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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| Accesso online: | https://arxiv.org/abs/2306.00291 |
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| _version_ | 1866912985692241920 |
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| author | Chen, Xie Lam, Ho Tat Ma, Xiuqi |
| author_facet | Chen, Xie Lam, Ho Tat Ma, Xiuqi |
| contents | Infinite-component Chern-Simons-Maxwell theories with a block-Toeplitz K matrix provide a vast landscape of gapped and gapless, foliated and non-foliated fracton orders. In this paper, we investigate the ground state degeneracy (GSD) of these theories, classifying distinct behaviors of the GSD as a function of the linear system size, i.e. the size of the K matrix. We find that the GSD can exhibit exponential or polynomial growth, cyclic variations across a finite set of values, or erratic fluctuations within an exponential envelope. We relate these different patterns to the roots of the determinant polynomial - a Laurent polynomial associated with the block-Toeplitz K matrix. These roots also play a crucial role in determining whether the theory is gapped or gapless. In addition, we propose a necessary condition for a gapped infinite-component Chern-Simons-Maxwell theory to be a foliated fracton order, based on the porperties of the determinant polynomial. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2306_00291 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Ground State Degeneracy of Infinite-Component Chern-Simons-Maxwell Theories: Foliated vs. Non-foliated Fracton Orders Chen, Xie Lam, Ho Tat Ma, Xiuqi Strongly Correlated Electrons High Energy Physics - Theory Infinite-component Chern-Simons-Maxwell theories with a block-Toeplitz K matrix provide a vast landscape of gapped and gapless, foliated and non-foliated fracton orders. In this paper, we investigate the ground state degeneracy (GSD) of these theories, classifying distinct behaviors of the GSD as a function of the linear system size, i.e. the size of the K matrix. We find that the GSD can exhibit exponential or polynomial growth, cyclic variations across a finite set of values, or erratic fluctuations within an exponential envelope. We relate these different patterns to the roots of the determinant polynomial - a Laurent polynomial associated with the block-Toeplitz K matrix. These roots also play a crucial role in determining whether the theory is gapped or gapless. In addition, we propose a necessary condition for a gapped infinite-component Chern-Simons-Maxwell theory to be a foliated fracton order, based on the porperties of the determinant polynomial. |
| title | Ground State Degeneracy of Infinite-Component Chern-Simons-Maxwell Theories: Foliated vs. Non-foliated Fracton Orders |
| topic | Strongly Correlated Electrons High Energy Physics - Theory |
| url | https://arxiv.org/abs/2306.00291 |