Flavoured Lattice Schwinger Model with Chiral Anomaly
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arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866910148399726592 |
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| author | Bakircioglu, Dogukan |
| author_facet | Bakircioglu, Dogukan |
| contents | We introduce the \emph{flavoured lattice Schwinger model}, a $(1{+}1)$-dimensional $U(1)$ lattice gauge theory in which the fermion doubling problem is resolved by staggering a $\mathbb{Z}_{2}$ flavour degree of freedom rather than staggering chirality. Unlike all standard approaches, the flavoured construction preserves an exact axial $U(1)$ symmetry at finite lattice spacing. We derive the continuum limit, showing the model reduces to two copies of the massless Schwinger model labelled by $α\in\{0,1\}$. The central result is that the flavoured construction admits a well-defined, regularized, gauge-invariant lattice axial charge $Q_{G}^{A}$ with chiral anomaly equation $\langle dQ_{G}^{A}/dt\rangle = -(2g/π)\int dx\,\langle E(x)\rangle$ in the continuum limit, derived as a direct dynamical consequence of minimal gauge coupling at finite lattice spacing. Restricting to the $α=0$ sector recovers the standard single-flavour result. We further show that spatial separation of the flavour sectors can be realised as a helical edge states living on the boundaries of a ribbon shaped $(2{+}1)$-dimensional Bernevig--Hughes--Zhang topological insulator. This provides a bulk-boundary picture solution to fermion doubling and allows the chiral anomaly to be put on the lattice for a single flavour. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_13146 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Flavoured Lattice Schwinger Model with Chiral Anomaly Bakircioglu, Dogukan High Energy Physics - Lattice High Energy Physics - Theory Quantum Physics We introduce the \emph{flavoured lattice Schwinger model}, a $(1{+}1)$-dimensional $U(1)$ lattice gauge theory in which the fermion doubling problem is resolved by staggering a $\mathbb{Z}_{2}$ flavour degree of freedom rather than staggering chirality. Unlike all standard approaches, the flavoured construction preserves an exact axial $U(1)$ symmetry at finite lattice spacing. We derive the continuum limit, showing the model reduces to two copies of the massless Schwinger model labelled by $α\in\{0,1\}$. The central result is that the flavoured construction admits a well-defined, regularized, gauge-invariant lattice axial charge $Q_{G}^{A}$ with chiral anomaly equation $\langle dQ_{G}^{A}/dt\rangle = -(2g/π)\int dx\,\langle E(x)\rangle$ in the continuum limit, derived as a direct dynamical consequence of minimal gauge coupling at finite lattice spacing. Restricting to the $α=0$ sector recovers the standard single-flavour result. We further show that spatial separation of the flavour sectors can be realised as a helical edge states living on the boundaries of a ribbon shaped $(2{+}1)$-dimensional Bernevig--Hughes--Zhang topological insulator. This provides a bulk-boundary picture solution to fermion doubling and allows the chiral anomaly to be put on the lattice for a single flavour. |
| title | Flavoured Lattice Schwinger Model with Chiral Anomaly |
| topic | High Energy Physics - Lattice High Energy Physics - Theory Quantum Physics |
| url | https://arxiv.org/abs/2604.13146 |