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| Format: | Preprint |
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2026
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| Online Access: | https://arxiv.org/abs/2605.09122 |
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| _version_ | 1866917477492981760 |
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| author | Ishtiaque, Nafiz Chakroborty, Shanto |
| author_facet | Ishtiaque, Nafiz Chakroborty, Shanto |
| contents | We study finite-temperature $P$-form $\mathbb Z_N$ homological codes via an exact finite-Trotter quantum-to-classical map to a $(d+1)$-dimensional spacetime model with electric and magnetic topological background charges. The resulting background-resolved partition functions admit an exact reformulation in terms of closed magnetic and electric defect polymers, with opposite-species interactions governed by linking phases. By bounding this complex polymer gas by positive same-species hard-core majorant gases, we obtain an explicit low-activity criterion under which all background-dependent partition functions are uniformly controlled and homologically nontrivial polymers are exponentially suppressed on the scale of the spacetime systole. We also derive an exact higher-form Kramers-Wannier duality exchanging electric and magnetic backgrounds, Wilson and 't Hooft operators, and $P$-form and $(d-P)$-form theories. Finally, for prime $N$, we identify an exact source-free gauge-theory specialization coupled to the plaquette random-cluster model, which imports sharp phase-transition results on special geometries into the spacetime framework. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_09122 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | An exact spacetime polymer gas for finite-temperature $\mathbb Z_N$ homological quantum code Ishtiaque, Nafiz Chakroborty, Shanto Mathematical Physics Statistical Mechanics High Energy Physics - Theory Quantum Physics We study finite-temperature $P$-form $\mathbb Z_N$ homological codes via an exact finite-Trotter quantum-to-classical map to a $(d+1)$-dimensional spacetime model with electric and magnetic topological background charges. The resulting background-resolved partition functions admit an exact reformulation in terms of closed magnetic and electric defect polymers, with opposite-species interactions governed by linking phases. By bounding this complex polymer gas by positive same-species hard-core majorant gases, we obtain an explicit low-activity criterion under which all background-dependent partition functions are uniformly controlled and homologically nontrivial polymers are exponentially suppressed on the scale of the spacetime systole. We also derive an exact higher-form Kramers-Wannier duality exchanging electric and magnetic backgrounds, Wilson and 't Hooft operators, and $P$-form and $(d-P)$-form theories. Finally, for prime $N$, we identify an exact source-free gauge-theory specialization coupled to the plaquette random-cluster model, which imports sharp phase-transition results on special geometries into the spacetime framework. |
| title | An exact spacetime polymer gas for finite-temperature $\mathbb Z_N$ homological quantum code |
| topic | Mathematical Physics Statistical Mechanics High Energy Physics - Theory Quantum Physics |
| url | https://arxiv.org/abs/2605.09122 |