Optimisation of complex integration contours at higher order

• Main Authors: Francis Bursa, Michael Kroyter
• Format: Article
• Language: English
• Published: SpringerOpen 2021-04-01
• Series: Journal of High Energy Physics
• Subjects: Lattice field theory simulation
• Online Access: https://doi.org/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.