Importance Sampling Scheme for the Stochastic Simulation of Quantum Spin Dynamics
arXiv:2103.16468 · doi:10.21468/SciPostPhys.11.3.048
Abstract
The numerical simulation of dynamical phenomena in interacting quantum systems is a notoriously hard problem. Although a number of promising numerical methods exist, they often have limited applicability due to the growth of entanglement or the presence of the so-called sign problem. In this work, we develop an importance sampling scheme for the simulation of quantum spin dynamics, building on a recent approach mapping quantum spin systems to classical stochastic processes. The importance sampling scheme is based on identifying the classical trajectory that yields the largest contribution to a given quantum observable. An exact transformation is then carried out to preferentially sample trajectories that are close to the dominant one. We demonstrate that this approach is capable of reducing the temporal growth of fluctuations in the stochastic quantities, thus extending the range of accessible times and system sizes compared to direct sampling. We discuss advantages and limitations of the proposed approach, outlining directions for further developments.
arXiv commentSubmission to SciPost, v2; 9 + 2 pages, 5 figures
References in corpus (31)
- Thermalization and its mechanism for generic isolated quantum systems
- Nonequilibrium dynamics of closed interacting quantum systems
- Many-body localization, thermalization, and entanglement
- Relaxation in a Completely Integrable Many-Body Quantum System: An Ab Initio Study of the Dynamics of the Highly Excited States of Lattice Hard-Core Bosons
- Quantum many-body scars
- Classical simulation of infinite-size quantum lattice systems in one spatial dimension
- Time-dependent variational principle for quantum lattices
- Dynamical Quantum Phase Transitions in the Transverse Field Ising Model
- Classical simulation of infinite-size quantum lattice systems in two spatial dimensions
- Dynamical quantum phase transitions: a review
- Time-evolution methods for matrix-product states
- Direct observation of dynamical quantum phase transitions in an interacting many-body system
- QuSpin: a Python Package for Dynamics and Exact Diagonalisation of Quantum Many Body Systems part I: spin chains
- Discrete Time Crystals
- Ultracold atoms out of equilibrium
- The computational complexity of PEPS
- Quantum many-body dynamics in two dimensions with artificial neural networks
- First order dynamical phase transitions
- Time Evolution of an Infinite Projected Entangled Pair State: an Efficient Algorithm
- Entanglement view of dynamical quantum phase transitions
- The critical behaviour of the 2D Ising model in Transverse Field; a Density Matrix Renormalization calculation
- Quantum-to-Classical Correspondence and Hubbard-Stratonovich Dynamical Systems, a Lie-Algebraic Approach
- Dynamical symmetry approach and topological field theory for path integrals of quantum spin systems
- Stochastic Approach to Non-Equilibrium Quantum Spin Systems
- Variational classical networks for dynamics in interacting quantum matter
- Quantum quench dynamics in the transverse-field Ising model: A numerical expansion in linked rectangular clusters
- Simulation of the Dynamics of Many-Body Quantum Spin Systems Using Phase-Space Techniques
- Non-Equilibrium Quantum Spin Dynamics from Classical Stochastic Processes
- 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