Optimisation of complex integration contours at higher order

Bursa, F. and Kroyter, M. (2021) Optimisation of complex integration contours at higher order. Journal of High Energy Physics, 2021(4), 181. (doi: 10.1007/JHEP04(2021)181)

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We continue our study of contour deformation as a practical tool for dealing with the sign problem using the d-dimensional Bose gas with non-zero chemical potential as a toy model. We derive explicit expressions for contours up to the second order with respect to a natural small parameter and generalise these contours to an ansatz for which the evaluation of the Jacobian is fast (O(1)). We examine the behaviour of the various proposed contours as a function of space-time dimensionality, the chemical potential, and lattice size and geometry and use the mean phase factor as a measure of the severity of the sign problem. In turns out that this method leads to a substantial reduction of the sign problem and that it becomes more efficient as space-time dimensionality is increased. Correlations among contributions to Im〈S〉play a key role in determining the mean phase factor and we examine these correlations in detail.

Item Type:Articles
Glasgow Author(s) Enlighten ID:Bursa, Dr Francis
Authors: Bursa, F., and Kroyter, M.
College/School:College of Science and Engineering > School of Physics and Astronomy
Journal Name:Journal of High Energy Physics
ISSN (Online):1029-8479
Published Online:19 April 2021
Copyright Holders:Copyright © 2021 The Authors
First Published:First published in Journal of High Energy Physics 2021(4): 181
Publisher Policy:Reproduced under a Creative Commons License

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