Non-Equilibrium Quantum Spin Dynamics from Classical Stochastic Processes

Abstract

Following on from our recent work, we investigate a stochastic approach to non-equilibrium quantum spin systems. We show how the method can be applied to a variety of physical observables and for different initial conditions. We provide exact formulae of broad applicability for the time-dependence of expectation values and correlation functions following a quantum quench in terms of averages over classical stochastic processes. We further explore the behavior of the classical stochastic variables in the presence of dynamical quantum phase transitions, including results for their distributions and correlation functions. We provide details on the numerical solution of the associated stochastic differential equations, and examine the growth of fluctuations in the classical description. We discuss the strengths and limitations of the current implementation of the stochastic approach and the potential for further development.

v1: 14 + 7 pages, 16 figures. v2: accepted version, minor changes

References in corpus (12)

• The density-matrix renormalization group in the age of matrix product states
• Thermalization and its mechanism for generic isolated quantum systems
• Real time evolution using the density matrix renormalization group
• Single-Spin Addressing in an Atomic Mott Insulator
• Dynamical quantum phase transitions: a review
• Experimental Observation of a Generalized Gibbs Ensemble
• QuSpin: a Python Package for Dynamics and Exact Diagonalisation of Quantum Many Body Systems part I: spin chains
• Ultracold atoms out of equilibrium
• Time evolution algorithms for Matrix Product States and DMRG
• Cluster Truncated Wigner Approximation in Strongly Interacting Systems
• Quantum-to-Classical Correspondence and Hubbard-Stratonovich Dynamical Systems, a Lie-Algebraic Approach
• Stochastic Approach to Non-Equilibrium Quantum Spin Systems

Cited by in corpus (12)

• Loschmidt amplitude spectrum in dynamical quantum phase transitions
• Entanglement and precession in two-dimensional dynamical quantum phase transitions
• Quantum spin fluctuations in dynamical quantum phase transitions
• Entanglement in quenched extended Su-Schrieffer-Heeger model with anomalous dynamical quantum phase transitions
• Lie-algebraic approach to one-dimensional translationally invariant free-fermionic dissipative systems
• Fluctuations and Non-Hermiticity in the Stochastic Approach to Quantum Spins
• Time-Evolving Weiss Fields in the Stochastic Approach to Quantum Spins
• Disentanglement Approach to Quantum Spin Ground States: Field Theory and Stochastic Simulation
• Correspondence between open bosonic systems and stochastic differential equations
• Importance Sampling Scheme for the Stochastic Simulation of Quantum Spin Dynamics
• Stochastic Representation of the Quantum Quartic Oscillator
• Trajectory-Resolved Weiss Fields for Quantum Spin Dynamics