Quantum critical behavior in three dimensional lattice Gross-Neveu models

TL;DR

This paper investigates quantum critical points in three-dimensional lattice Gross-Neveu models with two massless Dirac fermions, using a sign-problem-free fermion bag approach to compute critical exponents.

Contribution

It introduces a sign-problem-free method to study critical behavior in lattice Gross-Neveu models with SU(2) symmetry and different chiral symmetries, providing new critical exponent estimates.

Findings

Estimated critical exponents for Z2 model: ν=0.83(1), η=0.62(1), η_ψ=0.38(1)

Estimated critical exponents for U(1) model: ν=0.849(8), η=0.633(8), η_ψ=0.373(3)

Demonstrated effectiveness of fermion bag approach in sign-problematic models.

Abstract

We study quantum critical behavior in three dimensional lattice Gross-Neveu models containing two massless Dirac fermions. We focus on two models with SU(2) flavor symmetry and either a $Z_2$ or a U(1) chiral symmetry. Both models could not be studied earlier due to sign problems. We use the fermion bag approach which is free of sign problems and compute critical exponents at the phase transitions. We estimate $\nu = 0.83(1)$, $\eta = 0.62(1)$, $\eta_\psi = 0.38(1)$ in the $Z_2$ and $\nu = 0.849(8)$, $\eta = 0.633(8)$, $\eta_\psi = 0.373(3)$ in the U(1) model.