Selected applications of typicality to real-time dynamics of quantum many-body systems

Abstract

Loosely speaking, the concept of quantum typicality refers to the fact that a single pure state can imitate the full statistical ensemble. This fact has given rise to a rather simple but remarkably useful numerical approach to simulate the dynamics of quantum many-body systems, called dynamical quantum typicality (DQT). In this paper, we give a brief overview of selected applications of DQT, where particular emphasis is given to questions on transport and thermalization in low-dimensional lattice systems like chains or ladders of interacting spins or fermions. For these systems, we discuss that DQT provides an efficient means to obtain time-dependent equilibrium correlation functions for comparatively large Hilbert-space dimensions and long time scales, allowing the quantitative extraction of transport coefficients within the framework of, e.g., linear response theory. Furthermore, it is discussed that DQT can also be used to study the far-from-equilibrium dynamics resulting from sudden quench scenarios, where the initial state is a thermal Gibbs state of the pre-quench Hamiltonian. Eventually, we summarize a few combinations of DQT with other approaches such as numerical linked cluster expansions or projection operator techniques. In this way, we demonstrate the versatility of DQT.

arXiv comment11 pages, 9 figures

References in corpus (71)

• The density-matrix renormalization group in the age of matrix product states
• Chaos and Quantum Thermalization
• Thermalization and its mechanism for generic isolated quantum systems
• Nonequilibrium dynamics of closed interacting quantum systems
• Many body localization and thermalization in quantum statistical mechanics
• From Quantum Chaos and Eigenstate Thermalization to Statistical Mechanics and Thermodynamics
• A bound on chaos
• Average Entropy of a Subsystem
• Quantum many-body systems out of equilibrium
• The Kernel Polynomial Method
• The foundations of statistical mechanics from entanglement: Individual states vs. averages
• Equilibration, thermalisation, and the emergence of statistical mechanics in closed quantum systems
• Canonical Typicality
• Time-evolution methods for matrix-product states
• Operator spreading and the emergence of dissipative hydrodynamics under unitary evolution with conservation laws
• Testing whether all eigenstates obey the Eigenstate Thermalization Hypothesis
• Quantum Chaos and Thermalization in Isolated Systems of Interacting Particles
• Spin diffusion from an inhomogeneous quench in an integrable system
• Typicality for Generalized Microcanonical Ensembles
• Finite-size scaling of eigenstate thermalization
• Observation of universal dynamics in a spinor Bose gas far from equilibrium
• Quantum quench dynamics
• Canonical Thermal Pure Quantum State
• Localization and the effects of symmetries in the thermalization properties of one-dimensional quantum systems
• Observation of universal dynamics in an isolated one-dimensional Bose gas far from equilibrium
• Thermal Pure Quantum States at Finite Temperature
• Fast Algorithm for Finding the Eigenvalue Distribution of Very Large Matrices
• Eigenstate thermalization within isolated spin-chain systems
• Entanglement Entropy of Eigenstates of Quantum Chaotic Hamiltonians
• Dynamical typicality of quantum expectation values
• Numerical Linked-Cluster Approach to Quantum Lattice Models
• Information propagation in isolated quantum systems
• Pushing the limits of the eigenstate thermalization hypothesis towards mesoscopic quantum systems
• An efficient scheme for numerical simulations of the spin-bath decoherence
• Thouless and relaxation time scales in many-body quantum systems
• Eigenstate thermalization in the two-dimensional transverse field Ising model: II. Off-diagonal matrix elements of observables
• Spin-current autocorrelations from single pure-state propagation
• A Short Introduction to Numerical Linked-Cluster Expansions
• Eigenstate thermalization and quantum chaos in the Holstein polaron model
• Regression relation for pure quantum states and its implications for efficient computing
• Random phase vector for calculating the trace of a large matrix
• Eigenstate Thermalization, Random Matrix Theory and Behemoths
• Typicality approach to the optical conductivity in thermal and many-body localized phases
• Thermodynamic properties of the Shastry-Sutherland model throughout the dimer-product phase
• Spin and energy currents in integrable and nonintegrable spin-1/2 chains: A typicality approach to real-time autocorrelations
• Quantum spin liquid at finite temperature: proximate dynamics and persistent typicality
• Accuracy of the finite-temperature Lanczos method compared to simple typicality-based estimates
• Real-time broadening of non-equilibrium density profiles and the role of the specific initial-state realization
• Algorithm for Linear Response Functions at Finite Temperatures: Application to ESR spectrum of s=1/2 Antiferromagnet Cu benzoate
• Quantum Quenches and Relaxation Dynamics in the Thermodynamic Limit
• Combining Dynamical Quantum Typicality and Numerical Linked Cluster Expansions
• Dynamical typicality of isolated many-body quantum systems
• Scaling of diffusion constants in the spin-1/2 XX ladder
• Heat conductivity of the Heisenberg spin-1/2 ladder: From weak to strong breaking of integrability
• Decay of currents for strong interactions
• Impact of eigenstate thermalization on the route to equilibrium
• Finite-temperature charge transport in the one-dimensional Hubbard model
• Real-Time Dynamics of Typical and Untypical States in Non-Integrable Systems
• Accuracy of the microcanonical Lanczos method to compute real-frequency dynamical spectral functions of quantum models at finite temperatures
• From Linear to Nonlinear Responses of Thermal Pure Quantum States
• Magnetization and energy dynamics in spin ladders: Evidence of diffusion in time, frequency, position, and momentum
• Combined use of translational and spin-rotational invariance for spin systems
• Decay of spin-spin correlations in disordered quantum and classical spin chains
• Magnetization dynamics in clean and disordered spin-1 XXZ chains
• Charge diffusion in the one-dimensional Hubbard model
• Necessity of eigenstate thermalization for equilibration towards unique expectation values when starting from generic initial states
• Loschmidt-amplitude wave function spectroscopy and the physics of dynamically driven phase transitions
• Sudden removal of a static force in a disordered system: Induced dynamics, thermalization, and transport
• Lanczos Boosted Numerical Linked-Cluster Expansion for Quantum Lattice Models
• Relaxation of dynamically prepared out-of-equilibrium initial states within and beyond linear response theory
• Dynamical typicality for initial states with a preset measurement statistics of several commuting observables

Cited by in corpus (37)

• Entanglement spreading in non-equilibrium integrable systems
• Anomalous hydrodynamics in a class of scarred frustration-free Hamiltonians
• Eigenstate thermalization hypothesis and its deviations from random-matrix theory beyond the thermalization time
• Simulating hydrodynamics on noisy intermediate-scale quantum devices with random circuits
• Generalized hydrodynamics: a perspective
• Operator backflow and the classical simulation of quantum transport
• Transport and entanglement growth in long-range random Clifford circuits
• Quantum versus Classical Dynamics in Spin Models: Chains, Ladders, and Square Lattices
• Quantum dynamics in the interacting Fibonacci chain
• Efficient Large-Scale Many-Body Quantum Dynamics via Local-Information Time Evolution
• Diffusion constants from the recursion method
• Quantum quench dynamics in the transverse-field Ising model: A numerical expansion in linked rectangular clusters
• Density dynamics in the mass-imbalanced Hubbard chain
• Emergence of unitary symmetry of microcanonically truncated operators in chaotic quantum systems
• Estimation of equilibration time scales from nested fraction approximations
• Precursors to Anderson Localization in the Holstein Model: Quantum and Quantum-Classical Solutions
• Quantum master equation from the eigenstate thermalization hypothesis
• Dynamical quantum typicality: Simple method for investigating transport properties applied to the Holstein model
• Ensemble dependence of information-theoretic contributions to the entropy production
• 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
• Spatiotemporal dynamics of classical and quantum density profiles in low-dimensional spin systems
• Localisation and Sub-Diffusive Transport in Quantum Spin Chains With Dilute Disorder
• Lanczos-Pascal approach to correlation functions in chaotic quantum systems
• Nontrivial damping of quantum many-body dynamics
• Lindblad dynamics from spatio-temporal correlation functions in nonintegrable spin-1/2 chains with different boundary conditions
• Transport and integrability-breaking in non-Hermitian many-body quantum systems
• Many-Body Localization in Translational Invariant Diamond Ladders with Flat Bands
• Typical perturbation theory: conditions, accuracy and comparison with a mesoscopic case
• Scaling of diffusion constants in perturbed easy-axis Heisenberg spin chains
• Investigating Stark many-body localization with continuous unitary transformation flows
• Diagnostics of Hilbert space fragmentation, freezing transition, and its effects in the family of quantum East models involving varying range of constraints
• Typical Positivity of Nonequilibrium Entropy Production for Pure States
• Lindblad quantum dynamics from correlation functions of classical spin chains
• Nontrivial damping of magnetization currents in perturbed spin chains
• Quantum typicality approach to energy flow between two spin-chain domains at different temperatures
• Boundary-driven magnetization transport in the spin-$1/2$ XXZ chain: Role of the system-bath coupling strength and timescales