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

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• Fermi Surface Symmetric Mass Generation
• Conformal Field Theories generated by Chern Insulators under Quantum Decoherence
• Definition and Classification of Fermi Surface Anomalies
• Boundary conditions and anomalies of conformal field theories in 1+1 dimensions
• CT or P Problem and Symmetric Gapped Fermion Solution
• Dynamic mass generation and topological order in overscreened Kondo lattices
• Lattice Regularization of Reduced Kähler-Dirac Fermions and Connections to Chiral Fermions
• Luttinger liquid tensor network: sine versus tangent dispersion of massless Dirac fermions
• Dynamical symmetry breaking in Georgi-Glashow chiral-gauge theories
• RG Flows in 2d Chiral Gauge Theories
• Two-dimensional gauge anomalies and $p$-adic numbers
• Fermion Mass Generation without Symmetry Breaking
• Flavor Hierarchy from Smooth Confinement