Translation Groups for arbitrary Gauge Fields in Synthetic Crystals with real hopping amplitudes
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866914003725320192 |
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| author | Marciani, Marco |
| author_facet | Marciani, Marco |
| contents | The Cayley-crystals introduced in [F. R. Lux and E. Prodan, Annales Henri Poincaré 25(8), 3563 (2024)] are a class of lattices endowed with a Hamiltonian whose translation group $G$ is generic and possibly non-commutative. We show that these systems naturally realize the generalization of the so-called magnetic translation groups to arbitrary discrete gauge groups. A one-body dynamics emulates that of a particle carrying a superposition of charges, each coupled to distinct static gauge-field configuration. The possible types of gauge fields are determined by the irreducible representations of the commutator subgroup $C \subset G$, while the Wilson-loop configurations - which need not be homogeneous - are fixed by the embedding of $C$ in $G$. The role of other subgroups in shaping both the lattice geometry and the dynamics is analyze in depth assuming $C$ finite. We discuss a theorem of direct engineering relevance that, for any cyclic gauge group, yields all compatible translation groups. We then construct two-dimensional examples of Cayley-crystals equivalent to square lattices threaded by inhomogeneous magnetic fluxes. Importantly, Cayley-crystals can be realized with only real hopping amplitudes and in scalable geometries that can fit higher-than-3D dynamics, enabling experimental exploration and eventual exploitation in metamaterials, cQED, and other synthetic platforms. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2508_08461 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Translation Groups for arbitrary Gauge Fields in Synthetic Crystals with real hopping amplitudes Marciani, Marco Mesoscale and Nanoscale Physics Other Condensed Matter Soft Condensed Matter The Cayley-crystals introduced in [F. R. Lux and E. Prodan, Annales Henri Poincaré 25(8), 3563 (2024)] are a class of lattices endowed with a Hamiltonian whose translation group $G$ is generic and possibly non-commutative. We show that these systems naturally realize the generalization of the so-called magnetic translation groups to arbitrary discrete gauge groups. A one-body dynamics emulates that of a particle carrying a superposition of charges, each coupled to distinct static gauge-field configuration. The possible types of gauge fields are determined by the irreducible representations of the commutator subgroup $C \subset G$, while the Wilson-loop configurations - which need not be homogeneous - are fixed by the embedding of $C$ in $G$. The role of other subgroups in shaping both the lattice geometry and the dynamics is analyze in depth assuming $C$ finite. We discuss a theorem of direct engineering relevance that, for any cyclic gauge group, yields all compatible translation groups. We then construct two-dimensional examples of Cayley-crystals equivalent to square lattices threaded by inhomogeneous magnetic fluxes. Importantly, Cayley-crystals can be realized with only real hopping amplitudes and in scalable geometries that can fit higher-than-3D dynamics, enabling experimental exploration and eventual exploitation in metamaterials, cQED, and other synthetic platforms. |
| title | Translation Groups for arbitrary Gauge Fields in Synthetic Crystals with real hopping amplitudes |
| topic | Mesoscale and Nanoscale Physics Other Condensed Matter Soft Condensed Matter |
| url | https://arxiv.org/abs/2508.08461 |