Critical exponents for a spin-charge flip symmetric fixed point in 2+1d with massless Dirac fermions

TL;DR

This paper investigates a phase transition in a 2+1D lattice model of massless Dirac fermions with a novel interaction that preserves spin-charge symmetry, revealing a second-order transition with unique critical exponents.

Contribution

The study introduces a new lattice model with a spin-charge flip symmetric interaction and analyzes its phase transition using a fermion bag algorithm, identifying a distinct universality class.

Findings

Phase transition is second order.

Critical exponents differ from previous Hubbard models.

Universality class is unique for this interaction.

Abstract

In the Hamiltonian picture, free spin-$1/2$ Dirac fermions on a bipartite lattice have an $O(4)$ (spin-charge) symmetry. Here we construct an interacting lattice model with an interaction $V$, which is similar to the Hubbard interaction but preserves the spin-charge flip symmetry. By tuning the coupling $V$, we show that we can study the phase transition between the massless fermion phase at small-$V$ and a massive fermion phase at large-$V$. We construct a fermion bag algorithm to study this phase transition and find evidence for it to be second order. Numerical study shows that the universality class of the transition is different from the one studied earlier involving the Hubbard coupling $U$. Here we obtain some critical exponents using lattices up to $L=48$.