Stochastic Approach to Non-Equilibrium Quantum Spin Systems

Abstract

We investigate a stochastic approach to non-equilibrium quantum spin systems based on recent insights linking quantum and classical dynamics. Exploiting a sequence of exact transformations, quantum expectation values can be recast as averages over classical stochastic processes. We illustrate this approach for the quantum Ising model by extracting the Loschmidt amplitude and the magnetization dynamics from the numerical solution of stochastic differential equations. We show that dynamical quantum phase transitions are accompanied by clear signatures in the associated classical distribution functions, including the presence of enhanced fluctuations. We demonstrate that the method is capable of handling integrable and non-integrable problems in a unified framework, including those in higher dimensions.

5 pages, 5 figures

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Cited by in corpus (18)

• QuSpin: a Python Package for Dynamics and Exact Diagonalisation of Quantum Many Body Systems. Part II: bosons, fermions and higher spins
• Entanglement view of dynamical quantum phase transitions
• Dynamical phase transitions in the two-dimensional transverse-field Ising model
• Dynamical quantum phase transitions in collapse and revival oscillations of a quenched superfluid
• Dynamical quantum phase transitions in spin-$S$ $\mathrm{U}(1)$ quantum link models
• Entanglement and precession in two-dimensional dynamical quantum phase transitions
• Quantum quench dynamics in the transverse-field Ising model: A numerical expansion in linked rectangular clusters
• Non-Equilibrium Quantum Spin Dynamics from Classical Stochastic Processes
• Lie-algebraic approach to one-dimensional translationally invariant free-fermionic dissipative systems
• Fluctuations and Non-Hermiticity in the Stochastic Approach to Quantum Spins
• Quantum corrections to the classical field approximation for one-dimensional quantum many-body systems in equilibrium
• Probing Confinement Through Dynamical Quantum Phase Transitions: From Quantum Spin Models to Lattice Gauge Theories
• Time-Evolving Weiss Fields in the Stochastic Approach to Quantum Spins
• Disentanglement Approach to Quantum Spin Ground States: Field Theory and Stochastic Simulation
• Importance Sampling Scheme for the Stochastic Simulation of Quantum Spin Dynamics
• Stochastic Representation of the Quantum Quartic Oscillator
• Dynamical quantum phase transitions in strongly correlated two-dimensional spin lattices following a quench
• Trajectory-Resolved Weiss Fields for Quantum Spin Dynamics