Symmetric mass generation of interacting chiral fermions on a one-dimensional lattice without fermion doubling

Abstract:Symmetric mass generation is the interaction-induced opening of a fermion gap without spontaneous symmetry breaking. The anomaly-free 3-4-5-0 model of Wang and Wen provides a minimal one-dimensional setting for this phenomenon, but a direct lattice realization faces two obstacles: fermion doubling for local chiral discretizations and perturbative irrelevance of the six-fermion gapping interaction. We address both obstacles. First, we formulate the model on a strictly one-dimensional tangent-fermion lattice, where a nonlocal hopping produces a single chiral branch without a mirror partner while retaining an efficient tensor-network representation. Second, we add a Hubbard-type density-density interaction (Luttinger parameter $K$) that reduces the scaling dimension of the 3-4-5-0 interaction from $5$ to $5K$, making it relevant for $K<2/5$. Density-matrix renormalization group calculations show the opening of an excitation gap in this regime without the appearance of a degenerate ground state, the hallmark of symmetric mass generation.

11 pages, 5 figures. New appendix on a more general SMG senario. New zenodo version has the DMRG code

High Energy Physics - Theory (hep-th); Strongly Correlated Electrons (cond-mat.str-el); Quantum Physics (quant-ph)

arXiv:2606.24713 [hep-th]

(or arXiv:2606.24713v2 [hep-th] for this version)

https://doi.org/10.48550/arXiv.2606.24713 Focus to learn more arXiv-issued DOI via DataCite

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