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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2510.27215 |
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| _version_ | 1866913017484017664 |
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| author | Shen, Shun-Qing |
| author_facet | Shen, Shun-Qing |
| contents | The parity anomaly for Dirac fermions in two spatial dimensions has shaped perspectives in quantum field theory and condensed matter physics. In condensed matter it has evolved as a mechanism for half-quantized Hall responses in systems described by massive Dirac fermions. Here we reexamine the issue on a lattice and show that the half-quantized Hall conductivity is absent for massive Dirac fermions when lattice regularization is properly implemented and the translational invariant symmetry is taken into account. We realize that a single massive Dirac cone on a lattice always leads to an integer quantized Hall conductivity and to the half-quantized Hall conductivity only in the unphysical limit of infinite momentum cut-off. The half-quantized Hall conductivity appears with nonzero longitudinal conductance as a signature of a single massless Dirac cone on a lattice. Consequently, the parity anomaly is a property of massless Dirac fermions in a semimetal/metal, not of massive Dirac fermions in an insulator on a lattice. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_27215 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Absence of Parity Anomaly in Massive Dirac Fermions on a Lattice Shen, Shun-Qing Strongly Correlated Electrons Mesoscale and Nanoscale Physics The parity anomaly for Dirac fermions in two spatial dimensions has shaped perspectives in quantum field theory and condensed matter physics. In condensed matter it has evolved as a mechanism for half-quantized Hall responses in systems described by massive Dirac fermions. Here we reexamine the issue on a lattice and show that the half-quantized Hall conductivity is absent for massive Dirac fermions when lattice regularization is properly implemented and the translational invariant symmetry is taken into account. We realize that a single massive Dirac cone on a lattice always leads to an integer quantized Hall conductivity and to the half-quantized Hall conductivity only in the unphysical limit of infinite momentum cut-off. The half-quantized Hall conductivity appears with nonzero longitudinal conductance as a signature of a single massless Dirac cone on a lattice. Consequently, the parity anomaly is a property of massless Dirac fermions in a semimetal/metal, not of massive Dirac fermions in an insulator on a lattice. |
| title | Absence of Parity Anomaly in Massive Dirac Fermions on a Lattice |
| topic | Strongly Correlated Electrons Mesoscale and Nanoscale Physics |
| url | https://arxiv.org/abs/2510.27215 |