Reducing the numerical effort of finite-temperature density matrix renormalization group transport calculations

Abstract

Finite-temperature transport properties of one-dimensional systems can be studied using the time dependent density matrix renormalization group via the introduction of auxiliary degrees of freedom which purify the thermal statistical operator. We demonstrate how the numerical effort of such calculations is reduced when the physical time evolution is augmented by an additional time evolution within the auxiliary Hilbert space. Specifically, we explore a variety of integrable and non-integrable, gapless and gapped models at temperatures ranging from T=infty down to T/bandwidth=0.05 and study both (i) linear response where (heat and charge) transport coefficients are determined by the current-current correlation function and (ii) non-equilibrium driven by arbitrary large temperature gradients. The modified DMRG algorithm removes an 'artificial' build-up of entanglement between the auxiliary and physical degrees of freedom. Thus, longer time scales can be reached.

References in corpus (36)

• The density-matrix renormalization group in the age of matrix product states
• Matrix Product States, Projected Entangled Pair States, and variational renormalization group methods for quantum spin systems
• Real time evolution using the density matrix renormalization group
• Matrix Product Density Operators: Simulation of finite-T and dissipative systems
• Classical simulation of infinite-size quantum lattice systems in one spatial dimension
• Matrix product states represent ground states faithfully
• Open XXZ spin chain: Nonequilibrium steady state and strict bound on ballistic transport
• From density-matrix renormalization group to matrix product states
• Entropy scaling and simulability by Matrix Product States
• Spin transport in a one-dimensional anisotropic Heisenberg model
• Conservation laws, integrability and transport in one-dimensional quantum systems
• Matrix Product States for dynamical simulation of infinite chains
• Spectral functions in one-dimensional quantum systems at T>0
• Time-step targetting methods for real-time dynamics using DMRG
• Twofold advance in the theoretical understanding of far-from-equilibrium properties of interacting nanostructures
• Spectral Function for the S=1 Heisenberg Antiferromagetic Chain
• Chebyshev matrix product state approach for spectral functions
• A real-time study of diffusive and ballistic transport in spin-1/2 chains using the adaptive time-dependent density matrix renormalization group method
• Diffusive high-temperature transport in the one-dimensional Hubbard model
• Transport in open spin chains: A Monte Carlo wave-function approach
• Spin conductivity in almost integrable spin chains
• Thermal transport in one-dimensional spin gap systems
• New method for studying steady states in quantum impurity problems: The interacting resonant level model
• The Drude weight of the spin-1/2 XXZ chain: density matrix renormalization group versus exact diagonalization
• Real-time dynamics at finite temperature by DMRG: A path-integral approach
• Coexistence of diffusive and ballistic transport in a simple spin ladder
• The Ubiquitous 'c': from the Stefan-Boltzmann Law to Quantum Information
• Dynamical simulation of integrable and non-integrable models in the Heisenberg picture
• Theory of a resonant level coupled to several conduction electron channels in equilibrium and out-of-equilibrium
• Vector Perturbations in a Contracting Universe
• Adaptive Lanczos-vector method for dynamic properties within the density-matrix renormalization group
• Coefficients of bosonized dimer operators in spin-1/2 XXZ chains and their applications
• Spin diffusion and the anisotropic spin-1/2 Heisenberg chain
• Finite Drude weight for 1D low temperature conductors
• Comment on "Anomalous Thermal Conductivity of Frustrated Heisenberg Spin Chains and Ladders"
• Equivalence of transport coefficients in bath-induced and dynamical scenarios

Cited by in corpus (73)

• Time-evolution methods for matrix-product states
• Finite-temperature transport in one-dimensional quantum lattice models
• "Light-cone" dynamics after quantum quenches in spin chains
• Scrambling and thermalization in a diffusive quantum many-body system
• Microscopic origin of ideal conductivity in integrable quantum models
• Entanglement of purification: from spin chains to holography
• Many-body localization and delocalization in large quantum chains
• A positive tensor network approach for simulating open quantum many-body systems
• Multispinon continua at zero and finite temperature in a near-ideal Heisenberg chain
• The Tensor Networks Anthology: Simulation techniques for many-body quantum lattice systems
• Real-time and real-space spin- and energy dynamics in one-dimensional spin-1/2 systems induced by local quantum quenches at finite temperatures
• Quantum dynamics of thermalizing systems
• Anomalous spin diffusion in one-dimensional antiferromagnets
• Non-perturbative methodologies for low-dimensional strongly-correlated systems: From non-abelian bosonization to truncated spectrum methods
• Nonequilibrium thermal transport and its relation to linear response
• Non-equilibrium steady states in the Klein-Gordon theory
• Few-body Bose gases in low dimensions -- a laboratory for quantum dynamics
• Stability of superdiffusion in nearly integrable spin chains
• Energy transport in Heisenberg chains beyond the Luttinger liquid paradigm
• Energy transport between two integrable spin chains
• Anomalous relaxation and the high-temperature structure factor of XXZ spin chains
• Equilibration Properties of Classical Integrable Field Theories
• Energy transport in an integrable parafermionic chain via generalized hydrodynamics
• Finding purifications with minimal entanglement
• Extending the range of real time density matrix renormalization group simulations
• Shock waves, rarefaction waves and non-equilibrium steady states in quantum critical systems
• Spin and thermal conductivity of quantum spin ladders
• Matrix product state formulation of frequency-space dynamics at finite temperatures
• Far from equilibrium energy flow in quantum critical systems
• Expansion potentials for exact far-from-equilibrium spreading of particles and energy
• Finite temperature dynamics of the Mott insulating Hubbard chain
• Finite-temperature density-matrix renormalization group method for electron-phonon systems: Thermodynamics and Holstein-polaron spectral functions
• Symmetry Conserving Purification of Quantum States within the Density Matrix Renormalization Group
• Minimally entangled typical thermal states versus matrix product purifications for the simulation of equilibrium states and time evolution
• Overcoming the entanglement barrier in quantum many-body dynamics via space-time duality
• Generalization of the Time-Dependent Numerical Renormalization Group Method to Finite Temperatures and General Pulses
• Proposal for measuring the finite-temperature Drude weight of integrable systems
• Non-equilibrium transport in $d$-dimensional non-interacting Fermi gases
• Exceptional points in the one-dimensional Hubbard model
• Lower bounds for ballistic current and noise in non-equilibrium quantum steady states
• Diffusion from Convection
• Sharp entanglement thresholds in the logarithmic negativity of disjoint blocks in the transverse-field Ising chain
• Temperature dependence of the NMR relaxation rate 1/T_1 for quantum spin chains
• Real time evolution at finite temperatures with operator space matrix product states
• Thermal conductivity of the one-dimensional Fermi-Hubbard model
• Efficient Large-Scale Many-Body Quantum Dynamics via Local-Information Time Evolution
• Preparation of Low Entropy Correlated Many-body States via Conformal Cooling Quenches
• Low temperature dynamics of nonlinear Luttinger liquids
• Real-time non-adiabatic dynamics in the one-dimensional Holstein model: Trajectory-based vs exact methods
• Finite-temperature optical conductivity with density-matrix renormalization group methods for the Holstein polaron and bipolaron with dispersive phonons
• NMR relaxation in the spin-1 Heisenberg chain
• Symmetric Minimally Entangled Typical Thermal States
• Complex Time Evolution in Tensor Networks
• Dynamical properties of the sine-Gordon quantum spin magnet Cu-PM at zero and finite temperature
• Finite-temperature properties of interacting bosons on a two-leg flux ladder
• Multi-triplet bound states and finite-temperature dynamics in highly frustrated quantum spin ladders
• Density-matrix renormalization group method for the conductance of one-dimensional correlated systems using the Kubo formula
• Cooling schemes for two-component fermions in layered optical lattices
• Noncollinear phase of the antiferromagnetic sawtooth chain
• Low-energy excitations and transport functions of the one-dimensional Kondo insulator
• Dynamics of heat and mass transport in a quantum insulator
• Probing Off-diagonal Eigenstate Thermalization with Tensor Networks
• Thermal and optical conductivity in the Holstein model at half filling and at finite temperature in the Luttinger-liquid and charge-density-wave regime
• Energy transport between critical one-dimensional systems with different central charges
• Thermal Drude weight in an integrable chiral clock model
• Numerical study of the temperature dependence of the NMR relaxation rate across the superfluid-Bose glass transition in one dimension
• Spectroscopy and complex-time correlations using minimally entangled typical thermal states
• DMRG and Monte Carlo studies of ${\text{CrI}}_3$ magnetic phases and the phase transition
• A polynomial time algorithm for studying physical observables in chaotic eigenstates
• Geometrically Taming Dynamical Entanglement Growth in Purified Quantum States
• Transport in a System with a Tower of Quantum Many-Body Scars
• Minimal one-dimensional model of bad metal behavior from fast particle-hole scattering
• Locally accurate tensor networks for thermal states and time evolution