Hamiltonian models of lattice fermions solvable by the meron-cluster algorithm

TL;DR

This paper introduces a solvable lattice fermion model with a novel symmetry, enabling efficient numerical study of quantum phase transitions and valence bond solid states using the meron-cluster algorithm.

Contribution

The authors present a new lattice fermion model with enhanced symmetry and solvability, facilitating the study of quantum phases and transitions in one dimension.

Findings

Ground state at U=0 is a valence bond solid.

Quantum phase transition to a critical phase occurs with increasing U.

Numerical verification of correlation function scaling near criticality.

Abstract

We introduce a half-filled Hamiltonian of spin-half lattice fermions that can be studied with the efficient meron-cluster algorithm in any dimension. As with the usual bipartite half-filled Hubbard models, the na\"ive $U(2)$ symmetry is enhanced to $SO(4)$. On the other hand our model has a novel spin-charge flip ${\mathbb Z}^C_2$ symmetry which is an important ingredient of free massless fermions. In this work we focus on one spatial dimension, and show that our model can be viewed as a lattice-regularized two-flavor chiral-mass Gross-Neveu model. Our model remains solvable in the presence of the Hubbard coupling $U$, which maps to a combination of Gross-Neveu and Thirring couplings in one dimension. Using the meron-cluster algorithm we find that the ground state of our model is a valence bond solid when $U=0$. From our field theory analysis, we argue that the valence bond solid forms inevitably because of an interesting frustration between spin and charge sectors in the renormalization group flow enforced by the ${\mathbb Z}^C_2$ symmetry. This state spontaneously breaks translation symmetry by one lattice unit, which can be identified with a $\mathbb{Z}_2^\chi$ chiral symmetry in the continuum. We show that increasing $U$ induces a quantum phase transition to a critical phase described by the $SU(2)_1$ Wess-Zumino-Witten theory. The quantum critical point between these two phases is known to exhibit a novel symmetry enhancement between spin and dimer. Here we verify the scaling relations of these correlation functions near the critical point numerically. Our study opens up the exciting possibility of numerical access to similar novel phase transitions in higher dimensions in fermionic lattice models using the meron-cluster algorithm.