Remarks on effects of projective phase on eigenstate thermalization hypothesis
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2023
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| _version_ | 1866916200473165824 |
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| author | Fukushima, Osamu |
| author_facet | Fukushima, Osamu |
| contents | The existence of $p$-form symmetry in $(d+1)$-dimensional quantum field is known to always lead to the breakdown of the eigenstate thermalization hypothesis (ETH) for certain $(d-p)$-dimensional operators other than symmetry operators under some assumptions. The assumptions include the mixing of symmetry sectors within a given energy shell, which is rather challenging to verify because it requires information on the eigenstates in the middle of the spectrum. We reconsider this assumption from the viewpoint of projective representations to avoid this difficulty. In the case of $\mathbb{Z}_N$ symmetries, we can circumvent the difficulty by considering $\mathbb{Z}_N\times\mathbb{Z}_N$-symmetric theories with nontrivial projective phases, and perturbing the Hamiltonian while preserving one of the $\mathbb{Z}_N$ symmetries of our interest. We also perform numerical analyses for $(1+1)$-dimensional spin chains and the $(2+1)$-dimensional $\mathbb{Z}_2$ lattice gauge theory. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_11425 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Remarks on effects of projective phase on eigenstate thermalization hypothesis Fukushima, Osamu High Energy Physics - Theory Statistical Mechanics Strongly Correlated Electrons Quantum Physics The existence of $p$-form symmetry in $(d+1)$-dimensional quantum field is known to always lead to the breakdown of the eigenstate thermalization hypothesis (ETH) for certain $(d-p)$-dimensional operators other than symmetry operators under some assumptions. The assumptions include the mixing of symmetry sectors within a given energy shell, which is rather challenging to verify because it requires information on the eigenstates in the middle of the spectrum. We reconsider this assumption from the viewpoint of projective representations to avoid this difficulty. In the case of $\mathbb{Z}_N$ symmetries, we can circumvent the difficulty by considering $\mathbb{Z}_N\times\mathbb{Z}_N$-symmetric theories with nontrivial projective phases, and perturbing the Hamiltonian while preserving one of the $\mathbb{Z}_N$ symmetries of our interest. We also perform numerical analyses for $(1+1)$-dimensional spin chains and the $(2+1)$-dimensional $\mathbb{Z}_2$ lattice gauge theory. |
| title | Remarks on effects of projective phase on eigenstate thermalization hypothesis |
| topic | High Energy Physics - Theory Statistical Mechanics Strongly Correlated Electrons Quantum Physics |
| url | https://arxiv.org/abs/2310.11425 |