Fermion-bag inspired Hamiltonian lattice field theory for fermionic quantum criticality

TL;DR

This paper introduces a new Hamiltonian lattice field theory inspired by the fermion bag approach, enabling efficient study of fermionic quantum critical points with four-fermion interactions, and demonstrates its effectiveness in analyzing the Gross-Neveu universality class.

Contribution

The authors develop a novel class of Hamiltonian lattice theories that recover continuous-time models as the temporal lattice spacing approaches zero, improving computational efficiency for fermionic quantum criticality studies.

Findings

Able to simulate larger lattice sizes at =1 compared to 

Critical exponents match within errors across different temporal discretizations

Faster fermion bag algorithms at =1 facilitate studying quantum critical points

Abstract

Motivated by the fermion bag approach we construct a new class of Hamiltonian lattice field theories that can help us to study fermionic quantum critical points, particularly those with four-fermion interactions. Although these theories are constructed in discrete-time with a finite temporal lattice spacing $\varepsilon$, when $\varepsilon\rightarrow 0$, conventional continuous-time Hamiltonian lattice field theories are recovered. The fermion bag algorithms run relatively faster when $\varepsilon=1$ as compared to $\varepsilon \rightarrow 0$, but still allow us to compute universal quantities near the quantum critical point even at such a large value of $\varepsilon$. As an example of this new approach, here we study the $N_f=1$ Gross-Neveu chiral Ising universality class in $2+1$ dimensions by calculating the critical scaling of the staggered mass order parameter. We show that we are able to study lattice sizes up to $100^2$ sites when $\varepsilon=1$, while with comparable resources we can only reach lattice sizes of up to $64^2$ when $\varepsilon \rightarrow 0$. The critical exponents obtained in both these studies match within errors.