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

Vladimir A. Zakharov, Atsushi Ueda, Frank Verstraete, C. W. J. Beenakker

Published Jun 23, 2026• 1 citation

Abstract

Code, data and a notebook to reproduce the figures of V. A. Zakharov, A. Ueda, F. Verstraete, C. W. J. Beenakker, "Symmetric mass generation of interacting chiral fermions on a one-dimensional lattice without fermion doubling".

DOI: 10.5281/zenodo.20816064

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

Vladimir A. Zakharov, Atsushi Ueda, Frank Verstraete, C. W. J. Beenakker

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Publisher

Abstract

DOI: 10.5281/zenodo.20816064

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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.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.

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K

) that reduces the scaling dimension of the 3-4-5-0 interaction from

5

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.

(1+1)

-dimensional

[(1+1)\mathrm{D}]

and

(2+1)

-dimensional FL systems when several FSs together cancel the FS anomaly. However, the U(1) loop group symmetry in these cases is still restrictive enough to rule out all possible fermion bilinear gapping terms, such that a nonperturbative interaction mechanism is the only way to gap out the FSs. This symmetric FS reconstruction is in contrast to the conventional symmetry-breaking gapping mechanism in the FL. As a side product, our model provides a pristine one-dimensional lattice regularization for the

(1+1)\mathrm{D}

U(1) symmetric chiral fermion model (e.g., the 3-4-5-0 model) by utilizing a lattice translation symmetry as an emergent U(1) symmetry at low energy. This opens up the opportunity for efficient numerical simulations of chiral fermions in their own dimensions without introducing mirror fermions under the domain wall fermion construction.

\mathbb{Z}_2

symmetry above a critical interaction strength. Across all three boundary phases, we find quantized charge pumping with the same pumped charge per flux quantum. The spatial distribution of the pumped charge varies between phases. Besides charge pumping, we study how a single injected fermion propagates under open boundary conditions. In the SMG phase, an interaction-induced flavor-mixing current develops at the endpoints of the gapped edge, which is absent in the weak- and strong-coupling limits. This current reveals a charge-redistribution mechanism unique to the SMG phase. Additionally, we propose an analogy between charge pumping in this model and a topological leptogenesis scenario in the (3+1)d Standard Model. The anomaly-free chiral U(1) symmetries of the 3-4-5-0 model play a role analogous to the baryon-minus-lepton symmetry of the Standard Model. In both settings, charge pumping can be associated with a continuous deformation along a classically defined but quantum-anomalous direction, while a discrete subgroup remains an exact quantum symmetry.