Fast Convergence of Path Integrals for Many-body Systems

TL;DR

This paper introduces a hierarchy of effective actions that significantly accelerates the convergence of path integral calculations in many-body quantum systems, enabling more efficient computation of energy levels and expectation values.

Contribution

It develops an analytic hierarchy of effective actions up to level p=5, improving convergence rates from 1/N to 1/N^p for many-body path integrals.

Findings

Achieved convergence improvements up to level p=5.

Validated method with two-particle quartic interaction model.

Demonstrated increased efficiency in calculating energy levels.

Abstract

We generalize a recently developed method for accelerated Monte Carlo calculation of path integrals to the physically relevant case of generic many-body systems. This is done by developing an analytic procedure for constructing a hierarchy of effective actions leading to improvements in convergence of $N$-fold discretized many-body path integral expressions from 1/N to $1/N^p$ for generic $p$. In this paper we present explicit solutions within this hierarchy up to level $p=5$. Using this we calculate the low lying energy levels of a two particle model with quartic interactions for several values of coupling and demonstrate agreement with analytical results governing the increase in efficiency of the new method. The applicability of the developed scheme is further extended to the calculation of energy expectation values through the construction of associated energy estimators exhibiting the same speedup in convergence.