Relevant long-range interaction of the entanglement Hamiltonian emerges from a short-range gapped system
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arXiv
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| Main Authors: | , , , , , |
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| Format: | Preprint |
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2023
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| _version_ | 1866929377756839936 |
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| author | Li, Chuhao Huang, Rui-Zhen Ding, Yi-Ming Meng, Zi Yang Wang, Yan-Cheng Yan, Zheng |
| author_facet | Li, Chuhao Huang, Rui-Zhen Ding, Yi-Ming Meng, Zi Yang Wang, Yan-Cheng Yan, Zheng |
| contents | Beyond the Li-Haldane-Poilblanc conjecture, we find the entanglement Hamiltonian (EH) is actually not closely similar to the original Hamiltonian on the virtual edge. Unexpectedly, the EH has some relevant long-range interacting terms which hugely affect the physics. Without loss of generality, we study a spin-1/2 Heisenberg bilayer to obtain the entanglement information between the two layers through our newly developed quantum Monte Carlo scheme, which can simulate large-scale EH. Although the entanglement spectrum carrying the Goldstone mode seems like a Heisenberg model on a single layer, which is consistent with Li-Haldane-Poilblanc conjecture, we demonstrate that there actually exists a finite-temperature phase transition of the EH. The results violate the Mermin-Wagner theorem, which means there should be relevant long-range terms in the EH. It reveals that the Li-Haldane-Poilblanc conjecture ignores necessary corrections for the EH which may lead totally different physics. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2309_16089 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Relevant long-range interaction of the entanglement Hamiltonian emerges from a short-range gapped system Li, Chuhao Huang, Rui-Zhen Ding, Yi-Ming Meng, Zi Yang Wang, Yan-Cheng Yan, Zheng Strongly Correlated Electrons Statistical Mechanics Quantum Physics Beyond the Li-Haldane-Poilblanc conjecture, we find the entanglement Hamiltonian (EH) is actually not closely similar to the original Hamiltonian on the virtual edge. Unexpectedly, the EH has some relevant long-range interacting terms which hugely affect the physics. Without loss of generality, we study a spin-1/2 Heisenberg bilayer to obtain the entanglement information between the two layers through our newly developed quantum Monte Carlo scheme, which can simulate large-scale EH. Although the entanglement spectrum carrying the Goldstone mode seems like a Heisenberg model on a single layer, which is consistent with Li-Haldane-Poilblanc conjecture, we demonstrate that there actually exists a finite-temperature phase transition of the EH. The results violate the Mermin-Wagner theorem, which means there should be relevant long-range terms in the EH. It reveals that the Li-Haldane-Poilblanc conjecture ignores necessary corrections for the EH which may lead totally different physics. |
| title | Relevant long-range interaction of the entanglement Hamiltonian emerges from a short-range gapped system |
| topic | Strongly Correlated Electrons Statistical Mechanics Quantum Physics |
| url | https://arxiv.org/abs/2309.16089 |