Regression relation for pure quantum states and its implications for efficient computing

Abstract

We obtain a modified version of the Onsager regression relation for the expectation values of quantum-mechanical operators in pure quantum states of isolated many-body quantum systems. We use the insights gained from this relation to show that high-temperature time correlation functions in many-body quantum systems can be controllably computed without complete diagonalization of the Hamiltonians, using instead the direct integration of the Schroedinger equation for randomly sampled pure states. This method is also applicable to quantum quenches and other situations describable by time-dependent many-body Hamiltonians. The method implies exponential reduction of the computer memory requirement in comparison with the complete diagonalization. We illustrate the method by numerically computing infinite-temperature correlation functions for translationally invariant Heisenberg chains of up to 29 spins 1/2. Thereby, we also test the spin diffusion hypothesis and find it in a satisfactory agreement with the numerical results. Both the derivation of the modified regression relation and the justification of the computational method are based on the notion of quantum typicality.

16 pages, 4 figures; minor textual corrections; parts rearranged

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• Spin transport in a one-dimensional anisotropic Heisenberg model
• Typicality for Generalized Microcanonical Ensembles
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Cited by in corpus (79)

• Finite-temperature transport in one-dimensional quantum lattice models
• The Ergodic Side of the Many-Body Localization Transition
• Pushing the limits of the eigenstate thermalization hypothesis towards mesoscopic quantum systems
• Spin-current autocorrelations from single pure-state propagation
• Typicality approach to the optical conductivity in thermal and many-body localized phases
• Absence of exponential sensitivity to small perturbations in nonintegrable systems of spins 1/2
• Spin and energy currents in integrable and nonintegrable spin-1/2 chains: A typicality approach to real-time autocorrelations
• Eigenstate thermalization hypothesis and its deviations from random-matrix theory beyond the thermalization time
• Quantum spin liquid at finite temperature: proximate dynamics and persistent typicality
• Accuracy of the finite-temperature Lanczos method compared to simple typicality-based estimates
• Relevance of the eigenstate thermalization hypothesis for thermal relaxation
• Real-time broadening of non-equilibrium density profiles and the role of the specific initial-state realization
• Entanglement of midspectrum eigenstates of chaotic many-body systems: Reasons for deviation from random ensembles
• Combining Dynamical Quantum Typicality and Numerical Linked Cluster Expansions
• Simulating hydrodynamics on noisy intermediate-scale quantum devices with random circuits
• Random State Technology
• 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
• Selected applications of typicality to real-time dynamics of quantum many-body systems
• Quantum versus Classical Dynamics in Spin Models: Chains, Ladders, and Square Lattices
• Impact of eigenstate thermalization on the route to equilibrium
• Finite-temperature charge transport in the one-dimensional Hubbard model
• Taking the temperature of a pure quantum state
• Real-Time Dynamics of Typical and Untypical States in Non-Integrable Systems
• Sensitivity to small perturbations in systems of large quantum spins
• From Linear to Nonlinear Responses of Thermal Pure Quantum States
• Signatures of Chaos in Time Series Generated by Many-Spin Systems at High Temperatures
• Exponential damping induced by random and realistic perturbations
• Magnetization and energy dynamics in spin ladders: Evidence of diffusion in time, frequency, position, and momentum
• Decay of spin-spin correlations in disordered quantum and classical spin chains
• Magnetization dynamics in clean and disordered spin-1 XXZ chains
• Effectiveness of classical spin simulations for describing NMR relaxation of quantum spins
• Hydrodynamics and the eigenstate thermalization hypothesis
• Quantum quench dynamics in the transverse-field Ising model: A numerical expansion in linked rectangular clusters
• Charge diffusion in the one-dimensional Hubbard model
• Macroscopically deterministic, Markovian thermalization in finite quantum spin systems
• Stiffness of Probability Distributions of Work and Jarzynski Relation for Non-Gibbsian Initial States
• Loschmidt echo in many-spin systems: contrasting time-scales of local and global measurements
• Hybrid quantum-classical method for simulating high-temperature dynamics of nuclear spins in solids
• Density dynamics in the mass-imbalanced Hubbard chain
• Free induction decays in nuclear spin-1/2 lattices with small number of interacting neighbors: the cases of silicon and fluorapatite
• Loschmidt echo in many-spin systems: a quest for intrinsic decoherence and emergent irreversibility
• Relation between far-from-equilibrium dynamics and equilibrium correlation functions for binary operators
• Quantum simulation using noisy unitary circuits and measurements
• Sudden removal of a static force in a disordered system: Induced dynamics, thermalization, and transport
• Typicality-Based Variational Cluster Approach to Thermodynamic Properties of the Hubbard Model
• Dynamical quantum typicality: Simple method for investigating transport properties applied to the Holstein model
• Long-living prethermalization in nearly integrable spin ladders
• Stability of Quantum Statistical Ensembles with Respect to Local Measurements
• Bounding the finite-size error of quantum many-body dynamics simulations
• GPU accelerated Trotter-Suzuki solver for quantum spin dynamics
• Finite-size scaling of typicality-based estimates
• Interaction-Induced Weakening of Localization in Few-Particle Disordered Heisenberg Chains
• Spatiotemporal dynamics of classical and quantum density profiles in low-dimensional spin systems
• 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
• Transport in tight-binding bond percolation models
• Spectral response of disorder-free localized lattice gauge theories
• Initial State Independent Equilibration at the Breakdown of the Eigenstate Thermalization Hypothesis
• Nontrivial damping of quantum many-body dynamics
• Onsager's regression hypothesis adjusted to quantum systems
• Localisation and Sub-Diffusive Transport in Quantum Spin Chains With Dilute Disorder
• Dynamical typicality for initial states with a preset measurement statistics of several commuting observables
• Hilbert space average of transition probabilities
• 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
• Thermalization as an Invisibility Cloak for Fragile Quantum Superpositions
• Enhanced Convergence of Quantum Typicality using a Randomized Low-Rank Approximation
• Lindblad quantum dynamics from correlation functions of classical spin chains
• Classical periodic trajectories and quantum scars in many-spin systems
• Hierarchy of timescales in a disordered spin-$1/2$ XX ladder
• Interplay of decoherence and relaxation in a two-level system interacting with an infinite-temperature reservoir
• Classical spin simulations with a quantum two-spin correction
• Quantifying Stability of Quantum Statistical Ensembles
• Measurement-based cooling of many-body quantum systems
• Quantum typicality approach to energy flow between two spin-chain domains at different temperatures
• Nontrivial damping of magnetization currents in perturbed spin chains
• Identifying mobility edge from finite temperature spectral form factor