arXiv subjects

Hiroshi Shinaoka

Publications and source records attributed to Hiroshi Shinaoka.

At least 19 recordsLinked to original sources

arXiv2026

Generalized Keldysh formalism for nonequilibrium correlation functions and its application to fluctuation dynamics

Recent advances in time-resolved spectroscopies provide increasing access to collective dynamics in correlated quantum materials. However, computing the corresponding nonequilibrium two-particle correlation functions remains a major challenge. Here, by introducing a contour-dependent virtual probe field within the generalized Keldysh formalism, we propose an approach that computes such correlation functions with the vertex corrections essential for describing collective dynamics. In particular, we introduce a linear integral equation that computes the correlation functions without explicitly constructing the four-time vertex kernel, and develop its matrix-free Krylov solver based on quantics tensor trains. Combining our method with nonequilibrium dynamical mean-field theory, we show that the fluctuation dynamics of the order parameter in a nonequilibrium symmetry-broken state depends significantly on whether vertex corrections are included, and that the fluctuation and its decay time grow near the nonthermal critical point. Our approach thus provides a practical route for evaluating nonequilibrium correlation functions, which are emerging as key observables for characterizing states far from equilibrium.

cond-mat.str-el↗

arXiv2026

Weak-coupling tensor cross interpolation impurity solver for nonequilibrium dynamical mean-field theory

Simulating nonequilibrium quantum many-body systems remains a major challenge due to the exponential growth of the computational complexity with real time. Here we implement a nonequilibrium impurity solver based on the weak-coupling expansion and the tensor cross interpolation (TCI), and apply it to nonequilibrium dynamical mean-field theory (DMFT). The method approximates the integrands of the high-dimensional integrals arising in the weak-coupling expansion in a tensor-train form, enabling efficient evaluations without stochastic sampling and thereby mitigating the sign problem affecting continuous-time quantum Monte Carlo (CT-QMC) methods. Benchmark calculations for an exactly solvable nonequilibrium impurity model agree well with the exact results and reveal a low-rank structure of the integrands. When applied to interaction-quench problems in the half-filled Hubbard model, the method reproduces fast thermalization at a critical interaction strength with accuracy comparable to CT-QMC. Away from half filling, where the sign problem becomes even more severe, the present approach remains well controlled, revealing a crossover instead of a sharply defined fast thermalization point in the 3/4-filled case. The solver can also be applied to steady-state DMFT problems, yielding accurate spectral functions in the metallic regime without analytic continuation.

cond-mat.str-el↗

arXiv2026

Parallelized contraction of tensor trains or matrix product operators

Tensor Trains (TT), also known as Matrix Product States (MPS) and Matrix Product Operators (MPO), provide a compact and structured representation for high-dimensional data and operators. One of the most expensive manipulations involving tensor trains is the contraction of two MPOs. A popular and accurate method for mitigating this cost is the fit algorithm. However, it is still comparatively costly since it involves 2-site updates. Moreover, the parallelization of the fit algorithm when used for MPO-MPO contractions has received comparatively little attention. In this work, we present two strategies for accelerating the fit algorithm, usable in combination: (1) We use MPI-based distributed-memory parallelization tailored for MPO-MPO contractions, employing one of two MPO gauge choices: (1a) the inverse canonical gauge, which yields near-ideal parallelization speedup across all problem sizes; and (1b) the site-canonical gauge, which avoids the inversion of singular values but requires extra computations to ensure global consistency, thus yielding excellent parallelization speedup only for large problems requiring several sweeps before convergence. (2) We use randomized projections to reduce the cost of local updates from 2-site to 1-site costs while retaining 2-site accuracy, and to speed up contractions of environment tensors with MPO tensors.

physics.comp-ph↗

arXiv2026

Diagnosing phase transitions through time-scale entanglement

Spatial entanglement of quantum states has become a central paradigm of many-body physics. Here, we unearth a fundamentally different form of entanglement, the entanglement between imaginary time scales. This time-scale entanglement is accessible through quantics tensor train diagnostics (QTTD), where the bond dimension of an $n$-particle correlator encodes the coupling between temporal scales. Our central result is that time-scale entanglement is generically enhanced in the vicinity of phase transitions and crossovers. At quantum critical points, it becomes scale-invariant. We demonstrate time-scale entanglement across a range of systems, including finite-size Hubbard rings, the transverse-field Ising model, the single-impurity Anderson model, and the Mott transition in the Hubbard model. Remarkably, the enhanced time-scale entanglement is largely independent of the specific observable, establishing QTTD as a universal and unbiased diagnostic of criticality.

cond-mat.str-el↗

arXiv2026

Adaptive Patching for Tensor Train Computations

Quantics Tensor Train (QTT) operations such as matrix product operator contractions are prohibitively expensive for large bond dimensions. We propose an adaptive patching scheme that exploits block-sparse QTT structures to reduce costs through divide-and-conquer, adaptively partitioning tensors into smaller patches with reduced bond dimensions. We demonstrate substantial improvements for sharply localized functions and show efficient computation of bubble diagrams and Bethe-Salpeter equations, opening the door to practical large-scale QTT-based computations previously beyond reach.

physics.comp-ph↗

arXiv2025

A causality-based divide-and-conquer algorithm for nonequilibrium Green's function calculations with quantics tensor trains

We propose a causality-based divide-and-conquer algorithm for nonequilibrium Green's function calculations with quantics tensor trains. This algorithm enables stable and efficient extensions of the simulated time domain by exploiting the causality of Green's functions. We apply this approach within the framework of nonequilibrium dynamical mean-field theory to the simulation of quench dynamics in symmetry-broken phases, where long-time simulations are often required to capture slow relaxation dynamics. We demonstrate that our algorithm allows to extend the simulated time domain without a significant increase in the cost of storing the Green's function.

cond-mat.str-el↗

arXiv2025

Memory-Efficient Nonequilibrium Green's Function Framework Built On Quantics Tensor Trains

One of the challenges in diagrammatic simulations of nonequilibrium phenomena in lattice models is the large memory demand for storing momentum-dependent two-time correlation functions. This problem can be overcome with the recently introduced quantics tensor train (QTT) representation of multivariable functions. Here, we demonstrate nonequilibrium Green's function simulations within the $GW$ and Migdal approximations with high momentum resolution, up to times which exceed the capabilities of standard implementations and are long enough to study, e.g., transient Floquet physics during multi-cycle electric field pulses and thermalization dynamics. The self-consistent calculation on the three-leg Kadanoff-Baym contour is fully self-contained, employing only QTT-compressed functions and input functions which are either generated directly in QTT form or obtained via quantics tensor cross interpolation.

cond-mat.str-el↗

arXiv2025

Predictor-corrector method based on dynamic mode decomposition for tensor-train nonequilibrium Green's function calculations

The nonequilibrium Green's function (NEGF) formalism is a powerful tool to study the nonequilibrium dynamics of correlated lattice systems, but its applicability to realistic system sizes and long timescales is limited by unfavorable memory scaling. While compressed representations, such as the recently introduced quantics tensor train (QTT) format, alleviate the memory bottleneck, the efficiency of QTT-NEGF calculations is hindered by poor initializations and slow or unstable convergence of globally updated self-consistent iterations. Here, we introduce a predictor-corrector solver for QTT-NEGF simulations that combines dynamic mode decomposition (DMD) extrapolation with the recently proposed causality-preserving block-time-stepping updates. The DMD predictor supplies accurate initial guesses that reduce the iteration count of the calculation, while the block-time-stepping correction ensures stable convergence even for long propagation intervals. Applying this method to the Hubbard model on a $32\times 32$ lattice within the nonequilibrium $GW$ approximation, we demonstrate stable propagation up to times of $t_\mathrm{max}=512$ inverse hoppings, surpassing the capabilities of both matrix-based implementations and previous QTT solvers. Our contribution is twofold. (i) We integrate tensor dynamic mode decomposition with the QTT representation, which establishes a general framework that is not limited to NEGFs. (ii) We demonstrate its practical benefits in NEGF simulations, where it enables stable and efficient access to unprecedented timescales at high momentum resolution, thereby advancing controlled studies of long-time dynamics and nonequilibrium steady states in correlated lattice systems.

cond-mat.str-el↗

arXiv2025

Uniform electron benchmark for the first-principles $GW_{0}$-Eliashberg theory

We investigate the numerical behavior of the Eliashberg equations for phonon-mediated superconductivity, incorporating normal-state self-energy calculations within the consistent $GW_{0}$ approximation. We account for the full wavenumber and frequency dependences of both the screened Coulomb interaction and phonon-mediated attraction. We present results for the prototypical uniform electron gas system with model Einstein phonons at temperatures of a few kelvin. At extremely low temperatures, we efficiently execute the required convolutions of Green's functions and interactions in Matsubara frequency and wavenumber using intermediate representation and Fourier convolution techniques. In particular, we elucidate the interplay between electron-phonon $ω$-mass and $k$-mass renormalizations of the electronic self-energy in determining the normal-state effective mass, spectral weight and the superconducting transition temperature. The electron density regimes where the plasmon effect enhances or suppresses the phonon-mediated superconductivity on top of the static Coulomb effect are revealed. We compare our comprehensive Eliashberg calculation results with those from density functional theory for superconductors, where the functionals have been constructed with reference to Eliashberg theory. Our model, methods, and results provide a valuable benchmark for first-principles superconducting calculations that treat screened Coulomb interaction effects non-empirically.

cond-mat.supr-con↗

arXiv2025

Low-rank quantics tensor train representations of Feynman diagrams for multiorbital electron-phonon models

Feynman diagrams are an essential tool for simulating strongly correlated electron systems. However, stochastic quantum Monte Carlo sampling suffers from the sign problem, particularly when solving a multiorbital quantum impurity model. Recently, two approaches have been proposed for efficient numerical treatment of Feynman diagrams: Tensor Cross Interpolation (TCI) to replace stochastic sampling and the Quantics Tensor Train (QTT) representation for compressing space-time dependence. One of the remaining challenges is the nontrivial task of identifying low-rank structures in weak-coupling Feynman diagrams for multiorbital electron-phonon systems. In particular, the traditional TCI algorithm faces an ergodicity problem, which prevents it from fully exploring the multiorbital space. To address this, we incorporate a new algorithm called global search, which resolves this issue. By combining this approach with QTT, we uncover low-rank structures and achieve efficient numerical integration with exponential resolution in time and faster-than-power-law convergence of error relative to computational cost. Additionally, our approach does not require the division of discontinuous regions necessary in non-quantics TCI.

cond-mat.str-el↗

arXiv2025

Adaptive sampling-based optimization of quantics tensor trains for noisy functions: applications to quantum simulations

Tensor cross interpolation (TCI) is a powerful technique for learning a tensor train (TT) by adaptively sampling a target tensor based on an interpolation formula. However, when the tensor evaluations contain random noise, optimizing the TT is more advantageous than interpolating the noise. Here, we propose a new method that starts with an initial guess of TT and optimizes it using non-linear least-squares by fitting it to measured points obtained from TCI. We use quantics TCI (QTCI) in this method and demonstrate its effectiveness on sine and two-time correlation functions, with each evaluated with random noise. The resulting QTT exhibits increased robustness against noise compared to the QTCI method. Furthermore, we employ this optimized QTT of the correlation function in quantum simulation based on pseudo-imaginary-time evolution, resulting in ground-state energy with higher accuracy than the QTCI or Monte Carlo methods.

quant-ph↗

arXiv2025

Tensor cross interpolation approach for quantum impurity problems based on the weak-coupling expansion

We apply the tensor cross interpolation (TCI) algorithm to solve equilibrium quantum impurity problems with high precision based on the weak-coupling expansion. The TCI algorithm, a kind of active learning method, factorizes high-dimensional integrals that appear in the perturbative expansion into a product of low-dimensional ones, enabling us to evaluate higher-order terms efficiently. This method is free from the sign problem which quantum Monte Carlo methods sometimes suffer from, and allows one to directly calculate the free energy. We benchmark the TCI impurity solver on an exactly solvable impurity model, and find good agreement with the exact solutions. We also incorporate the TCI impurity solver into the dynamical mean-field theory to solve the Hubbard model, and show that the metal-to-Mott insulator transition is correctly described with comparable accuracy to the Monte Carlo methods. Behind the effectiveness of the TCI approach for quantum impurity problems lies the fact that the integrands in the weak-coupling expansion naturally have a low-rank structure in the tensor-train representation.

cond-mat.str-el↗

arXiv2025

Two-particle calculations with quantics tensor trains: Solving the parquet equations

We present the first application of quantics tensor trains (QTTs) and tensor cross interpolation (TCI) to the solution of a full set of self-consistent equations for multivariate functions, the so-called parquet equations. We show that the steps needed to evaluate the equations (Bethe--Salpeter equations, parquet equation and Schwinger--Dyson equation) can be decomposed into basic operations on the QTT-TCI (QTCI) compressed objects. The repeated application of these operations does not lead to a loss of accuracy beyond a specified tolerance and the iterative scheme converges even for numerically demanding parameters. As examples we take the Hubbard model in the atomic limit and the single impurity Anderson model, where the basic objects in parquet equations, the two-particle vertices, depend on three frequencies, but not on momenta. The results show that this approach is able to overcome major computational bottlenecks of standard numerical methods. The applied methods allow for an exponential increase of the number of grid points included in the calculations leading to an exponentially improving computational error for a linear increase in computational cost.

cond-mat.str-el↗

arXiv2024

Learning tensor networks with tensor cross interpolation: new algorithms and libraries

The tensor cross interpolation (TCI) algorithm is a rank-revealing algorithm for decomposing low-rank, high-dimensional tensors into tensor trains/matrix product states (MPS). TCI learns a compact MPS representation of the entire object from a tiny training data set. Once obtained, the large existing MPS toolbox provides exponentially fast algorithms for performing a large set of operations. We discuss several improvements and variants of TCI. In particular, we show that replacing the cross interpolation by the partially rank-revealing LU decomposition yields a more stable and more flexible algorithm than the original algorithm. We also present two open source libraries, xfac in Python/C++ and TensorCrossInterpolation.jl in Julia, that implement these improved algorithms, and illustrate them on several applications. These include sign-problem-free integration in large dimension, the superhigh-resolution quantics representation of functions, the solution of partial differential equations, the superfast Fourier transform, the computation of partition functions, and the construction of matrix product operators.

physics.comp-ph↗

arXiv2024

Physics-informed neural network model for quantum impurity problems based on Lehmann representation

We propose a physics-informed neural network (PINN) model to efficiently predict the self-energy of Anderson impurity models (AIMs) based on the Lehmann representation. As an example, we apply the PINN model to a single-orbital AIM (SAIM) for a noninteracting electron bath with a semicircular density of states. Trained across a wide range of onsite Coulomb interactions $U$ and hybridization strengths $V$, the PINN model demonstrates high accuracy in both $U$-$V$ and Matsubara-frequency spaces. Additionally, we investigate the effectiveness of physical constraints implemented in the PINN model. For example, We show that the Lehmann representation allows the PINN model to reduce the maximum test error in an electron filling by a factor of approximately 7.8.

cond-mat.str-el↗

arXiv2024

Ab initio study on heavy-fermion behavior in LiV$_2$O$_4$: Role of Hund's coupling and stability

LiV$_2$O$_4$ is a member of the so-called $3d$ heavy fermion compounds, with effective electron mass exceeding 60 times the free electron mass, comparable to $4f$ heavy fermion compounds. The origin of the strong electron correlation in combination with its metallic character have been a subject of intense theoretical and experimental discussion, with Kondo-like physics and Mott-physics being suggested as its physical origin. Here we report state-of-the art \textit{ab initio} Density Functional Theory + dynamical mean-field theory calculations for LiV$_2$O$_4$ for the full three orbital V $t_\mathrm{2g}$ manifold, and present temperature-dependent spectral properties. We map out the phase diagram for a representative 3-orbital model system as a function of doping and interaction strength, which indicates that LiV$_2$O$_4$ is located between two orbital-selective Mott phases, giving rise to a robust strongly correlated Hund's metal behavior. At low temperature we find the emergence of a strongly renormalized sharp quasi-particle peak a few meV above the Fermi level of V $a_\mathrm{1g}$ character, in agreement with experimental reports.

cond-mat.str-el↗

arXiv2024

Compactness of quantics tensor train representations of local imaginary-time propagators

Space-time dependence of imaginary-time propagators, vital for \textit{ab initio} and many-body calculations based on quantum field theories, has been revealed to be compressible using Quantum Tensor Trains (QTTs) [Phys. Rev. X {\bf 13}, 021015 (2023)]. However, the impact of system parameters, like temperature, on data size remains underexplored. This paper provides a comprehensive numerical analysis of the compactness of local imaginary-time propagators in QTT for one-time/-frequency objects and two-time/-frequency objects, considering truncation in terms of the Frobenius and maximum norms. To study worst-case scenarios, we employ random pole models, where the number of poles grows logarithmically with the inverse temperature and coefficients are random. The Green's functions generated by these models are expected to be more difficult to compress than those from physical systems. The numerical analysis reveals that these propagators are highly compressible in QTT, outperforming the state-of-the-art approaches such as intermediate representation and discrete Lehmann representation. For one-time/-frequency objects and two-time/-frequency objects, the bond dimensions saturate at low temperatures, especially for truncation in terms of the Frobenius norm. We provide counting-number arguments for the saturation of bond dimensions for the one-time/-frequency objects, while the origin of this saturation for two-time/-frequency objects remains to be clarified. This paper's findings highlight the critical need for further research on the selection of truncation methods, tolerance levels, and the choice between imaginary-time and imaginary-frequency representations in practical applications.

cond-mat.str-el↗

arXiv2024

Robust analytic continuation using sparse modeling approach imposed by semi-positive definiteness for multi-orbital systems

Analytic continuation (AC) from imaginary-time Green's function to spectral function is essential in the numerical analysis of dynamical properties in quantum many-body systems. However, this process faces a fundamental challenge: it is an ill-posed problem, leading to unstable spectra against the noise in the Green's function. This instability is further complicated in multi-orbital systems with hybridization between spin-orbitals, where off-diagonal Green's functions yield a spectral matrix with off-diagonal elements, necessitating the matrix's semi-positive definiteness to satisfy the causality. We propose an advanced AC method using sparse modeling for multi-orbital systems, which reduces the effect of noise and ensures the matrix's semi-positive definiteness. We demonstrate the effectiveness of this approach by contrasting it with the conventional sparse modeling method, focusing on handling Green's functions with off-diagonal elements, thereby demonstrating our proposed method's enhanced stability and precision.

cond-mat.str-el↗