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Quantized axial charge of staggered fermions and the chiral anomaly

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arxiv 2409.12220 v3 pith:RP3PB32S submitted 2024-09-18 hep-th cond-mat.str-elhep-lat

Arkya Chatterjee , Salvatore D. Pace , Shu-Heng Shao This is my paper · ORCID
classification hep-thcond-mat.str-elhep-lat
keywords chargeslatticeanomalycontinuumsymmetriesalgebraaxialchiral
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In the 1+1D ultra-local lattice Hamiltonian for staggered fermions with a finite-dimensional Hilbert space, there are two conserved, integer-valued charges that flow in the continuum limit to the vector and axial charges of a massless Dirac fermion with a perturbative anomaly. Each of the two lattice charges generates an ordinary U(1) global symmetry that acts locally on operators and can be gauged individually. Interestingly, they do not commute on a finite lattice and generate the Onsager algebra, but their commutator goes to zero in the continuum limit. The chiral anomaly is matched by this non-abelian algebra, which is consistent with the Nielsen-Ninomiya theorem. We further prove that the presence of these two conserved lattice charges forces the low-energy phase to be gapless, reminiscent of the consequence from perturbative anomalies of continuous global symmetries in continuum field theory. Upon bosonization, these two charges lead to two exact U(1) symmetries in the XX model that flow to the momentum and winding symmetries in the free boson conformal field theory.

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Cited by 5 Pith papers

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  1. Exactly Solvable 1+1d Chiral Lattice Gauge Theories

    hep-th 2026-01 conditional novelty 7.0 of 10

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  3. Bosonization versus the Nielsen-Ninomiya theorem

    hep-th 2026-07 conditional novelty 6.5 of 10

    The 2D modified Villain model's Weyl operators reproduce free Dirac correlations in the continuum, and their no-doubler Dirac kernel is non-local, showing exactly how bosonization evades the Nielsen-Ninomiya theorem.

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    QSP implements the overlap fermion Hamiltonian with Ginsparg-Wilson violation O(ε_e) at cost only a log(1/ε_e)/κ factor above Wilson-Dirac, trading qubits for gates versus domain-wall fermions.

  5. Quantum Many-Body Lattice C-R-T Symmetry: Fractionalization, Anomaly, and Symmetric Mass Generation

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