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A modified $GW$ approximation to many - body systems is developed. The approximation has the same computational complexity as the traditional $GW$ approach, but uses a different truncation scheme. This scheme neglects high order connected correlation functions. A covariant (preserving Ward identities due to charge conservation) scheme for two - body correlators is employed, which holds the relation between the charge correlator and charge susceptibility. The method is tested on the two - dimensional one - band Hubbard model. Results are compared with exact diagonalization, the fluctuation - exchange (FLEX) theory and determinantal quantum Monte Carlo (DQMC) approach. The comparison for the (one - body) Green's function demonstrates that it is more precise in strong - coupling regime (especially away from half - filling) than similar - complexity approximations $GW$ or FLEX. The charge correlator is in excellent agreement with the numerically exact result obtained from DQMC., Comment: 21 pages, 7 figures

We present a rigorous quasinormal mode approach to describe the strong coupling behavior between a monolayer of ${\mathrm{MoSe}}_{2}$ and a single gold nanoparticle. The onset of strong coupling, described through a classical spectral mode splitting (analog of vacuum Rabi splitting) is quantified by computing the full three-dimensional hybrid quasinormal modes of the combined structure, allowing one to accurately model light-matter interactions without invoking the usual phenomenological theories of strong coupling. We explore the hybrid quasinormal modes as a function of gap size and temperature, and find spectral splittings in the range of around 80--110 meV, with no fitting parameters for the material models. We also show how the hybrid modes exhibit Fano-like resonances and quantify the complex poles of the hybrid modes as well as the Purcell factor resonances from embedded dipole emitters. The Rabi splitting is found to be larger at elevated temperatures for very small gap separations between the metal nanoparticle and the monolayer, but smaller at elevated temperatures for larger gaps. We also show how these spectral splittings can differ qualitatively from the actual complex poles of the hybrid quasinormal modes.

We generate the perturbative expansion of the single particle Green's function and related self-energy for a half-filled single-band Hubbard model on a square lattice. We invoke algorithmic Matsubara integration to evaluate single-particle quantities for real and Matsubara frequencies and verify results through comparison to existing data on the Matsubara axis. With low-order expansions at weak coupling we observe a number of outcomes expected at higher orders: the opening of a gap, pseudogap behavior, and Fermi-surface reconstruction. Based on low-order perturbations, we consider the phase diagram that arises from truncated expansions of the self-energy and Green's function and their relation via the Dyson equation. From Matsubara axis data, we observe insulating behavior in direct expansions of the Green's function, whereas the same order of truncation of the self-energy produces metallic behavior. This observation is supported by additional calculations for real frequencies. We attribute this difference to the order in which diagrams are implicitly summed in the Dyson series. By separating the reducible and irreducible contributions at each order we show that the reducible diagrams implicitly summed in the Dyson equation lead to incorrect physics in the half-filled Hubbard model. Our observations for this particular case lead us to question the utility of the Dyson equation for any problem that shows a disparity between reducible and irreducible contributions to the expansion of the Green's function.

The statistical properties of spectra of quantum systems within the framework of random matrix theory is widely used in many areas of physics. These properties are affected, if two or more sets of spectra are superposed, resulting from the discrete symmetries present in the system. Superposition of spectra of $m$ such circular orthogonal, unitary and symplectic ensembles are studied numerically using higher-order spacing ratios. For given $m$ and the Dyson index $\beta$, the modified index $\beta'$ is tabulated whose nearest neighbor spacing distribution is identical to that of $k$-th order spacing ratio. For the case of $m=2$ ($m=3$) in COE (CUE) a scaling relation between $\beta'$ and $k$ is given. For COE, it is conjectured that for $k=m+1$ ($m\geq2$) and $k=m-3$-th ($m\geq5$) order spacing ratio distribution the $\beta'$ is $m+2$ and $m-4$ respectively. Whereas in the case of CSE, for $k=m+1$ ($m\geq2$) and $k=m-1$-th ($m\geq3$) the $\beta'$ is $2m+3$ and $2(m-2)$ respectively. We also conjecture that for given $m$ ($k$) and $\beta$, the sequence of $\beta'$ as a function of $k$ ($m$) is unique. Strong numerical evidence in support of these results is presented. These results are tested on complex systems like the measured nuclear resonances, quantum chaotic kicked top and spin chains., Comment: 14 pages, 16 figures, 11 tables. This paper is accepted in Physical Review B. This is a substantially improved version and few results overlap with arXiv:1905.02585v2 [cond-mat.stat-mech]. Comments are welcome

We compute the Casimir force between two parallel and infinitely long carbon nanotubes. The force induced by fluctuations of the electromagnetic field follows from the Maxwell stress tensor, expressed in terms of the correlators of the fields which are obtained from the Green's function and the fluctuation-dissipation theorem for the current density. We show how the force depends on the distance between the nanotubes, as well as on their chiralities and semiconducting or metallic natures. We also analyze the convergence of the approximation we use that replaces integrals in frequency by sums over complex Matsubara frequencies. The methodology presented and the results obtained can contribute to the understanding of how electromagnetic fluctuations induce Casimir forces in complex microstructured geometries.

We introduce three new analytical and semi-analytical tools that allow one to determine the topological character of impurity Shiba chains. The analytical methods are based on calculating the effective Green's function of an infinite embedded chain using the T-matrix formalism and describing the chain as a {\it line impurity}. We thus provide a solution to the longstanding size-effects problem affecting the only general alternative method, the numerical tight-binding analysis. As an example we consider a chain of magnetic impurities deposited on an s-wave superconducting substrate with Rashba spin-orbit and we calculate its topological phase diagram as a function of the magnetic impurity strength and the chemical potential. We find a perfect agreement between all our new techniques and a numerical analysis.

We apply the cluster expansion (CE) method to determine the effective cluster interactions (ECIs) from a simple energetic model that depends on both local and global composition. This model is defined by the site energies of random solid solutions of a one-dimensional alloy Co-Pt. We explore how these local and global dependencies are reflected on the cluster interactions. The energies of the structures are not well reproduced with concentration-independent interactions. Moreover, the interactions have a larger range than the energetic model which is limited to the nearest neighbors. This problem does not seem to have been addressed until now. By fitting the ECIs on the site energies we suggest a mean-field type weighting of the excess variables present in large clusters size. We show that the site energy formalism controls the clusters size required for CE convergence and their concentration dependence. Finally, we take advantage of the site energy formalism to describe the elastic and chemical effects that control the thermodynamics of the alloy as a function of the ECIs.

The auxiliary and itinerant coherent potential approximations (ACPA and ICPA) have been proposed as effective methods for treating both mass and force-constant disorder in lattice vibration. In this work we make a direct comparison of ACPA and ICPA to identify the differences between these two methods for simulating vibrational properties of disordered materials and devices. We investigate the major approximations in the disorder self-energies of these two methods by using the diagrammatic method. The single-site ACPA neglects the crossing diagrams describing nonlocal correlations, while ICPA utilizes only the single-fluctuation states in the self-consistency and presents extra errors due to a change in the terms with nearest-neighbor fluctuation. To further demonstrate the important differences between the ACPA and ICPA in the phonon spectral and transport properties, we extend ICPA in combination with the Keldysh nonequilibrium Green's function technique to simulate quantum transport and introduce a Green's-function-based spectral unfolding technique to use with molecular ACPA and the supercell methods for comparison. By studying the disordered one- and three-dimensional alloys, we find that ACPA and ICPA agree very well in the weak scattering regime due to weak force-constant disorder or low phonon frequency. However, for the strong scattering of force-constant disorder, it is found that the two methods present important deviations in the linewidth (and height) of disorder-averaged phonon spectra. Compared to the ACPA and exact results, the problematic treatment of the nearest-neighbor fluctuation in ICPA can present unphysical scattering and induce large errors in the phonon transport, presenting important limitations of ICPA for transport simulation.

The ultrafast hole dynamics triggered by the photoexcitation of molecular targets is a highly correlated process even for those systems, such as organic molecules, having a weakly correlated ground state. We provide a unifying framework and a numerically efficient matrix formulation of state-of-the-art nonequilibrium Green's function (NEGF) methods such as second-Born as well as $GW$ and $T$-matrix without and with exchange diagrams. Numerical simulations are presented for a paradigmatic, exactly solvable molecular system, and the shortcomings of the established NEGF methods are highlighted. We then develop a NEGF scheme based on the Faddeev treatment of three-particle correlations; the exceptional improvement over established methods is explained and demonstrated. The Faddeev NEGF scheme scales linearly with the maximum propagation time, thereby opening up prospects for femtosecond simulations of large molecules.

We compare the pole structure of the electronic Green's function obtained by cluster dynamical mean-field theory to the results from the fractionalized pair density wave idea. In the superconducting phase, we can consider the system in a state with coexistence of superconducting and charge order. Writing the Green's function in a way analogous to the previously proposed ``hidden-fermions'' model [Sakai et al., Phys. Rev. Lett. 116, 057003 (2016)] leads to a similar pole structure for the self-energy. The fractionalization of the pair density wave order also describes the pseudogap phase as a superposition of superconducting and charge order fluctuations. Considering a phenomenological lifetime for the particle-particle and particle-hole pairs leads to an electronic spectral function that matches the numerical results.

A perspective of the Green's function in a boundary value problem as the only eigenstate in an auxiliary formulation is introduced. In this treatment, the Green's function can be perceived as a defect state in the presence of a $\ensuremath{\delta}$-function potential, the height of which depends on the Green's function itself. This approach is illustrated in one-dimensional and two-dimensional Helmholtz equation problems, with an emphasis on systems that are open and have a non-Hermitian potential. We then draw an analogy between the Green's function obtained this way and a chiral edge state circumventing a defect in a topological lattice, which shines light on the local minimum of the Green's function at the source position.

We apply the Green's function coupled cluster singles and doubles (GFCCSD) impurity solver to realistic impurity problems arising for strongly correlated solids within the self-energy embedding theory (SEET) framework. We describe the details of our GFCC solver implementation, investigate its performance, and highlight potential advantages and problems on examples of impurities created during the self-consistent SEET for antiferromagnetic MnO and paramagnetic $\mathrm{Sr}\mathrm{Mn}{\mathrm{O}}_{3}$. GFCCSD provides satisfactory descriptions for weakly and moderately correlated impurities with sizes that are intractable by existing accurate impurity solvers such as exact diagonalization. However, our data also shows that when correlations become strong, the singles and doubles approximation used in GFCC could lead to instabilities in searching for the particle number present in impurity problems. These instabilities appear especially severe when the impurity size gets larger and multiple degenerate orbitals with strong correlations are present. We conclude that, to fully check the reliability of GFCCSD results and use them in fully ab initio calculations in the absence of experiments, a verification from a GFCC solver with higher order excitations is necessary.

We present a microscopic study of the behavior of the order parameters near boundaries of a two-band superconducting material, described by the standard tight-binding Bardeen-Cooper-Schrieffer model. We find superconducting surface states. The relative difference between bulk and surface critical temperatures is a nontrivial function of the interband coupling strength. For superconductors with weak interband coupling, boundaries induce variations of the gaps with the presence of multiple length scales, despite non-zero interband Josephson coupling., 7 pages, 7 figures

Unlike their Hermitian counterparts, non-Hermitian (NH) systems may display an exponential sensitivity to boundary conditions and an extensive number of edge-localized states in systems with open boundaries, a phenomena dubbed the "non-Hermitian skin effect." The NH skin effect is one of the primary challenges to defining a topological theory of NH Hamiltonians, as the sensitivity to boundary conditions invalidates the traditional bulk-boundary correspondence. The NH skin effect has recently been connected to the winding number, a topological invariant unique to NH systems. In this paper, we extend the definition of the winding number to disordered NH systems by generalizing established results on disordered Hermitian topological insulators. Our real-space winding number is self-averaging, continuous as a function of the parameters in the problem, and remains quantized even in the presence of strong disorder. We verify that our real-space formula still predicts the NH skin effect, allowing for the possibility of predicting and observing the NH skin effect in strongly disordered NH systems. As an application we apply our results to predict a NH Anderson skin effect where a skin effect is developed as disorder is added to a clean system, and to explain recent results in optical funnels., Comment: 6 pages, 3 pages supplement

The quality of a quantum operation determines the performance of quantum information processing, such as the sensitivity of quantum sensing. Different from the fidelity of quantum operation in quantum computation, we present an effective function to evaluate the performance and diagnose the imperfection of operations in multi-pulse based quantum sensing. The evaluation function directly links the realistic sensitivity with intrinsic sensitivity in a simple way. Moreover, guided by this evaluation function, we optimize a composite pulse sequence for high sensitivity nitrogen-vacancycenter based magnetometry against spectrum inhomogeneities and control errors to improve the signal-to-noise ratio of nanoscale nuclear magnetic resonance by 1 order of magnitude. It marks an important step towards quantitative quantum sensing with imperfect quantum control in practical applications., Comment: 10 pages, 9 figures

We present a Greens function approach to calculate the Dzyaloshinskii-Moriya interactions (DMI) from first principles electronic structure calculations, that is computationally more efficient and accurate than the most-commonly employed supercell and generalized Bloch-based approaches. The method is applied to the (111) Co/Pt bilayer where the Co- and/or Pt-thickness dependence of the DMI coefficients are calculated. Overall, the calculated DMI are in relatively good agreement with the corresponding values reported experimentally. Furthermore, we investigate the effect of strain in the DMI tensor elements and show that the isotropic N\'{e}el DMI can be significantly modulated by the normal strains, $\epsilon_{xx},\epsilon_{yy}$ and is relatively insensitive to the shear strain, $\epsilon_{xy}$. Moreover, we show that anisotropic strains, $(\epsilon_{xx}-\epsilon_{yy})$ and $\epsilon_{xy}$, result in the emergence of anisotropic N\'{e}el- and Bloch-type DMIs, respectively., Comment: 10 pages, 5 figures

The ground state at 4/11 filling factor is very well understood [Phys. Rev. Lett. 112, 016801 (2014)] in terms of the 1/3 filled second effective Landau level of the composite fermions whose correlations resemble with that of electrons in the ground state of two-body Haldane pseudo-potential of relative angular momentum 3, $V_3$. We here propose a closed-form ground state wave function for $V_3$ at 1/3 filling factor. We successfully compare it with the exact wave function for the systems with a few electrons, by calculating their mutual overlap, pair-correlation function, and entanglement spectra. By numerical exact diagonalization for a few electron systems, we find a window of nonzero $V_3$ is essential together with $V_1$ for being 4/11 state incompressible. The constructed wave function for 4/11 state using this proposed wave function has satisfactorily high overlap with the previously studied composite-fermion-diagonalized ground state wave function., Comment: 10 pages, 5 figures

The specific heat of a two-layer He-4 film adsorbed on a graphite substrate is estimated as a function of temperature by Quantum Monte Carlo simulations. The results are consistent with recent experimental observations, in that they broadly reproduce their most important features. However, neither the "supersolid" nor the "superfluid hexatic" phases, of which experimental data are claimed to be evidence, are observed. It is contended that heat capacity measurements alone may not be a good predictor of structural and superfluid transitions in this system, as their interpretation is often ambiguous., Replaced with published version

Magneto-optical studies of Weyl semimetals have been proposed as a versatile tool for observing low-energy Weyl fermions in candidate materials including the chiral Landau level. However, previous theoretical results have been restricted to the linearized regime around the Weyl node and are at odds with experimental findings. Here, we derive a closed form expression for the magneto-optical conductivity of generic Weyl semimetals in the presence of an external magnetic field aligned with the tilt of the spectrum. The systems are taken to have linear dispersion in two directions, while the tilting direction can consist of any arbitrary continuously differentiable function. This general calculation is then used to analytically evaluate the magneto-optical conductivity of Weyl semimetals expanded to cubic order in momentum. In particular, systems with arbitrary tilt, as well as systems hosting trivial Fermi pockets are investigated. The higher-order terms in momentum close the Fermi pockets in the type-II regime, removing the need for unphysical cutoffs when evaluating the magneto-optical conductivity. Crucially, the ability to take into account closed over-tilted and additional trivial Fermi pockets allows us to treat model systems closer to actual materials and we propose a simple explanation why the presence of parasitic trivial Fermi pockets can mask the characteristic signature of Weyl fermions in magneto-optical conductivity measurements., Comment: 16 pages, 6 figures

We demonstrate a first order metal-insulator phase transition in the repulsive, fully frustrated, single-band Hubbard model as a function of the coupling to a fermion bath. Time dependent manipulation of the bath coupling allows switching between metallic and insulating states both across the phase transition and within the coexistence region. We propose a simple nanoelectronic device for experimentally realizing dynamic control of the bath coupling. Analysis of the device characteristics shows that it can act as a two-terminal memristor.

We study the energy dispersion relation of the $\ensuremath{\pi}$ and ${\ensuremath{\pi}}^{*}$ bands in epitaxial monolayer graphene on a semi-infinite Ir(111) substrate by a first-principles density-functional calculation. For this purpose, we employ a realistic surface structure in which the $(10\ifmmode\times\else\texttimes\fi{}10)$ unit cell of graphene matches a $(9\ifmmode\times\else\texttimes\fi{}9)$ cell of Ir(111). We determine the surface geometry by using a slab model containing four Ir layers, and the optimized structure is used as input for the subsequent surface embedded Green's function calculation. By taking advantage of semi-infinite calculations, we discuss mini energy gaps at the crossing of the $\ensuremath{\pi}$ band and its replicas, the Rashba-type spin splitting of the $\ensuremath{\pi}$ and ${\ensuremath{\pi}}^{*}$ bands, and also the energy width of both bands arising from interactions with the energy continuum of bulk Ir bands.

We study the ballistic-to-diffusive transition induced by the weak breaking of integrability in a boundary-driven XXZ spin-chain. Studying the evolution of the spin current density $\mathcal J^s$ as a function of the system size $L$, we show that, accounting for boundary effects, the transition has a non-trivial universal behavior close to the XX limit. It is controlled by the scattering length $L^*\propto V^{-2}$, where $V$ is the strength of the integrability breaking term. In the XXZ model, the interplay of interactions controls the emergence of a transient "quasi-ballistic" regime at length scales much shorter than $L^*$. This parametrically large regime is characterized by a strong renormalization of the current which forbids a universal scaling, unlike the XX model. Our results are based on Matrix Product Operator numerical simulations and agree with perturbative analytical calculations., 13 pages, 9 figures

This paper investigates the temperature dependence of quantum information scrambling in local systems with an energy gap, $m$, above the ground state. We study the speed and shape of growing Heisenberg operators as quantified by out-of-time-order correlators, with particular attention paid to so-called contour dependence, i.e. dependence on the way operators are distributed around the thermal circle. We report large scale tensor network numerics on a gapped chaotic spin chain down to temperatures comparable to the gap which show that the speed of operator growth is strongly contour dependent. The numerics also show a characteristic broadening of the operator wavefront at finite temperature $T$. To study the behavior at temperatures much below the gap, we perform a perturbative calculation in the paramagnetic phase of a 2+1D O($N$) non-linear sigma model, which is analytically tractable at large $N$. Using the ladder diagram technique, we find that operators spread at a speed $\sqrt{T/m}$ at low temperatures, $T\ll m$. In contrast to the numerical findings of spin chain, the large $N$ computation is insensitive to the contour dependence and does not show broadening of operator front. We discuss these results in the context of a recently proposed state-dependent bound on scrambling., Comment: 28+17 pages

We present a numerical investigation of the performance of the micropillar cavity single-photon source in terms of collection efficiency and indistinguishability of the emitted photons in the presence of non-Markovian phonon-induced decoherence. We analyze the physics governing the efficiency using a single-mode model, and we optimize efficiency $\ensuremath{\varepsilon}$ and the indistinguishability $\ensuremath{\eta}$ on an equal footing by computing $\ensuremath{\varepsilon}\ensuremath{\eta}$ as function of the micropillar design parameters. We show that $\ensuremath{\varepsilon}\ensuremath{\eta}$ is limited to $\ensuremath{\sim}0.96$ for the ideal geometry due to an inherent tradeoff between efficiency and indistinguishability. Finally, we subsequently consider the influence of realistic fabrication imperfections and Markovian pure dephasing noise on the performance.

The pairing temperature of superconducting thin films is expected to display, within the Bardeen-Cooper-Schrieffer theory, oscillations as a function of the film thickness. We show that the pattern of these oscillations switches between two different periodicities at a density-dependent value of the superconducting coupling. The transition is most abrupt in the anti-adiabatic regime, where the Fermi energy is less than the Debye energy. To support our numerical data, we provide new analytical expressions for the chemical potential and the pairing temperature as a function of thickness, which only differ from the exact solution at weak coupling by exponentially-small corrections., Published version

We analyze local operator growth in nonintegrable quantum many-body systems. A recently introduced universal operator growth hypothesis proposes that the maximal growth of Lanczos coefficients in the continued fraction expansion of the Green's function reflects chaos of the underlying system. We first show that the continued fraction expansion, and the recursion method in general, should be understood in the context of a completely integrable classical dynamics in Krylov space. In particular, the time-correlation function of a physical observable analytically continued to imaginary time is a tau-function of integrable Toda hierarchy. We use this relation to generalize the universal operator growth hypothesis to include arbitrarily ordered correlation functions. We then proceed to analyze the singularity of the time-correlation function, which is an equivalent sign of chaos to the maximal growth of Lanczos coefficients, and we show that it is due to delocalization in Krylov space. We illustrate the general relation between chaos and delocalization using an explicit example of the Sachdev-Ye-Kietaev model.

We consider the ``transport'' of the state of a spin across a Heisenberg-coupled spin chain via the use of repeated SWAP gates, starting with one of two states---one in which the leftmost spin is down and the others up, and one in which the leftmost two spins are in a singlet state (i.e., they are entangled), and the others are again all up. More specifically, we ``transport'' the state of the leftmost spin in the first case and the next-to-leftmost spin in the second to the other end of the chain, and then back again. We accomplish our SWAP operations here by increasing the exchange coupling between the two spins that we operate on from a base value $J$ to a larger value $J_\text{SWAP}$ for a time $t=\pi\hbar/4J_\text{SWAP}$. We determine the fidelity of this sequence of operations in a number of situations---one in which only nearest-neighbor coupling exists between spins and there is no magnetic dipole-dipole coupling or noise (the most ideal case), one in which we introduce next-nearest-neighbor coupling, but none of the other effects, and one in which all of these effects are present. In the last case, the noise is assumed to be quasistatic, i.e., the exchange couplings are each drawn from a Gaussian distribution, truncated to only nonnegative values. We plot the fidelity as a function of $J_\text{SWAP}$ to illustrate various effects, namely crosstalk due to coupling to other spins, as well as noise, that are detrimental to our ability to perform a SWAP operation. Our theory should be useful to the ongoing experimental efforts in building semiconductor-based spin quantum computer architectures., Comment: 8 pages, 9 figures. Added brief discussions of the effects of a finite rise time and the global $e^{-i\pi/4}$ phase on the SWAP operations. Also added a discussion of the oscillations in fidelity for small exchange ($J\leq 5J_0$). Published in Phys. Rev. B; this is the published version

We propose a machine-learning-based (ML-based) method for efficiently predicting atomic diffusivity in crystals, in which the potential energy surface (PES) of a diffusion carrier is partially evaluated by first-principles calculations. To preferentially evaluate the region of interest governing the atomic diffusivity, a statistical PES model based on a Gaussian process (GP-PES) is constructed and updated iteratively from known information on already-computed potential energies (PEs). In the proposed method, all local energy minima (stable & metastable sites) and elementary processes of atomic diffusion (atomic jumps) are explored on the predictive mean of the GP-PES. The uncertainty of jump frequency in each elementary process is then estimated on the basis of the variance of the GP-PES. The acquisition function determining the next grid point to be computed is designed to reflect the impacts of the uncertainties of jump frequencies on the uncertainty of the macroscopic atomic diffusivity. The numerical solution of the master equation is here employed to readily estimate the atomic diffusivity, which enables us to design the acquisition function reflecting the centrality of each elementary process.

When the period of unit cells constituting metamaterials is no longer much smaller than the wavelength but only smaller, local material laws fail to describe the propagation of light in such composite media when considered at the effective level. Instead, nonlocal material laws are required. They have to be derived by approximating a general response function of the electric field in the metamaterial at the effective level that is accurate but cannot be handled practically. But how to perform this approximation is not obvious at all. Indeed, many approximations can be perceived and one should be able to decide as quickly as possible which of these possible material laws are mathematically and physically meaningful at all. Here, at the example of a second order Pad\'e approximation of the general response function of the electric field, we present a checklist of each possible constitutive relation that has to pass in order to be physically and mathematically liable. As will be shown, only two out of these nine Pad\'e approximations pass the checklist. The work is meant to be a guideline applicable to decide which constitutive relation actually makes any sense at all. It is an essential ingredient for future research on composite media as any possible constitutive relation to be discussed should pass it.

Quantum point contacts (QPC) are fundamental building blocks of nanoelectronic circuits. For their emission dynamics as well as for interaction effects such as the 0.7-anomaly the details of the electrostatic potential are important, but the precise potential shapes are usually unknown. Here, we measure the one-dimensional subband spacings of various QPCs as a function of their conductance and compare our findings with models of lateral parabolic versus hard wall confinement. We find that a gate-defined QPC near pinch-off is compatible with the parabolic saddle point scenario. However, as the number of populated subbands is increased Coulomb screening flattens the potential bottom and a description in terms of a finite hard wall potential becomes more realistic., 7+2 pager, 7 figures, v2: published version (minor changes)

With an auxiliary weak external magnetic field, we reexamine the fundamental thermodynamic function, Gibbs free energy $G(T,h)$, to study phase transitions in classical spin lattice models. A cross derivative, i.e., the second-order partial derivative of $G(T,h)$ with respect to both temperature and field, is calculated to precisely locate the critical temperature, which also reveals the nature of a transition. The strategy is efficient and universal, as exemplified by the five-state clock model, two-dimensional (2D) and 3D Ising models, and the $XY$ model, no matter if a transition is trivial or exotic with complex excitations. More importantly, other conjugate pairs could also be integrated into a similar cross derivative if necessary, which would greatly enrich our vision and means to investigate phase transitions both theoretically and experimentally.

The discovery of room-temperature skyrmions in some magnetic materials has boosted the investigation of their dynamics in view of future applications. We study the dynamics of skyrmions in the presence of defects or borders using a deterministic (finding and solving a deterministic Fokker-Planck differential equation) while probabilistic (the solution is the probability density for the presence of a skyrmion) approach. The probability that a skyrmion becomes trapped in a pinning center or the probability of the survival of a skyrmion along a racetrack are obtained as a function of temperature. The present work can be relevant in the design of skyrmionic devices where the probability of finding skyrmions at a given position and time is crucial for their feasibility.

We apply our generalized input-output method (GIOM), introduced in the previous paper of this series, to prototype molecular junction models describing vibrationally coupled electron transport. In short junctions where analytic treatments are available, we show that the charge current obtained by the GIOM reduces to known limits and reasonably agrees with exact numerical simulations (when available). For extended junctions, we numerically reveal that the current displays a turnover from phonon-assisted to phonon-suppressed transport as a function of electronic and vibrational parameters. As an additional application, we consider a cavity-coupled molecular junction. Here we identify a cavity-induced suppression of charge current in the single-site case, and observe the coexistence of phononic and photonic sidebands in the current-voltage characteristics when both strong light-matter interaction and electron-vibration coupling are present. Together with the first paper of this series, we demonstrate that the input-output framework, which is normally employed in quantum optics, can serve as a powerful and feasible tool in the realm of electron transport junctions.

We study the properties of the Luttinger-Ward functional (LWF) in a simplified Hubbard-type model without time or spatial dimensions, but with $N$ identical replicas located on a single site. The simplicity of this $(0+0)d$ model permits an exact solution for all $N$ and for both bosonic and fermionic statistics. We show that fermionic statistics are directly linked to the fact that multiple values of the noninteracting Green's function ${G}_{0}$ map to the same value of the interacting Green's function $G$; that is, the mapping ${G}_{0}\ensuremath{\mapsto}G$ is noninjective. This implies that with fermionic statistics the $(0+0)d\phantom{\rule{4pt}{0ex}}N$-replica model has a multiply valued LWF. The number of LWF values in the fermionic model increases proportionally to the number of replicas $N$, while in the bosonic model the LWF has a single value regardless of $N$. We also discuss the formal connection between the $N$-replica model and the $(0+1)d$ Hubbard atom which was used in previous studies of LWF's multivaluedness.

We formulate and solve the Eliashberg equations on the imaginary frequency axis at temperatures below $T_c$ in the weak-coupling limit. We find an excellent scaling at all temperatures, for a given coupling strength, and the normalized order parameter exhibits a BCS-like temperature dependence. The hybrid real-imaginary axis equations are also solved to obtain numerically exact analytic continuations from the imaginary frequency axis to the real frequency axis. This provides a determination of the gap edge, which, in the weak-coupling limit, is identical to the order parameter from the imaginary axis. The analytical result for the zero-temperature gap edge deviates from the BCS result by a factor of $1/\sqrt{e}$, which was also obtained for the transition temperature $T_c$. We show that the normalized gap function on both the real and imaginary frequency axes, for an electron-phonon Einstein spectrum ($\delta$-function) of a given strength, is a universal function of frequency, independent of temperature. The $1/\sqrt{e}$ correction is a result of this non-trivial frequency dependence in the gap function. This modification, in the gap edge and in $T_{c}$, serves to preserve various dimensionless ratios to their BCS values., Comment: 11 pages, 8 figures

Efficient ab initio calculations of correlated materials at finite temperature require compact representations of the Green's functions both in imaginary time and Matsubara frequency. In this paper, we introduce a general procedure which generates sparse sampling points in time and frequency from compact orthogonal basis representations, such as Chebyshev polynomials and intermediate representation (IR) basis functions. These sampling points accurately resolve the information contained in the Green's function, and efficient transforms between different representations are formulated with minimal loss of information. As a demonstration, we apply the sparse sampling scheme to diagrammatic $GW$ and GF2 calculations of a hydrogen chain, of noble gas atoms and of a silicon crystal., Comment: 13 pages, 8 figures

We study the Anderson transition for three-dimensional (3D) $N \times N \times N$ tightly bound cubic lattices where both real and imaginary parts of onsite energies are independent random variables distributed uniformly between $-W/2$ and $W/2$. Such a non-Hermitian analog of the Anderson model is used to describe random-laser medium with local loss and amplification. We employ eigenvalue statistics to search for the Anderson transition. For 25\% smallest-modulus complex eigenvalues we find the average ratio $r$ of distances to the first and the second nearest neighbor as a function of $W$. For a given $N$ the function $r(W)$ crosses from $0.72$ to 2/3 with a growing $W$ demonstrating a transition from delocalized to localized states. When plotted at different $N$ all $r(W)$ cross at $W_c = 6.0 \pm 0.1$ (in units of nearest neighbor overlap integral) clearly demonstrating the 3D Anderson transition. We find that in the non-Hermitian 2D Anderson model, the transition is replaced by a crossover., Comment: 3 pages, 3 figures

Superconductivity in two dimensions is nontrivial. One way to achieve global superconductivity is via the Berezinskii-Kosterlitz-Thouless (BKT) transition due to proliferation of vortex-antivortex pairs. This transition is expected to have a clear signature on the specific heat. The singularity at the transition temperature ${T}_{\mathrm{BKT}}$ is predicted to be immeasurable, and a broad nonuniversal peak is expected at $Tg{T}_{\mathrm{BKT}}$. Up to date, this has not been observed in two-dimensional superconductors; this work is then dedicated to investigate ${c}_{p}$ signatures in the limit of ultrathin 2d superconductors. We use a unique highly sensitive technique to measure the specific heat of quench condensed ultrathin Pb films. We find that thick films exhibit a specific heat jump at ${T}_{C}$ that is consistent with BCS theory. As the film thickness is reduced below the superconducting coherence length and the systems enter the 2D limit, the specific heat reveals BKT-like behavior in what can appear as to be a continuous BCS-BKT crossover as a function of film thickness. However, a number of problems arise with this interpretation. We discuss the experimental results and the possible significance of various scenarios involving BKT physics.

We propose a density-based nonlocal correlation energy functional, corresponding to a revised form of the seamless van der Waals (vdW) density functional developed by Dobson and coauthors in the late nineties. The functional, termed as rDW99 in this work, has the same energy expression as the random phase approximation (RPA), but its key ingredient---the noninteracting density response function---is expressed entirely in terms of the electron density and density gradient. This is enabled by generalizing the Lindhard function from the homogeneous electron gas (HEG) to inhomogeneous electron systems. Compared to the original DW99 functional of Dobson and coauthors, we have introduced two revisions in rDW99: (1) A gap correction is incorporated into the generalized Lindhard function, making the functional more suitable for describing inhomogeneous, and in particular insulating, systems; (2) an approximate, yet fairly accurate, analytical form of the Lindhard function in real space is developed which facilitates the numerical evaluation of the rDW99 functional. In contrast with previously developed vdW density functionals, the nonlocal polarization effect is naturally captured in the rDW99 functional. The functional form, as it stands right now, is computationally still rather involving in a straightforward implementation. However, we anticipate that numerical techniques can be developed to significantly reduce the computational cost. As a first step, we assess the quality of rDW99 for describing the vdW interactions in the nonoverlapping asymptotic regime by computing the ${C}_{6}$ coefficients for a set of 43 atoms and molecules. With only one adjustable parameter, the mean absolute percentage error (MAPE) of the ${C}_{6}$ coefficients is estimated to be $8.7%$. In this work, ${C}_{6}$ coefficients corresponding to the standard RPA method are also computed for the same test set, and the MAPE for the RPA ${C}_{6}$ coefficients is estimated to be $13.2%$.

We report the auxiliary coherent potential approximation (ACPA) for calculating the phonon dispersion of three-dimensional alloys with both mass and force-constant disorders. To obtain the average spectra function of disordered alloys, the average coherent scattering structure factors are derived from the auxiliary coherent medium in single-site approximation. We provide an analytical proof of the sum rule in the auxiliary coherent medium, which ensures the analyticity of physical properties. To demonstrate the accuracy and applicability of the ACPA method, we apply the ACPA to calculate phonon dispersion of several alloys, including CuPd CuAu, PdFe, and NiPt with different disorder concentrations. We find the ACPA phonon dispersion results agree very well with the itinerant coherent potential approximation calculations and experimental measurements. The approximate separable force-constant model used in the ACPA can very well represent the first-principles disordered force constants, presenting minor or even negligible influence on the phonon dispersion of the alloy. The ACPA model features easy implementation and high computational efficiency, providing an effective method for simulating vibrational properties of realistic alloys.

Simulation-size effect in evaluating the melting temperature of material is studied systematically by combining thermodynamic integration (TI) based on first-principles molecular-dynamics (FPMD) simulations and machine learning. Since the numerical integration to determine the free energies of two different phases as a function of temperature is very time consuming, the FPMD-based TI method has only been applied to small systems, i.e., less than 100 atoms. To accelerate the numerical integration, we here construct an interatomic potential based on the artificial neural-network (ANN) method, which retains the first-principles accuracy at a significantly lower computational cost. The free energies of the solid and liquid phases of rubidium are accurately obtained by the ANN potential, where its weight parameters are optimized to reproduce FPMD results. The ANN results reveal a significant size dependence up to 500 atoms.

A computational method has been developed to compute the electron-phonon interactions using the projector augmented wave method and finite displacements. Aluminium and diamond crystals are considered to test our strategy. It is found that the potential derivatives are quickly convergent with respect to the supercell size. Moreover the method is found to be efficient enough to densely sample the Brillouin zone and compute the Eliashberg function and phonon lifetime without requiring the use to interpolations.

Parafermions are non-Abelian anyons which generalize Majorana fermions and hold great promise for topological quantum computation. We study the braiding of $\mathbb{Z}_{2n}$ parafermions which have been predicted to emerge as bound states in fractional quantum Hall systems at filling factor $\nu = 1/n$ ($n$ odd). Using a combination of bosonization and refermionization, we calculate the energy splitting as a function of distance and chemical potential for a pair of parafermions separated by a gapped region. Braiding of parafermions in quantum Hall edge states can be implemented by repeated fusion and nucleation of parafermion pairs. We simulate the conventional braiding protocol of parafermions numerically, taking into account the finite separation and finite chemical potential. We show that a nonzero chemical potential poses challenges for the adiabaticity of the braiding process because it leads to accidental crossings in the spectrum. To remedy this, we propose an improved braiding protocol which avoids those degeneracies., Comment: 17 pages, 30 figures

We obtain the density-density correlation structure in molecular dynamics (MD) simulations of graphene, and analyze it within the capillary wave theory (CWT), developed for fluid surfaces, to describe the thermal corrugations of the graphene sheet with a wave-vector-dependent surface tension $\ensuremath{\gamma}({q}_{x})$. The density correlation function (from the atomic positions) is compared with the theoretical prediction by Bedeaux and Weeks (BW), within the CWT, in terms of $\ensuremath{\gamma}({q}_{x})$ and the density profile. The agreement is very good, even for relatively large ${q}_{x}\ensuremath{\approx}0.2{\AA{}}^{\ensuremath{-}1}$, and with very little role for the correlation background, which sets an important difficulty for liquid surfaces. We present and test a generic prediction for the structure factor $S({q}_{x},{q}_{z})$ from $\ensuremath{\gamma}({q}_{x})$, that contains and goes beyond the classical asymptotic expression, developed by Sinha, for the analysis of x-ray surface scattering. We compare our prediction with the formula used in the interpretation of experimental data, that assumes a direct relationship between $\ensuremath{\gamma}({q}_{x})$ and the correlation structure for the same wave vector ${q}_{x}$. That relation is exact only for the first (Wertheim's) term of the BW series, and we use our results to test the accuracy of the function $\ensuremath{\gamma}({q}_{x})$ estimated through that method.

A physical system exposes to us in a real space, while its description often refers to its reciprocal momentum space. A connection between them can be established by exploring patterns of quasiparticles interference (QPI), which is experimentally accessible by Fourier transformation of the scanning tunneling spectroscopy (FT-STS). We here investigate how local and global features of QPI patterns are related to the geometry and topology of electronic structure in the considered physical system. A reduced response function (RRF) approach is developed that can analyze QPI patterns with clear physical pictures. It is justified that the generalized joint density of states, which is the imaginary part of RRF, for studying QPI. Moreover, we reveal that global patterns of QPI may be indicators of topological numbers for gapless systems, and demonstrate that robustness of such indicators against distractive local features of QPI for topological materials with complicated band structures., Comment: 10 pages, 9 figures

The superconducting state of metals has long provided a classic example of particle-hole symmetry at low energy. Fermionic self-energy results based on first-principles theory for the electron-phonon coupling in ${\mathrm{H}}_{3}\mathrm{S}$ presented here illustrate strong particle-hole asymmetry in the dynamics arising from the underlying sharp structure in the fermionic density of states. Thus ${\mathrm{H}}_{3}\mathrm{S}$ not only is the superconductor with the highest critical temperature ${T}_{c}$ (through 2018), but its low-energy, low-temperature properties deviate strongly from textbook behavior. The minor momentum and band dependence of the fermionic self-energy allows evaluation of the momentum-resolved and zone-averaged spectral densities and interacting thermal distribution function, all of which clearly illustrate strong particle-hole asymmetry.

We investigate the behavior of the critical temperature ${T}_{c}$ in superconductor/ferromagnet/superconductor (S/F/S) trilayers in the dirty limit as a function of the ferromagnetic layer thickness ${d}_{f}$ and the S/F interface transparency. We perform ${T}_{c}$ calculations using the general self-consistent multimode approach based on the Usadel equations in Matsubara Green's functions technique, and compare the results with the single-mode approximation, widely used in literature. Both methods produce similar results for sufficiently low interface transparency. For transparent interfaces, we obtain a qualitatively different ${T}_{c}({d}_{f})$ behavior. Using the multimode approach, we observe multiple 0-$\ensuremath{\pi}$ transitions in critical temperature, which cannot be resolved by the single-mode approximation. We also calculate the critical S layer thickness at given ${d}_{f}$ when an S/F/S trilayer still has a nonzero critical temperature. Finally, we establish the limits of applicability of the single-mode approximation.

Free electrons have a uniform kinetic energy density (KED), which evolves into a spatially varying quantity as the electrons respond to the gradual imposition of an external potential. In this paper and a companion paper, we examine two sets of functionals for describing the local, non-negative KED that emerges after such a perturbation. In this paper, we emphasize potential functionals, deriving the first- and second-order deviations from the free-electron KED as functionals of the perturbing potential, also reconsidering the analogous functionals for the local density of states and the electron density. (In the second paper, we use these results to re-express the KED response in terms of functionals of the induced electron density.) We develop reciprocal-space formulations of the response kernels to complement previously known real-space forms. The first-order function is straightforward to obtain, but the second-order function requires considerable effort. To manage the derivations, we relate the KED response to that of the one-electron Green function, and then examine the latter in detail. Finally, we provide extensive validation of the derived response functions based on asymptotic analysis of an integral representation, numerical integration of the same generating integral, and application to the linear potential model.

A classic example of a quantum quench concerns the release of a interacting Bose gas from an optical lattice. The local properties of quenches such as this have been extensively studied however the global properties of these non-equilibrium quantum systems have received far less attention. Here we study several aspects of global non-equilibrium behavior by calculating the amount of work done by the quench as measured through the work distribution function. Using Bethe Ansatz techniques we determine the Loschmidt amplitude and work distribution function of the Lieb-Liniger gas after it is released from an optical lattice. We find the average work and its universal edge exponents from which we determine the long time decay of the Loshcmidt echo and highlight striking differences caused by the the interactions as well as changes in the geometry of the system. We extend our calculation to the attractive regime of the model and show that the system exhibits properties similar to the super Tonks-Girardaeu gas. Finally we examine the prominent role played by bound states in the work distribution and show that, with low probability, they allow for work to be extracted from the quench., Comment: 7 pages, 2 figures