Solutions to sign problems in lattice Yukawa models

TL;DR

This paper demonstrates that sign problems in certain lattice Yukawa models can be eliminated by reformulating fermions with fermion bags and bosons with worldline representations, enabling Monte Carlo studies of quantum phase transitions.

Contribution

It introduces a method to completely solve sign problems in specific three-dimensional lattice Yukawa models using fermion bag and worldline formulations.

Findings

Sign problems are eliminated in the models studied.

Quantum phase transitions can be investigated with Monte Carlo methods.

The approach applies to models with staggered and Wilson fermions.

Abstract

We prove that sign problems in the traditional approach to some lattice Yukawa models can be completely solved when the fermions are formulated using fermion bags and the bosons are formulated in the worldline representation. We prove this within the context of two examples of three dimensional models, symmetric under $U_L(1) \times U_R(1) \times Z_2 ({Parity})$ transformations, one involving staggered fermions and the other involving Wilson fermions. We argue that these models have interesting quantum phase transitions that can now be studied using Monte Carlo methods.