Path integral Monte Carlo for dissipative many-body systems

TL;DR

This paper develops a Fourier path-integral Monte Carlo method to simulate the thermodynamics of quantum dissipative systems within the Caldeira-Leggett framework, addressing numerical challenges posed by singular dissipation kernels.

Contribution

It introduces a novel Fourier-based Monte Carlo approach for dissipative quantum systems, improving control over the Trotter limit and enabling simulations of complex models.

Findings

Successfully implemented for a nonlinear particle with Ohmic dissipation

Extended to a phi^4 chain with Drude-like dissipation

Enhanced numerical stability and convergence in dissipative quantum simulations

Abstract

We address the possibility of performing numerical Monte Carlo simulations for the thermodynamics of quantum dissipative systems. Dissipation is considered within the Caldeira-Leggett formulation, which describes the system in the path-integral formalism through the inclusion of an influence action that is bilocal and quadratic in the system's coordinates. At a first sight the usual direct approach of discretizing the path integral could seem feasible, but complications arise when one tries to introduce a physically meaningful dissipation kernel: in particular its imaginary-time dependence turns out to be severely singular and difficult to evaluate analytically, in spite of the simple expressions for its Matsubara components. We therefore propose to face the numerical problem using Fourier path-integral Monte Carlo, that can be formulated in two different ways: transforming the continuous paths and then truncating the high Fourier components (with possible improvements upon the truncation procedure), or performing the Fourier transformation upon the discretized paths. The latter choice leads to a simpler formulation and allows for a better control of the extrapolation to the limit of infinite Trotter number. The method is implemented for a single nonlinear particle with Ohmic dissipation and for a phi^4 chain with Drude-like dissipation.