Fast Convergence of Path Integrals for Many-body Systems

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.

20 pages, 6 figures, 1 table

References in corpus (3)

• Efficient Calculation of Energy Spectra Using Path Integrals
• Energy Estimators and Calculation of Energy Expectation Values in the Path Integral Formalism
• Analysis of path integrals at low temperature : Box formula, occupation time and ergodic approximation

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