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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Materias: | |
| Acceso en línea: | https://arxiv.org/abs/2509.16880 |
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| _version_ | 1866914049508245504 |
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| author | He, Tianhao Wu, Xintian |
| author_facet | He, Tianhao Wu, Xintian |
| contents | The entanglement entropies of $XY$ chains and quantum Ising chains (QICs) with fixed boundary conditions are studied here. Three kinds of boundary conditions (BCs) are considered: fixed up--up or down--down (the spins at both ends are aligned in the same direction), fixed up--down or down--up (the spins at the two ends are aligned in opposite directions), and fixed--free (the spin at one end is aligned, and the other end is free). It is shown that i) the entanglement entropy of an $XY$ chain with a fixed--free BC is the sum of those of QICs with a fixed--free BC and with a free--free BC; ii) the entanglement entropy of an $XY$ chain with a fixed up--up boundary condition is the sum of those of QICs with a fixed up--up BC and with a free--free BC; and iii) the entanglement entropy of an $XY$ chain with a fixed up--down BC is the sum of that of a QIC with a fixed up--up BC and that of the first excited state of a QIC with a free--free BC. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_16880 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The exact relation between the entanglement entropies of the $XY$ and quantum Ising chains with free and fixed boundary conditions He, Tianhao Wu, Xintian Statistical Mechanics The entanglement entropies of $XY$ chains and quantum Ising chains (QICs) with fixed boundary conditions are studied here. Three kinds of boundary conditions (BCs) are considered: fixed up--up or down--down (the spins at both ends are aligned in the same direction), fixed up--down or down--up (the spins at the two ends are aligned in opposite directions), and fixed--free (the spin at one end is aligned, and the other end is free). It is shown that i) the entanglement entropy of an $XY$ chain with a fixed--free BC is the sum of those of QICs with a fixed--free BC and with a free--free BC; ii) the entanglement entropy of an $XY$ chain with a fixed up--up boundary condition is the sum of those of QICs with a fixed up--up BC and with a free--free BC; and iii) the entanglement entropy of an $XY$ chain with a fixed up--down BC is the sum of that of a QIC with a fixed up--up BC and that of the first excited state of a QIC with a free--free BC. |
| title | The exact relation between the entanglement entropies of the $XY$ and quantum Ising chains with free and fixed boundary conditions |
| topic | Statistical Mechanics |
| url | https://arxiv.org/abs/2509.16880 |