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

Comments: 7 pages, 3 figures, proceeding of 37th International Symposium on Lattice Field Theory(Lattice2019), 16-22 June 2019, Wuhan, China