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Abstract: We generalize a recently developed method for accelerated Monte Carlocalculation of path integrals to the physically relevant case of genericmany-body systems. This is done by developing an analytic procedure forconstructing a hierarchy of effective actions leading to improvements inconvergence of $N$-fold discretized many-body path integral expressions from1-N to $1-N^p$ for generic $p$. In this paper we present explicit solutionswithin this hierarchy up to level $p=5$. Using this we calculate the low lyingenergy levels of a two particle model with quartic interactions for severalvalues of coupling and demonstrate agreement with analytical results governingthe increase in efficiency of the new method. The applicability of thedeveloped scheme is further extended to the calculation of energy expectationvalues through the construction of associated energy estimators exhibiting thesame speedup in convergence.



Author: Aleksandar Bogojevic, Ivana Vidanovic, Antun Balaz, Aleksandar Belic

Source: https://arxiv.org/







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