Quantum Critical Phenomena in an $O(4)$ Fermion Chain

TL;DR

This paper introduces an $O(4)$ symmetric fermionic lattice model that exhibits a quantum phase transition from a massive phase with broken chiral symmetry to a massless topological phase, studied via quantum Monte Carlo simulations.

Contribution

The authors construct and analyze a novel $O(4)$ fermion lattice model with a $bZ_2$ chiral symmetry, revealing a quantum phase transition using Monte Carlo methods.

Findings

At zero Hubbard interaction, the model maps to a 2-flavor Gross-Neveu model with spontaneous chiral symmetry breaking.

Small Hubbard interactions do not immediately restore masslessness, maintaining a massive phase.

Large Hubbard interactions lead to a topologically massless phase equivalent to the Heisenberg antiferromagnetic chain.

Abstract

We construct a fermionic lattice model containing interacting spin-$\frac{1}{2}$ fermions with an $O(4)$ symmetry. In addition the model contains a $\mathbb{Z}_2$ chiral symmetry which prevents a fermion mass term. Our model is motivated by the ability to study its physics using the meron-cluster algorithm. By adding a strong repulsive Hubbard interaction $U$, we can transform it into the regular Heisenberg anti-ferromagnet. While we can study our model in any dimension, as a first project we study it in one spatial dimension. We discover that our model at $U=0$ can be described as a lattice-regularized 2-flavor Gross-Neveu model, where fermions become massive since the $\mathbb{Z}_2$ chiral symmetry of the model is spontaneously broken. We show numerically that the theory remains massive when $U$ is small. At large values of $U$ the model is equivalent to the isotropic spin-half anti-ferromagnetic chain, which is massless for topological reasons. This implies that our model has a quantum phase transition from a $\mathbb{Z}_2$ broken massive phase to a topologically massless phase as we increase $U$. We present results obtained from our quantum Monte Carlo method near this phase transition.