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)

Abstract

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
• Status: Published
• Refereed: Yes
• 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
• Publisher: Springer
• ISSN: 1126-6708
• 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