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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2022
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| Materias: | |
| Acceso en línea: | https://arxiv.org/abs/2202.01173 |
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| _version_ | 1866908165104205824 |
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| author | Huang, Yichen |
| author_facet | Huang, Yichen |
| contents | In a spin chain governed by a local Hamiltonian, we consider a microcanonical ensemble in the middle of the energy spectrum and a contiguous subsystem whose length is a constant fraction of the system size. We prove that if the bandwidth of the ensemble is greater than a certain constant, then the average entanglement entropy (between the subsystem and the rest of the system) of eigenstates in the ensemble deviates from the maximum entropy by at least a positive constant. This result highlights the difference between the entanglement entropy of mid-spectrum eigenstates of (chaotic) local Hamiltonians and that of random states. We also prove that the former deviates from the thermodynamic entropy at the same energy by at least a positive constant. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2202_01173 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Deviation from maximal entanglement for mid-spectrum eigenstates of local Hamiltonians Huang, Yichen Quantum Physics Statistical Mechanics Strongly Correlated Electrons In a spin chain governed by a local Hamiltonian, we consider a microcanonical ensemble in the middle of the energy spectrum and a contiguous subsystem whose length is a constant fraction of the system size. We prove that if the bandwidth of the ensemble is greater than a certain constant, then the average entanglement entropy (between the subsystem and the rest of the system) of eigenstates in the ensemble deviates from the maximum entropy by at least a positive constant. This result highlights the difference between the entanglement entropy of mid-spectrum eigenstates of (chaotic) local Hamiltonians and that of random states. We also prove that the former deviates from the thermodynamic entropy at the same energy by at least a positive constant. |
| title | Deviation from maximal entanglement for mid-spectrum eigenstates of local Hamiltonians |
| topic | Quantum Physics Statistical Mechanics Strongly Correlated Electrons |
| url | https://arxiv.org/abs/2202.01173 |