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| Autori principali: | , , , |
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| Natura: | Preprint |
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2024
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| Accesso online: | https://arxiv.org/abs/2412.06396 |
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| _version_ | 1866917862934839296 |
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| author | Zhou, Huan-Qiang Shi, Qian-Qian McCulloch, Ian P. Batchelor, Murray T. |
| author_facet | Zhou, Huan-Qiang Shi, Qian-Qian McCulloch, Ian P. Batchelor, Murray T. |
| contents | A generic scheme is proposed to investigate the entanglement entropy for a type of scale-invariant states, valid for orthonormal basis states in the ground state subspace of quantum many-body systems undergoing spontaneous symmetry breaking with type-B Goldstone modes in two spatial dimensions and beyond. It is argued that a contribution from the area law to the entanglement entropy is absent, since the closeness to the boundary between a subsystem and its environment is not well-defined, given that a permutation symmetry group with respect to the unit cells of degenerate ground state wave functions emerges. Three physical constraints imposed lead to a universal finite-system size scaling function in the dominant logarithmic contribution to the entanglement entropy. As a result, an abstract fractal underlying the ground state subspace is revealed, characterized by the fractal dimension. The latter in turn is identical to the number of type-B Goldstone modes for the orthonormal basis states. The prediction is numerically confirmed for the ${\rm SU}(2)$ spin-$s$ ferromagnetic Heisenberg model, the ${\rm SU}(2s+1)$ ferromagnetic model, and the staggered ${\rm SU}(3)$ spin-1 ferromagnetic biquadratic model. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_06396 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Entanglement entropy for a type of scale-invariant states in two spatial dimensions and beyond: universal finite-size scaling Zhou, Huan-Qiang Shi, Qian-Qian McCulloch, Ian P. Batchelor, Murray T. Statistical Mechanics A generic scheme is proposed to investigate the entanglement entropy for a type of scale-invariant states, valid for orthonormal basis states in the ground state subspace of quantum many-body systems undergoing spontaneous symmetry breaking with type-B Goldstone modes in two spatial dimensions and beyond. It is argued that a contribution from the area law to the entanglement entropy is absent, since the closeness to the boundary between a subsystem and its environment is not well-defined, given that a permutation symmetry group with respect to the unit cells of degenerate ground state wave functions emerges. Three physical constraints imposed lead to a universal finite-system size scaling function in the dominant logarithmic contribution to the entanglement entropy. As a result, an abstract fractal underlying the ground state subspace is revealed, characterized by the fractal dimension. The latter in turn is identical to the number of type-B Goldstone modes for the orthonormal basis states. The prediction is numerically confirmed for the ${\rm SU}(2)$ spin-$s$ ferromagnetic Heisenberg model, the ${\rm SU}(2s+1)$ ferromagnetic model, and the staggered ${\rm SU}(3)$ spin-1 ferromagnetic biquadratic model. |
| title | Entanglement entropy for a type of scale-invariant states in two spatial dimensions and beyond: universal finite-size scaling |
| topic | Statistical Mechanics |
| url | https://arxiv.org/abs/2412.06396 |