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

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.

5 + 3 pages, Symmetric Mass Generation of the chiral fermion model arXiv:1307.7480

References in corpus (5)

• Topological boundary conditions in abelian Chern-Simons theory
• Symmetry Protected Topological States of Interacting Fermions and Bosons
• Massive fermions without fermion bilinear condensates
• Generating a non-perturbative mass gap using Feynman diagrams in an asymptotically free theory
• A Novel Non-Perturbative Lattice Regularization of an Anomaly-Free $1+1d$ Chiral $SU(2)$ Gauge Theory