamics of correlated complex systems., Comment: 8+8 pages, 3+1 figures

Hot QCD physics studies the nuclear strong force under extreme temperature and densities. Experimentally these conditions are achieved via high-energy collisions of heavy ions at the Relativistic Heavy Ion Collider (RHIC) and the Large Hadron Collider (LHC). In the past decade, a unique and substantial suite of data was collected at RHIC and the LHC, probing hydrodynamics at the nucleon scale, the temperature dependence of the transport properties of quark-gluon plasma, the phase diagram of nuclear matter, the interaction of quarks and gluons at different scales and much more. This document, as part of the 2023 nuclear science long range planning process, was written to review the progress in hot QCD since the 2015 Long Range Plan for Nuclear Science, as well as highlight the realization of previous recommendations, and present opportunities for the next decade, building on the accomplishments and investments made in theoretical developments and the construction of new detectors. Furthermore, this document provides additional context to support the recommendations voted on at the Joint Hot and Cold QCD Town Hall Meeting, which are reported in a separate document., Comment: 190 pages, 69 figures

This White Paper presents the community inputs and scientific conclusions from the Hot and Cold QCD Town Meeting that took place September 23-25, 2022 at MIT, as part of the Nuclear Science Advisory Committee (NSAC) 2023 Long Range Planning process. A total of 424 physicists registered for the meeting. The meeting highlighted progress in Quantum Chromodynamics (QCD) nuclear physics since the 2015 LRP (LRP15) and identified key questions and plausible paths to obtaining answers to those questions, defining priorities for our research over the coming decade. In defining the priority of outstanding physics opportunities for the future, both prospects for the short (~ 5 years) and longer term (5-10 years and beyond) are identified together with the facilities, personnel and other resources needed to maximize the discovery potential and maintain United States leadership in QCD physics worldwide. This White Paper is organized as follows: In the Executive Summary, we detail the Recommendations and Initiatives that were presented and discussed at the Town Meeting, and their supporting rationales. Section 2 highlights major progress and accomplishments of the past seven years. It is followed, in Section 3, by an overview of the physics opportunities for the immediate future, and in relation with the next QCD frontier: the EIC. Section 4 provides an overview of the physics motivations and goals associated with the EIC. Section 5 is devoted to the workforce development and support of diversity, equity and inclusion. This is followed by a dedicated section on computing in Section 6. Section 7 describes the national need for nuclear data science and the relevance to QCD research., Comment: QCD Town Meeting White Paper, as submitted to 2023 NSAC LRP committee on Feb. 28, 2023

We introduce a spin-symmetry-broken extension of the connected determinant algorithm [Phys. Rev. Lett. 119, 045701 (2017)]. The resulting systematic perturbative expansions around an antiferromagnetic state allow for numerically exact calculations directly inside a magnetically ordered phase. We show new precise results for the magnetic phase diagram and thermodynamics of the three-dimensional cubic Hubbard model at half-filling. With detailed computations of the order parameter in the low to intermediate-coupling regime, we establish the N{\'e}el phase boundary. The critical behavior in its vicinity is shown to be compatible with the $O(3)$ Heisenberg universality class. By determining the evolution of the entropy with decreasing temperature through the phase transition we identify the different physical regimes at $U/t\!=\!4$. We provide quantitative results for several thermodynamic quantities deep inside the antiferromagnetic dome up to large interaction strengths and investigate the crossover between the Slater and Heisenberg regimes., Comment: 13 pages, 10 figures

We advocate for an active US participation in the international collaboration of the CBM experiment that will allow the US nuclear physics program to build on its successful exploration of the QCD phase diagram, use the expertise gained at RHIC to make complementary measurements at FAIR, and contribute to achieving the scientific goals of the beam energy scan (BES) program., Comment: 30 pages, 7 figures

Can we really "read the mind in the eyes"? Moreover, can AI assist us in this task? This paper answers these two questions by introducing a machine learning system that predicts personality characteristics of individuals on the basis of their face. It does so by tracking the emotional response of the individual's face through facial emotion recognition (FER) while watching a series of 15 short videos of different genres. To calibrate the system, we invited 85 people to watch the videos, while their emotional responses were analyzed through their facial expression. At the same time, these individuals also took four well-validated surveys of personality characteristics and moral values: the revised NEO FFI personality inventory, the Haidt moral foundations test, the Schwartz personal value system, and the domain-specific risk-taking scale (DOSPERT). We found that personality characteristics and moral values of an individual can be predicted through their emotional response to the videos as shown in their face, with an accuracy of up to 86% using gradient-boosted trees. We also found that different personality characteristics are better predicted by different videos, in other words, there is no single video that will provide accurate predictions for all personality characteristics, but it is the response to the mix of different videos that allows for accurate prediction.

We report a comprehensive study of magnetic correlations in LaNiO$_{2}$, a parent compound of the recently discovered family of infinite-layer (IL) nickelate superconductors, using multiple experimental and theoretical methods. Our specific heat, muon-spin rotation ($\mu$SR), and magnetic susceptibility measurements on polycrystalline LaNiO$_{2}$ show that long-range magnetic order remains absent down to 2 K. Nevertheless, we detect residual entropy in the low-temperature specific heat, which is compatible with a model fit that includes paramagnon excitations. The $\mu$SR and low-field static and dynamic magnetic susceptibility measurements indicate the presence of short-range magnetic correlations and glassy spin dynamics, which we attribute to local oxygen non-stoichiometry in the average infinite-layer crystal structure. This glassy behavior can be suppressed in strong external fields, allowing us to extract the intrinsic paramagnetic susceptibility. Remarkably, we find that the intrinsic susceptibility shows non-Curie-Weiss behavior at high temperatures, in analogy to doped cuprates that possess robust non-local spin fluctuations. The distinct temperature dependence of the intrinsic susceptibility of LaNiO$_{2}$ can be theoretically understood by a multi-method study of the single-band Hubbard model in which we apply complementary cutting-edge quantum many-body techniques (dynamical mean-field theory, cellular dynamical mean-field theory and the dynamical vertex approximation) to investigate the influence of both short- and long-ranged correlations. Our results suggest a profound analogy between the magnetic correlations in parent (undoped) IL nickelates and doped cuprates., Comment: 18 pages, 14 figures

While calculations and measurements of single-particle spectral properties often offer the most direct route to study correlated electron systems, the underlying physics may remain quite elusive, if information at higher particle levels is not explicitly included. Here, we present a comprehensive overview of the different approaches which have been recently developed and applied to identify the dominant two-particle scattering processes controlling the shape of the one-particle spectral functions and, in some cases, of the physical response of the system. In particular, we will discuss the underlying general idea, the common threads and the specific peculiarities of all the proposed approaches. While all of them rely on a selective analysis of the Schwinger-Dyson (or the Bethe-Salpeter) equation, the methodological differences originate from the specific two-particle vertex functions to be computed and decomposed. Finally, we illustrate the potential strength of these methodologies by means of their applications the two-dimensional Hubbard model, and we provide an outlook over the future perspective and developments of this route for understanding the physics of correlated electrons., Comment: 20 pages, 17 figures

We investigate the non-linear transport processes and hydrodynamization of a system of gluons undergoing longitudinal boost-invariant expansion. The dynamics is described within the framework of the Boltzmann equation in the small-angle approximation. The kinetic equations for a suitable set of moments of the one-particle distribution function are derived. By investigating the stability and asymptotic resurgent properties of this dynamical system, we demonstrate, that its solutions exhibit a rather different behavior for large (UV) and small (IR) effective Knudsen numbers. Close to the forward attractor in the IR regime the constitutive relations of each moment can be written as a multiparameter transseries. This resummation scheme allows us to extend the definition of a transport coefficient to the non-equilibrium regime naturally. Each transport coefficient is renormalized by the non-perturbative contributions of the non-hydrodynamic modes. The Knudsen number dependence of the transport coefficient is governed by the corresponding renormalization group flow equation. An interesting feature of the Yang-Mills plasma in this regime is that it exhibits transient non-Newtonian behavior while hydrodynamizing. In the UV regime the solution for the moments can be written as a power-law asymptotic series with a finite radius of convergence. We show that radius of convergence of the UV perturbative expansion grows linearly as a function of the shear viscosity to entropy density ratio. Finally, we compare the universal properties in the pullback and forward attracting regions to other kinetic models including the relaxation time approximation and the effective kinetic Arnold-Moore-Yaffe (AMY) theory., Comment: v2: 23 pages + appendices, 7 figures, updated references. Added new subsection IVB which is related with transasymptotic matching and RG flow equations of 1st. and 2nd. order transport coefficients for the most general case. Accepted for publication in PRD

This report summarizes the presentations and discussions during the Rapid Reaction Task Force "Dynamics of critical fluctuations: Theory -- phenomenology -- heavy-ion collisions", which was organized by the ExtreMe Matter Institute EMMI and held at GSI, Darmstadt, Germany in April 2019. We address the current understanding of the dynamics of critical fluctuations in QCD and their measurement in heavy-ion collision experiments. In addition, we outline what might be learned from studying correlations in other physical systems, such as cold atomic gases., Comment: 89 pages, 11 figures, report on an ExtreMe Matter Institute EMMI Rapid Reaction Task Force

We study the phase diagram and quantum critical region of one of the fundamental models for electronic correlations: the periodic Anderson model. Employing the recently developed dynamical vertex approximation, we find a phase transition between a zero-temperature antiferromagnetic insulator and a Kondo insulator. In the quantum critical region, we determine a critical exponent $\gamma\!=\!2$ for the antiferromagnetic susceptibility. At higher temperatures, we have free spins with $\gamma\!=\!1$ instead, whereas at lower temperatures, there is an even stronger increase and suppression of the susceptibility below and above the quantum critical point, respectively., Comment: 6 pages, 4 figures (+ 6 pages Supplemental Material)

In this work, we analyze in detail the occurrence of divergences in the irreducible vertex functions for one of the fundamental models of many-body physics: the Anderson impurity model (AIM). These divergences -- a surprising hallmark of the breakdown of many-electron perturbation theory -- have been recently observed in several contexts, including the dynamical mean-field solution of the Hubbard model. The numerical calculations for the AIM presented in this work, as well as their comparison with the corresponding results for the Hubbard model, allow us to clarify several open questions about the origin and the properties of vertex divergences in a particularly interesting context, the correlated metallic regime at low-temperatures. Specifically, our analysis (i) rules out explicitly the transition to a Mott insulating phase, but not the more general suppression of charge fluctuations (proposed in [Phys.\,Rev.\,B {\bf 93},\,245102\,(2016)]), as a necessary condition for the occurrence of vertex divergences, (ii) clarifies their relation with the underlying Kondo physics, and, eventually, (iii) individuates which divergences might also appear on the real frequency axis in the limit of zero temperature, through the discovered scaling properties of the singular eigenvectors., Comment: 16 pages, 13 figures, published version

We study the relation between the microscopic properties of a many-body system and the electron spectra, experimentally accessible by photoemission. In a recent paper [Phys. Rev. Lett. 114, 236402 (2015)], we introduced the "fluctuation diagnostics" approach, to extract the dominant wave vector dependent bosonic fluctuations from the electronic self-energy. Here, we first reformulate the theory in terms of fermionic modes, to render its connection with resonance valence bond (RVB) fluctuations more transparent. Secondly, by using a large-U expansion, where U is the Coulomb interaction, we relate the fluctuations to real space correlations. Therefore, it becomes possible to study how electron spectra are related to charge, spin, superconductivity and RVB-like real space correlations, broadening the analysis of an earlier work [Phys. Rev. B 89, 245130 (2014)]. This formalism is applied to the pseudogap physics of the two-dimensional Hubbard model, studied in the dynamical cluster approximation. We perform calculations for embedded clusters with up to 32 sites, having three inequivalent K-points at the Fermi surface. We find that as U is increased, correlation functions gradually attain values consistent with an RVB state. This first happens for correlation functions involving the antinodal point and gradually spreads to the nodal point along the Fermi surface. Simultaneously a pseudogap opens up along the Fermi surface. We relate this to a crossover from a Kondo-like state to an RVB-like localized cluster state and to the presence of RVB and spin fluctuations. These changes are caused by a strong momentum dependence in the cluster bath-couplings along the Fermi surface. We also show, from a more algorithmic perspective, how the time-consuming calculations in fluctuation diagnostics can be drastically simplified., Comment: 19 pages, 8 figures

Starting from the (Hubbard) model of an atom, we demonstrate that the uniqueness of the mapping from the interacting to the noninteracting Green's function, $G\to G_0$, is strongly violated, by providing numerous explicit examples of different $G_0$ leading to the same physical $G$. We argue that there are indeed infinitely many such $G_0$, with numerous crossings with the physical solution. We show that this rich functional structure is directly related to the divergence of certain classes of (irreducible vertex) diagrams, with important consequences for traditional many-body physics based on diagrammatic expansions. Physically, we ascribe the onset of these highly non-perturbative manifestations to the progressive suppression of the charge susceptibility induced by the formation of local magnetic moments and/or RVB states in strongly correlated electron systems., Comment: 5 pages, 3 figures

We investigate the scaling behavior of longitudinal and transverse structure functions in homogeneous and isotropic magneto-hydrodynamic (MHD) turbulence by means of an exact hierarchy of structure function equations as well as by direct numerical simulations of two- and three-dimensional MHD turbulence. In particular, rescaling relations between longitudinal and transverse structure functions are derived and utilized in order to compare different scaling behavior in the inertial range. It is found that there are no substantial differences between longitudinal and transverse structure functions in MHD turbulence. This finding stands in contrast to the case of hydrodynamic turbulence which shows persistent differences even at high Reynolds numbers. We propose a physical picture that is based on an effective reduction of pressure contributions due to local regions of same magnitude and alignment of velocity and magnetic field fluctuations. Finally, our findings underline the importance of the pressure term for the actually observed scaling differences in hydrodynamic turbulence., Comment: 34 pages, 14 figures

We analyze the highly non-perturbative regime surrounding the Mott-Hubbard metal-to-insulator transition (MIT) by means of dynamical mean field theory calculations at the two-particle level. By extending the results of Sch\"afer, et al. [Phys. Rev. Lett. 110, 246405 (2013)] we show the existence of infinitely many lines in the phase diagram of the Hubbard model where the local Bethe-Salpeter equations, and the related irreducible vertex functions, become singular in the charge as well as the particle-particle channel. These divergence lines accumulate around the critical Mott endpoint in accordance with the interpretation as precursors of the MIT. By comparing our numerical data with analytical calculations of increasing complexity, such as for the disordered Binary Mixture and Falicov-Kimball (FK) models, as well as for the atomic limit (AL) case, (i) we identify two different kinds of divergences lines; (ii) we classify them in terms of the frequency-structure of the associated singular eigenvectors; (iii) we investigate their relation to the multiple branches in the Luttinger-Ward formalism. Moreover, we could distinguish the situations where the multiple divergences simply reflect the emergence of an underlying, unique energy scale $\nu^*$ below which perturbation theory does no longer apply, from those where the breakdown of perturbation theory affects, not trivially, different energy regimes. Finally, we discuss the implications of our results on the theoretical understanding of the non-perturbative physics around the MIT and for future developments of many-body algorithms applicable in this regime., Comment: 28 pages, 15 figures

A general understanding of quantum phase transitions in strongly correlated materials is still lacking. By exploiting a cutting-edge quantum many-body approach, the dynamical vertex approximation, we make an important progress, determining the quantum critical properties of the antiferromagnetic transition in the fundamental model for correlated electrons, the Hubbard model in three dimensions. In particular, we demonstrate that -in contradiction to the conventional Hertz-Millis-Moriya theory- its quantum critical behavior is driven by the Kohn anomalies of the Fermi surface, even when electronic correlations become strong., Comment: 6 pages, 4 figures (8 pages Supplemental Material)

The parquet decomposition of the self-energy into classes of diagrams, those associated with specific scattering processes, can be exploited for different scopes. In this work, the parquet decomposition is used to unravel the underlying physics of non-perturbative numerical calculations. We show the specific example of dynamical mean field theory (DMFT) and its cluster extensions (DCA) applied to the Hubbard model at half-filling and with hole doping: These techniques allow for a simultaneous determination of two-particle vertex functions and self-energies, and hence, for an essentially "exact" parquet decomposition at the single-site or at the cluster level. Our calculations show that the self-energies in the underdoped regime are dominated by spin scattering processes, consistent with the conclusions obtained by means of the fluctuation diagnostics approach [Phys. Rev. Lett. 114, 236402 (2015)]. However, differently from the latter approach, the parquet procedure displays important changes with increasing interaction: Even for relatively moderate couplings, well before the Mott transition, singularities appear in different terms, with the notable exception of the predominant spin-channel. We explain precisely how these singularities, which partly limit the utility of the parquet decomposition, and - more generally - of parquet-based algorithms, are never found in the fluctuation diagnostics procedure. Finally, by a more refined analysis, we link the occurrence of the parquet singularities in our calculations to a progressive suppression of charge fluctuations and the formation of an RVB state, which are typical hallmarks of a pseudogap state in DCA., Comment: 19 pages, 16 figures

Recently, diagrammatic extensions of dynamical mean field theory (DMFT) have been proposed for including short- and long-range correlations beyond DMFT on an equal footing. We employ one of these, the dynamical vertex approximation (D$\Gamma$A), and study the two-dimensional Hubbard model on a square lattice. We define two transition lines in the phase diagram which correspond, respectively, to the opening of the gap in the nodal direction and throughout the Fermi surface. Our self-energy data show that the evolution between the two regimes occurs in a gradual way (crossover) and also that at low enough temperatures the whole Fermi surface is always gapped. Furthermore, we present a comparison of our D$\Gamma$A calculations at a parameter set where data obtained by other techniques are available., Comment: 9 pages, 6 figures, Contribution for the Proceedings of the ICM2015 conference

We demonstrate how to identify which physical processes dominate the low-energy spectral functions of correlated electron systems. We obtain an unambiguous classification through an analysis of the equation of motion for the electron self-energy in its charge, spin and particle-particle representations. Our procedure is then employed to clarify the controversial physics responsible for the appearance of the pseudogap in correlated systems. We illustrate our method by examining the attractive and repulsive Hubbard model in two-dimensions. In the latter, spin fluctuations are identified as the origin of the pseudogap, and we also explain why $d-$wave pairing fluctuations play a marginal role in suppressing the low-energy spectral weight, independent of their actual strength., Comment: 6 pages, 2 figures + 4 pages supplementary

While second-order phase transitions always cause strong non-local fluctuations, their effect on spectral properties crucially depends on the dimensionality. For the important case of three dimensions, we show that the electron self-energy is well separable into a local dynamical part and static non-local contributions. In particular, our non-perturbative many-body calculations for the 3D Hubbard model at different fillings demonstrate that the quasi-particle weight remains essentially momentum-independent, also in the presence of overall large non-local corrections to the self-energy. Relying on this insight we propose a "space-time-separated" scheme for many-body perturbation theory that is up to ten times more efficient than current implementations. Besides these far-reaching implications for state-of-the-art electronic structure schemes, our analysis will also provide guidance to the quest of going beyond them., Comment: 5 pages, 3 figures and supplementary material

We have implemented the dynamical vertex approximation (D$\Gamma$A) in its full parquet-based version to include spatial correlations on all length scales and in {\sl all} scattering channels. The algorithm is applied to study the electronic self-energies and the spectral properties of finite-size one-dimensional Hubbard models with periodic boundary conditions (nanoscopic Hubbard rings). From a methodological point of view, our calculations and their comparison to the results obtained within dynamical mean-field theory, plain parquet approximation, and the exact numerical solution, allow us to evaluate the performance of the D$\Gamma$A algorithm in the most challenging situation of low dimensions. From a physical perspective, our results unveil how non-local correlations affect the spectral properties of nanoscopic systems of various sizes in different regimes of interaction strength., Comment: 15 pages, 16 figures

We have studied the impact of non-local electronic correlations at all length scales on the Mott-Hubbard metal-insulator transition in the unfrustrated two-dimensional Hubbard model. Combining dynamical vertex approximation, lattice quantum Monte-Carlo and variational cluster approximation, we demonstrate that scattering at long-range fluctuations, i.e., Slater-like paramagnons, opens a spectral gap at weak-to-intermediate coupling -- irrespectively of the preformation of localized or short-ranged magnetic moments. This is the reason, why the two-dimensional Hubbard model is insulating at low enough temperatures for any (finite) interaction and no Mott-Hubbard transition is observed., Comment: 5 pages, 3 figures

In this paper we describe a new variant of null ellipsometry to determine thicknesses and optical properties of thin films on a substrate at cryogenic temperatures. In the PCSA arrangement of ellipsometry the polarizer and the compensator are placed before the substrate and the analyzer after it. Usually, the polarizer and the analyzer are rotated to find the intensity minimum searched for in null ellipsometry. In our variant we rotate the polarizer and the compensator instead, both being placed in the incoming beam before the substrate. Therefore the polarization analysis of the reflected beam can be realized by an analyzer at fixed orientation. We developed this method for investigations of thin cryogenic films inside a vacuum chamber, where the analyzer and detector had to be placed inside the cold shield at a temperature of T approx. 90K close to the substrate. All other optical components were installed at the incoming beam line outside the vacuum chamber, including all components which need to be rotated during the measurements. Our null ellipsometry variant has been tested with condensed krypton films on a highly oriented pyrolytic graphite substrate (HOPG) at a temperature of T approx. 25K. We show that it is possible to determine the indices of refraction of condensed krypton and of the HOPG substrate as well as thickness of krypton films with reasonable accuracy., Comment: 22 pages, 12 figures

Identifying the fingerprints of the Mott-Hubbard metal-insulator transition may be quite elusive in correlated metallic systems if the analysis is limited to the single particle level. However, our dynamical mean-field calculations demonstrate that the situation changes completely if the frequency dependence of the two-particle vertex functions is considered: The first non-perturbative precursors of the Mott physics are unambiguously identified well inside the metallic regime by the divergence of the local Bethe-Salpeter equation in the charge channel. At low temperatures this occurs in the region where incoherent high-energy features emerge in the spectral function, while at high temperatures it is traceable up to the atomic-limit., Comment: 5 pages, 2 figures