Solution to new sign problems with Hamiltonian Lattice Fermions

TL;DR

This paper introduces a fermion bag-based method to solve the sign problem in certain lattice fermion models, enabling new simulations of massless four-fermion systems with minimal fermion doubling and odd fermion flavors.

Contribution

It presents a novel solution to the sign problem in particle-hole symmetric lattice fermion models, even with broken symmetry, facilitating studies of previously inaccessible quantum phase transitions.

Findings

Enables simulations of massless four-fermion models with minimal fermion doubling

Allows study of quantum phase transitions with odd fermion flavors

Removes sign problem constraints in specific lattice fermion models

Abstract

We present a solution to the sign problem in a class of particle-hole symmetric Hamiltonian lattice fermion models on bipartite lattices using the idea of fermion bags. The solution remains valid when the particle-hole symmetry is broken through a staggered chemical potential term. This solution allows, for the first time, simulations of some massless four-fermion models with minimal fermion doubling and with an odd number of fermion flavors using ultra-local actions. One can thus study a variety of quantum phase transitions that have remained unexplored so far due to sign problems.