Simulating lattice field theories on multiple thimbles

Francesco Di Renzo,M Della Morte,C Pena Ruano,P Fritzsch,E Gámiz Sánchez

doi:10.1051/epjconf/201817507015

Abstract

Simulating thimble regularization of lattice field theory can be tricky when more than one thimble is to be taken into account. A couple of years ago we proposed a solution for this problem. More recently this solution proved to be effective in the case of 0+1 dimensional QCD. A few lessons we can learnt, including the role of symmetries and general hints on algorithmic solutions.

Highlights

Thimble regularization of lattice field theories was put forward as a possible solution to the sign problem [1, 2]
We improve on that work, showing a better way to take into account the three contributions which are expected in the thimble decomposition of the problem at hand
Results are better than the previous ones due to two improvements: first of all, a symmetry argument can reduce the number of contributions that we have to sum to solve the theory; in the second place, we make use of a better Monte Carlo strategy

Summary

Introduction

Thimble regularization of lattice field theories was put forward as a possible solution to the sign problem [1, 2]. Results are better than the previous ones due to two improvements: first of all, a symmetry argument can reduce the number of contributions that we have to sum to solve the theory (it turns out that there are essentially two distinct contributions); in the second place, we make use of a better Monte Carlo strategy. QCD in 0 + 1 dimensions provides a nice example of how a theory can be simulated on multiple thimbles

Thimble decomposition

A crude Monte Carlo on thimbles

Improving on previous results

Importance sampling

Conclusions