From Linear to Nonlinear Responses of Thermal Pure Quantum States

Abstract

We propose a self-validating scheme to calculate the unbiased responses of quantum many-body systems to external fields of arbibraty strength at any temperature. By switching on a specified field to a thermal pure quantum state of an isolated system, and tracking its time evolution, one can observe an intrinsic thermalization process driven solely by many-body effects. The transient behavior before thermalization contains rich information on excited states, giving the linear and nonlinear response functions at all frequencies. We uncover the necessary conditions to clarify the applicability of this formalism, supported by a proper definition of the nonlinear response function. The accuracy of the protocol is guaranteed by a rigorous upper bound of error exponentially decreasing with system size, and is well implemented in the simple ferromagnetic Heisenberg chain, whose response at high fields exhibits a nonlinear band deformation. We further extract the characteristic features of excitation of the spin-1/2 kagome antiferromagnet; the wavenumber-insensitive linear responses from the possible spin liquid ground state, and the significantly broad nonlinear peaks which should be generated from numerous collisions of quasi-particles, that are beyond the perturbative description.

arXiv commentpublished version; 6 pages with 3 figures, and Supplemental Material

References in corpus (40)

• Chaos and Quantum Thermalization
• Thermalization and its mechanism for generic isolated quantum systems
• Nonequilibrium dynamics of closed interacting quantum systems
• From Quantum Chaos and Eigenstate Thermalization to Statistical Mechanics and Thermodynamics
• Observation of giant bandgap renormalization and excitonic effects in a monolayer transition metal dichalcogenide semiconductor
• Universal High-Frequency Behavior of Periodically Driven Systems: from Dynamical Stabilization to Floquet Engineering
• Quantum many-body systems out of equilibrium
• Spin Liquid Ground State of the $S=1/2$ Kagome Heisenberg Model
• The Kernel Polynomial Method
• The foundations of statistical mechanics from entanglement: Individual states vs. averages
• Probing the relaxation towards equilibrium in an isolated strongly correlated 1D Bose gas
• Canonical Typicality
• Microscopic observation of magnon bound states and their dynamics
• From Quantum Dynamics to the Canonical Distribution: General Picture and a Rigorous Example
• Dynamical density-matrix renormalization-group method
• First excitations of the spin 1/2 Heisenberg antiferromagnet on the kagomé lattice
• Gapless spin-liquid phase in the kagome spin-1/2 Heisenberg antiferromagnet
• Typicality for Generalized Microcanonical Ensembles
• Controlling frustrated liquids and solids with an applied field in a kagome Heisenberg antiferromagnet
• Canonical Thermal Pure Quantum State
• Thermal Pure Quantum States at Finite Temperature
• Density matrix algorithm for the calculation of dynamical properties of low dimensional systems
• Spectral functions in one-dimensional quantum systems at T>0
• Dynamics of the Kitaev-Heisenberg Model
• Spin-current autocorrelations from single pure-state propagation
• Gapless quantum spin liquid, stripe and antiferromagnetic phases in frustrated Hubbard models in two dimensions
• Regression relation for pure quantum states and its implications for efficient computing
• 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 parallelism as a tool for ensemble spin dynamics calculations
• Thermal Pure Quantum States of Many-Particle Systems
• Nonlinear Optics Quantum Computing with Circuit-QED
• Spin-Dynamics of the antiferromagnetic S=1/2-Chain at finite magnetic Fields and intermediate Temperatures
• Kinetic frustration induced supersolid in the $S=1/2$ kagome lattice antiferromagnet in a magnetic field
• Spin hydrodynamics in the S = 1/2 anisotropic Heisenberg chain
• Quantum Violation of Fluctuation-Dissipation Theorem
• Temperature- and Size-dependence of Line shape of ESR spectra of XXZ antiferromagnetic chain
• The ESR intensity and the Dzyaloshinsky-Moriya interaction of the nanoscale molecular magnet V15
• Universal Property of Quantum Measurements of Equilibrium Fluctuations and Violation of Fluctuation-Dissipation Theorem
• Pump Built-in Hamiltonian Method for Pump-Probe Spectroscopy

Cited by in corpus (21)

• Finite-temperature transport in one-dimensional quantum lattice models
• Entanglement of midspectrum eigenstates of chaotic many-body systems: Reasons for deviation from random ensembles
• Toward Quantum Computing Phase Diagrams of Gauge Theories with Thermal Pure Quantum States
• Selected applications of typicality to real-time dynamics of quantum many-body systems
• Predicting Gibbs-State Expectation Values with Pure Thermal Shadows
• Proof of absence of local conserved quantities in the mixed-field Ising chain
• Relation between far-from-equilibrium dynamics and equilibrium correlation functions for binary operators
• Quantum simulation using noisy unitary circuits and measurements
• Thermally enhanced Majorana-mediated spin transport in the Kitaev model
• Thermal Pure States for Systems with Antiunitary Symmetries and Their Tensor Network Representations
• Ensemble dependence of information-theoretic contributions to the entropy production
• Signatures of the finite-temperature mirror symmetry breaking in the $S$=1/2 Shastry-Sutherland model
• Relaxation of dynamically prepared out-of-equilibrium initial states within and beyond linear response theory
• Anomalous Behavior of Magnetic Susceptibility Obtained by Quench Experiments in Isolated Quantum Systems
• Thermal pure matrix product state in two dimensions: tracking thermal equilibrium from paramagnet down to the Kitaev honeycomb spin liquid state
• Quantum many-body simulation of finite-temperature systems with sampling a series expansion of a quantum imaginary-time evolution
• Entropic Quantum Machine
• Real-space spectral simulation of quantum spin models: Application to generalized Kitaev models
• Dynamical Spectral Function of the Kagome Quantum Spin Liquid
• Specific heat and susceptibility of S=1/2 antiferromagnets on square, triangular, and kagome lattices
• Quantum typicality approach to energy flow between two spin-chain domains at different temperatures