Combining Dynamical Quantum Typicality and Numerical Linked Cluster Expansions

Abstract

We demonstrate that numerical linked cluster expansions (NLCE) yield a powerful approach to calculate time-dependent correlation functions for quantum many-body systems in one dimension. As a paradigmatic example, we study the dynamics of the spin current in the spin-1/2 XXZ chain for different values of anisotropy, as well as in the presence of an integrability-breaking next-nearest neighbor interaction. For short to intermediate time scales, we unveil that NLCE yields a convergence towards the thermodynamic limit already for small cluster sizes, which is much faster than in direct calculations of the autocorrelation function for systems with open or periodic boundary conditions. Most importantly, we show that the range of accessible cluster sizes in NLCE can be extended by evaluating the contributions of larger clusters by means of a pure-state approach based on the concept of dynamical quantum typicality (DQT). Even for moderate computational effort, this combination of DQT and NLCE provides a competitive alternative to existing state-of-the-art techniques, which may be applied in higher dimensions as well.

7 pages, 6 figures

References in corpus (60)

• The density-matrix renormalization group in the age of matrix product states
• The density-matrix renormalization group
• Solving the Quantum Many-Body Problem with Artificial Neural Networks
• Efficient simulation of one-dimensional quantum many-body systems
• Real time evolution using the density matrix renormalization group
• Quantum many-body systems out of equilibrium
• The Kernel Polynomial Method
• The foundations of statistical mechanics from entanglement: Individual states vs. averages
• Transport in Out-of-Equilibrium XXZ Chains: Exact Profiles of Charges and Currents
• Nonequilibrium dynamical mean-field theory and its applications
• Canonical Typicality
• Quench dynamics and relaxation in isolated integrable quantum spin chains
• Emergent hydrodynamics in integrable quantum systems out of equilibrium
• Computational Studies of Quantum Spin Systems
• Quenching the Anisotropic Heisenberg Chain: Exact Solution and Generalized Gibbs Ensemble Predictions
• Ultracold atoms out of equilibrium
• Spin diffusion from an inhomogeneous quench in an integrable system
• Finite temperature Drude weight of the one dimensional spin 1/2 Heisenberg model}
• Typicality for Generalized Microcanonical Ensembles
• Diffusion and ballistic transport in one-dimensional quantum systems
• Matrix product simulations of non-equilibrium steady states of quantum spin chains
• Canonical Thermal Pure Quantum State
• Finite temperature dynamical DMRG and the Drude weight of spin-1/2 chains
• Fast Algorithm for Finding the Eigenvalue Distribution of Very Large Matrices
• Zero-frequency transport properties of one dimensional spin-1/2 systems
• The thermal conductivity of the spin-1/2 XXZ chain at arbitrary temperature
• Eigenstate thermalization within isolated spin-chain systems
• Dynamical typicality of quantum expectation values
• Numerical Linked-Cluster Approach to Quantum Lattice Models
• Dynamics at the Many-Body Localization Transition
• An efficient scheme for numerical simulations of the spin-bath decoherence
• Spin-current autocorrelations from single pure-state propagation
• Quantum Quenches in the Thermodynamic Limit
• A Short Introduction to Numerical Linked-Cluster Expansions
• Numerical Linked-Cluster Algorithms. I. Spin systems on square, triangular, and kagome lattices
• Entanglement at a Two-Dimensional Quantum Critical Point: a Numerical Linked Cluster Expansion Study
• Regression relation for pure quantum states and its implications for efficient computing
• Finite Temperature Dynamical Correlations using the Microcanonical Ensemble and the Lanczos Algorithm
• Spin transport in the XXZ chain at finite temperature and momentum
• Transport in open spin chains: A Monte Carlo wave-function approach
• The Drude weight of the spin-1/2 XXZ chain: density matrix renormalization group versus exact diagonalization
• Density dynamics in translationally invariant spin-1/2 chains at high temperatures: a current auto-correlation approach to finite time- and length-scales
• Spin and energy currents in integrable and nonintegrable spin-1/2 chains: A typicality approach to real-time autocorrelations
• Cluster Truncated Wigner Approximation in Strongly Interacting Systems
• Extending the range of real time density matrix renormalization group simulations
• Quantum Quenches and Relaxation Dynamics in the Thermodynamic Limit
• Algorithm for Linear Response Functions at Finite Temperatures: Application to ESR spectrum of s=1/2 Antiferromagnet Cu benzoate
• Linked cluster expansions for open quantum systems on a lattice
• Quantum dynamics in transverse-field Ising models from classical networks
• Spin and thermal conductivity of quantum spin ladders
• Energy diffusion in the ergodic phase of a many body localizable spin chain
• Decay of currents for strong interactions
• A time and spatially resolved quench of the fermionic Hubbard model showing restricted equilibration
• Real-Time Dynamics of Typical and Untypical States in Non-Integrable Systems
• Thermodynamics of the Antiferromagnetic Heisenberg Model on the Checkerboard Lattice
• Irreversible dynamics in quantum many-body systems
• Spin hydrodynamics in the S = 1/2 anisotropic Heisenberg chain
• Numerical linked cluster expansions for quantum quenches in one dimensional lattices
• Non-perturbative linked-cluster expansions for the trimerized ground state of the spin-one Kagome Heisenberg model
• Sudden removal of a static force in a disordered system: Induced dynamics, thermalization, and transport

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• Accuracy of the finite-temperature Lanczos method compared to simple typicality-based estimates
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• Selected applications of typicality to real-time dynamics of quantum many-body systems
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• Efficient Large-Scale Many-Body Quantum Dynamics via Local-Information Time Evolution
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• Decay of spin-spin correlations in disordered quantum and classical spin chains
• Magnetization dynamics in clean and disordered spin-1 XXZ chains
• Quantum quench dynamics in the transverse-field Ising model: A numerical expansion in linked rectangular clusters
• Numerical linked cluster expansions for inhomogeneous systems
• Enhanced symmetry-breaking tendencies in the $S=1$ pyrochlore antiferromagnet
• Quantum simulation using noisy unitary circuits and measurements
• Reconstructing effective Hamiltonians from nonequilibrium (pre-)thermal steady states
• Dynamical quantum typicality: Simple method for investigating transport properties applied to the Holstein model
• Typicality-Based Variational Cluster Approach to Thermodynamic Properties of the Hubbard Model
• Thermodynamics of the disordered Hubbard model studied via numerical linked-cluster expansions
• Real-time broadening of bath-induced density profiles from closed-system correlation functions
• Spin-1/2 XXZ chain coupled to two Lindblad baths: Constructing nonequilibrium steady states from equilibrium correlation functions
• Relaxation of dynamically prepared out-of-equilibrium initial states within and beyond linear response theory
• Many-body localization and delocalization dynamics in the thermodynamic limit
• Nanoscale engineering and dynamical stabilization of mesoscopic spin textures
• Nontrivial damping of quantum many-body dynamics
• Hilbert space average of transition probabilities
• Lindblad dynamics from spatio-temporal correlation functions in nonintegrable spin-1/2 chains with different boundary conditions
• Enhanced Convergence of Quantum Typicality using a Randomized Low-Rank Approximation
• Scaling of diffusion constants in perturbed easy-axis Heisenberg spin chains
• Yang-Lee Zeros of 2D Nearest-Neighbor Antiferromagnetic Ising Models: A Numerical Linked Cluster Expansion Study
• Quantum typicality approach to energy flow between two spin-chain domains at different temperatures