Optimisation of complex integration contours at higher order
- Resource Type
- Working Paper
- Authors
- Bursa, Francis; Kroyter, Michael
- Source
- JHEP04(2021)181
- Subject
- High Energy Physics - Lattice
Condensed Matter - Strongly Correlated Electrons
High Energy Physics - Theory
- Language
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 $\operatorname{Im}\langle S \rangle$ play a key role in determining the mean phase factor and we examine these correlations in detail.
Comment: 30 pages, 17 figures