A simple approach towards the sign problem using path optimisation

Bursa, F. and Kroyter, M. (2018) A simple approach towards the sign problem using path optimisation. Journal of High Energy Physics, 2018(12), 54. (doi: 10.1007/JHEP12(2018)054)

Abstract

We suggest an approach for simulating theories with a sign problem that relies on optimisation of complex integration contours that are not restricted to lie along Lefschetz thimbles. To that end we consider the toy model of a one-dimensional Bose gas with chemical potential. We identify the main contribution to the sign problem in this case as coming from a nearest neighbour interaction and approximately cancel it by an explicit deformation of the integration contour. We extend the obtained expressions to more general ones, depending on a small set of parameters. We find the optimal values of these parameters on a small lattice and study their range of validity. We also identify precursors for the onset of the sign problem. A fast method of evaluating the Jacobian related to the contour deformation is proposed and its numerical stability is examined. For a particular choice of lattice parameters, we find that our approach increases the lattice size at which the sign problem becomes serious from L ≈ 32 to L ≈ 700. The efficient evaluation of the Jacobian (O(L) for a sweep) results in running times that are of the order of a few minutes on a standard laptop.

• 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: 10 December 2018
• Copyright Holders: Copyright © 2018 The Authors
• First Published: First published in Journal of High Energy Physics 2018(12): 54
• Publisher Policy: Reproduced under a Creative Commons License