Symmetric Mass Generation in the 1+1 Dimensional Chiral Fermion 3-4-5-0 Model

TL;DR

This paper demonstrates a lattice regularization of (1+1)D chiral fermions using DMRG simulations, showing that mirror fermions can be gapped out via symmetric mass generation without breaking symmetry, confirming a new approach to regularize chiral fermions.

Contribution

The work introduces a novel lattice regularization method for chiral fermions using SMG in a (2+1)D lattice model, verified through DMRG simulations.

Findings

Mirror fermions are gapped out without symmetry breaking.

The transition is in the BKT universality class.

Light chiral fermions remain gapless after the transition.

Abstract

Lattice regularization of chiral fermions has been a long-standing problem in physics. In this work, we present the density matrix renormalization group (DMRG) simulation of the 3-4-5-0 model of (1+1)D chiral fermions with an anomaly-free chiral U(1) symmetry, which contains two left-moving and two right-moving fermions carrying U(1) charges 3,4 and 5,0, respectively. Following the Wang-Wen chiral fermion model, we realize the chiral fermions and their mirror partners on the opposite boundaries of a thin strip of (2+1)D lattice model of multi-layer Chern insulator, whose finite-width implies the quantum system is effectively (1+1)D. By introducing carefully designed two sets of six-fermion local interactions to the mirror sector only, we demonstrate that the mirror fermions can be gapped out by the interaction beyond a critical strength without breaking the chiral U(1) symmetry, via the symmetric mass generation (SMG) mechanism. We show that the interaction-driven gapping transition is in the Berezinskii-Kosterlitz-Thouless (BKT) universality class. We determine the evolution of Luttinger parameters before the transition, which confirms that the transition happens exactly at the point when the interaction term becomes marginal. As the mirror sector is gapped after the transition, we check that the fermions in the light chiral fermion sector remain gapless, which provides the desired lattice regularization of chiral fermions.