Discrete Abelian lattice gauge theories on a ladder and their dualities with quantum clock models
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arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2022
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| _version_ | 1866916119891148800 |
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| author | Pradhan, Sunny Maroncelli, Andrea Ercolessi, Elisa |
| author_facet | Pradhan, Sunny Maroncelli, Andrea Ercolessi, Elisa |
| contents | We study a duality transformation from the gauge-invariant subspace of a $\mathbb{Z}_N$ lattice gauge theory on a two-leg ladder geometry to an $N$-clock model on a single chain. The main feature of this mapping is the emergence of a longitudinal field in the clock model, whose value depends on the superselection sector of the gauge model, implying that the different sectors of the gauge theory can show quite different phase diagrams. In order to investigate this and see if confined phases might emerge, we perform a numerical analysis for $N = 2, 3, 4$, using exact diagonalization and DMRG. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2208_04182 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Discrete Abelian lattice gauge theories on a ladder and their dualities with quantum clock models Pradhan, Sunny Maroncelli, Andrea Ercolessi, Elisa High Energy Physics - Lattice Statistical Mechanics High Energy Physics - Theory Quantum Physics We study a duality transformation from the gauge-invariant subspace of a $\mathbb{Z}_N$ lattice gauge theory on a two-leg ladder geometry to an $N$-clock model on a single chain. The main feature of this mapping is the emergence of a longitudinal field in the clock model, whose value depends on the superselection sector of the gauge model, implying that the different sectors of the gauge theory can show quite different phase diagrams. In order to investigate this and see if confined phases might emerge, we perform a numerical analysis for $N = 2, 3, 4$, using exact diagonalization and DMRG. |
| title | Discrete Abelian lattice gauge theories on a ladder and their dualities with quantum clock models |
| topic | High Energy Physics - Lattice Statistical Mechanics High Energy Physics - Theory Quantum Physics |
| url | https://arxiv.org/abs/2208.04182 |