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Main Authors: Meyniel, Gabriel, Zhou, Fei
Format: Preprint
Published: 2025
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Online Access:https://arxiv.org/abs/2510.25959
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author Meyniel, Gabriel
Zhou, Fei
author_facet Meyniel, Gabriel
Zhou, Fei
contents In this article, we put forward a practical but generic approach towards constructing a large family of $(3+1)$ dimension lattice models which can naturally lead to a single Weyl cone in the infrared (IR) limit. Our proposal relies on spontaneous charge $U(1)$ symmetry breaking to evade the usual no-go theorem of a single Weyl cone in a 3d lattice. We have explored three concrete paths in this approach, all involving fermionic topological symmetry protected states (SPTs). Path a) is to push a gapped SPT in a 3d lattice with time-reversal symmetry (or $T$-symmetry) to a gapless topological quantum critical point (tQCP) which involves a minimum change of topologies,i.e. $δN_w=2$ where $δN_w$ is the change of winding numbers across the tQCP. Path b) is to peal off excessive degrees of freedom in the gapped SPT via applying $T$-symmetry breaking fields which naturally result in a pair of gapless nodal points of real fermions. Path c) is a hybrid of a) and b) where tQCPs, with $δN_w \geq 2$, are further subject to time-reversal-symmetry breaking actions. In the infrared limit, all the lattice models with single Weyl fermions studied here are isomorphic to either a tQCP in a DIII class topological superconductor with a protecting $T$-symmetry, or its dual, a $T$-symmetry breaking superconducting nodal point phase, and therefore form an equivalent class. For a generic $T$-symmetric tQCP along Path a), the conserved-charge operators span a six-dimensional linear space while for a $T$-symmetry breaking gapless state along Path b), c), charge operators typically span a two-dimensional linear space instead. Finally, we pinpoint connections between three spatial dimensional lattice chiral fermion models and gapless real fermions that can naturally appear in superfluids or superconductors studied previously.
format Preprint
id arxiv_https___arxiv_org_abs_2510_25959
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Equivalence class of Emergent Single Weyl fermion lattice models in 3 dimensions: gapless superconductors and superfluids versus chiral fermions
Meyniel, Gabriel
Zhou, Fei
High Energy Physics - Theory
Superconductivity
High Energy Physics - Lattice
Mathematical Physics
In this article, we put forward a practical but generic approach towards constructing a large family of $(3+1)$ dimension lattice models which can naturally lead to a single Weyl cone in the infrared (IR) limit. Our proposal relies on spontaneous charge $U(1)$ symmetry breaking to evade the usual no-go theorem of a single Weyl cone in a 3d lattice. We have explored three concrete paths in this approach, all involving fermionic topological symmetry protected states (SPTs). Path a) is to push a gapped SPT in a 3d lattice with time-reversal symmetry (or $T$-symmetry) to a gapless topological quantum critical point (tQCP) which involves a minimum change of topologies,i.e. $δN_w=2$ where $δN_w$ is the change of winding numbers across the tQCP. Path b) is to peal off excessive degrees of freedom in the gapped SPT via applying $T$-symmetry breaking fields which naturally result in a pair of gapless nodal points of real fermions. Path c) is a hybrid of a) and b) where tQCPs, with $δN_w \geq 2$, are further subject to time-reversal-symmetry breaking actions. In the infrared limit, all the lattice models with single Weyl fermions studied here are isomorphic to either a tQCP in a DIII class topological superconductor with a protecting $T$-symmetry, or its dual, a $T$-symmetry breaking superconducting nodal point phase, and therefore form an equivalent class. For a generic $T$-symmetric tQCP along Path a), the conserved-charge operators span a six-dimensional linear space while for a $T$-symmetry breaking gapless state along Path b), c), charge operators typically span a two-dimensional linear space instead. Finally, we pinpoint connections between three spatial dimensional lattice chiral fermion models and gapless real fermions that can naturally appear in superfluids or superconductors studied previously.
title Equivalence class of Emergent Single Weyl fermion lattice models in 3 dimensions: gapless superconductors and superfluids versus chiral fermions
topic High Energy Physics - Theory
Superconductivity
High Energy Physics - Lattice
Mathematical Physics
url https://arxiv.org/abs/2510.25959