Optimisation of complex integration contours at higher order

Journal of High Energy Physics

Michael Kroyter¹  Francis Bursa² 

[1] Department of Mathematics, Holon Institute of Technology, 52 Golomb St., 5810201, Holon, Israel;School of Physics and Astronomy, University of Glasgow, Kelvin Building, University Avenue, G12 8QQ, Glasgow, United Kingdom;

关键词: Lattice field theory simulation;   

DOI  :  10.1007/JHEP04(2021)181

来源: Springer

【 摘 要 】

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.

【 授权许可】

CC BY