A simple approach towards the sign problem using path optimisation

doi:10.1007/JHEP12(2018)054

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A simple approach towards the sign problem using path optimisation

2018-12-10

Francis Bursa *

Kroyter, Michael

DOI：10.1007/JHEP12(2018)054

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Abstract

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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 approximate to 32 to L approximate to 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.

Keywords:

Lattice field theory simulation

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