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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2410.20835 |
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| _version_ | 1866908994508947456 |
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| author | Kashuba, O. Mummadavarapu, R. Riwar, R. -P. |
| author_facet | Kashuba, O. Mummadavarapu, R. Riwar, R. -P. |
| contents | Compact scalar field theories on lattices are capable of describing a large class of many-body systems, such as interacting bosons, superconducting circuit networks, spin systems and more. We show that a generic quantum geometric many-body coupling induces quantized Chern couplings, implementing a lattice network version of a Florianini-Jackiw theory. Quantum geometry thus unlocks a direct mapping from scalar fields to anyons with fractional exchange phases, relevant for quantum error correction codes and quantum chemistry computation applications. In contrast to more familiar local Chern-Simons constructions with a uniform level, the compact-phase quantum geometry considered here yields pair-dependent topological couplings that can be nonlocal in node space and are encoded by a nonuniform first-Chern matrix. This feature introduces the notion of non-identical anyons, i.e., excitations that do not mutually satisfy the same exchange statistics. Such non-identical exchange statistics open up a microscopic pathway to a virtually unexplored class of non-local field theories breaking the Wigner superselection rule, allowing to explore non-local communication (all-to-all qubit gates) with local control. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_20835 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Non-identical anyon algebras from compact-field quantum geometry Kashuba, O. Mummadavarapu, R. Riwar, R. -P. Quantum Physics Superconductivity Compact scalar field theories on lattices are capable of describing a large class of many-body systems, such as interacting bosons, superconducting circuit networks, spin systems and more. We show that a generic quantum geometric many-body coupling induces quantized Chern couplings, implementing a lattice network version of a Florianini-Jackiw theory. Quantum geometry thus unlocks a direct mapping from scalar fields to anyons with fractional exchange phases, relevant for quantum error correction codes and quantum chemistry computation applications. In contrast to more familiar local Chern-Simons constructions with a uniform level, the compact-phase quantum geometry considered here yields pair-dependent topological couplings that can be nonlocal in node space and are encoded by a nonuniform first-Chern matrix. This feature introduces the notion of non-identical anyons, i.e., excitations that do not mutually satisfy the same exchange statistics. Such non-identical exchange statistics open up a microscopic pathway to a virtually unexplored class of non-local field theories breaking the Wigner superselection rule, allowing to explore non-local communication (all-to-all qubit gates) with local control. |
| title | Non-identical anyon algebras from compact-field quantum geometry |
| topic | Quantum Physics Superconductivity |
| url | https://arxiv.org/abs/2410.20835 |