Fast estimator of Jacobians in the Monte Carlo integration on Lefschetz thimbles - INSPIRE

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Fast estimator of Jacobians in the Monte Carlo integration on Lefschetz thimbles

Apr 4, 2016

8 pages

Published in:

Phys.Rev.D 93 (2016) 9, 094514

Published: May 26, 2016

e-Print:

1604.00956 [hep-lat]

DOI:

10.1103/PhysRevD.93.094514

View in:

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Abstract: (APS)

A solution to the sign problem is the so-called “Lefschetz thimble approach” where the domain of integration for field variables in the path integral is deformed from the real axis to a submanifold in the complex space. For properly chosen submanifolds (“thimbles”) the sign problem disappears or is drastically alleviated. The parametrization of the thimble by real coordinates requires the calculation of a Jacobian with a computational cost of order O(V3), where V is proportional to the spacetime volume. In this paper we propose two estimators for this Jacobian with a computational cost of order O(V). We discuss analytically the regimes where we expect the estimator to work and show numerical examples in two different models.

Note:

10 pages, 3 figures

action: complex
potential: chemical
numerical methods: efficiency
estimator
parametrization
path integral
numerical calculations: Monte Carlo
deformation
Thirring model
toy model

References(9)

Figures(4)

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AuroraScience

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