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.
Highlights
Experimental breakthroughs in the simulation of isolated many-body quantum systems [1, 2] have led to great theoretical interest in their far-from-equilibrium dynamics [3]
We have introduced an importance sampling scheme for the real-time dynamics of many-body quantum spin systems
The importance sampling method is based on the disentanglement approach, whereby unitary quantum dynamics is exactly mapped to an ensemble of classical stochastic processes
Summary
Experimental breakthroughs in the simulation of isolated many-body quantum systems [1, 2] have led to great theoretical interest in their far-from-equilibrium dynamics [3]. Recently applied to many-body quantum spin systems, consists in exactly mapping unitary quantum dynamics to an ensemble of classical stochastic processes [21,22,23,24,25] This approach is based on the disentanglement formalism [21,22,23, 26], which provides an exact functional integral representation of the time-evolution operator. The disentanglement formalism was applied in imaginary time, providing an analytical and numerical framework to study the ground states of quantum spin systems [31] In this context, the identification of the saddle point trajectory of a suitable action, which provides the dominant contribution to observables, was used to perform an exact measure transformation.
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