A spin-charge flip symmetric fixed point in 2+1d with massless Dirac fermions

TL;DR

This paper investigates a novel quantum critical point in a 2+1D lattice model with massless Dirac fermions, revealing a new fixed point with spin-charge flip symmetry through Monte Carlo simulations and renormalization group analysis.

Contribution

It introduces a new spin-charge flip symmetric fixed point in 2+1D Dirac fermion systems, supported by numerical and analytical methods.

Findings

Identified a second order quantum phase transition with simultaneous criticality of spin and charge.

Discovered a new fixed point with spin-charge flip symmetry in the continuum limit.

Calculated critical exponents for the novel fixed point.

Abstract

We study a quantum phase transition of electrons on a two-dimensional square lattice. Our lattice model preserves the full $\mathrm{O}(4)$ symmetry of free spin-$\frac{1}{2}$ Dirac fermions on a bipartite lattice. In particular, it not only preserves the usual $\mathrm{SO}(4)$ (spin-charge) symmetry like in the half-filling Hubbard model, but also preserves a $\mathbb{Z}_2$ spin-charge flip symmetry. Using sign-problem-free Monte Carlo simulation, we find a second order quantum phase transition from a massless Dirac phase to a massive phase with spontaneously chosen spin order or charge order, which become simultaneously critical at the critical point. We analyze all the possible 4-fermion couplings in the continuum respecting the lattice symmetry, and identify the terms whose effective potential in the broken phase is consistent with the numerical results. Using renormalization group calculations in the continuum, we show the existence of the new spin-charge flip symmetric fixed point and calculate its critical exponents.