Entanglement entropy for the one-dimensional flat-band ferromagnetic Tasaki model: spontaneous symmetry breaking with one type-B Goldstone mode
Fuente:
arXiv
Salvato in:
| Autori principali: | , , , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2024
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866917875507265536 |
|---|---|
| author | Zhou, Huan-Qiang Shi, Qian-Qian McCulloch, Ian P. Fjærestad, J. O. |
| author_facet | Zhou, Huan-Qiang Shi, Qian-Qian McCulloch, Ian P. Fjærestad, J. O. |
| contents | The one-dimensional flat-band ferromagnetic Tasaki model exhibits spontaneous symmetry breaking from ${\rm SU}(2)$ to ${\rm U}(1)$ with one type-B Goldstone mode, featuring that the highest weight state is entangled at quarter filling, but there is always a choice to keep the highest weight state unentangled away from quarter filling. It is found that the ground-state degeneracies under both periodic and open boundary conditions constitute essentially the Fibonacci sequences, behaving asymptotically as the golden spiral - a self-similar geometric object. A set of orthonormal basis states are generated from the repeated action of the lowering operator of the symmetry group ${\rm SU}(2)$ on the highest weight state at a specific filling. In particular, it is possible to construct the orthonormal basis states reflecting an abstract fractal underlying the ground-state subspace, which are permutation-invariant away from quarter filling, but not at quarter filling. As a consequence, there exists a singularity that accounts for the emergence of the saturated flat-band ferromagnetism at quarter filling. We perform a systematic finite system-size scaling analysis of the entanglement entropy, thus confirming that it scales logarithmically with the block size in the thermodynamic limit, with the prefactor being half the number of type-B Goldstone modes, for the orthonormal basis states at and away from quarter filling. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_15724 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Entanglement entropy for the one-dimensional flat-band ferromagnetic Tasaki model: spontaneous symmetry breaking with one type-B Goldstone mode Zhou, Huan-Qiang Shi, Qian-Qian McCulloch, Ian P. Fjærestad, J. O. Strongly Correlated Electrons The one-dimensional flat-band ferromagnetic Tasaki model exhibits spontaneous symmetry breaking from ${\rm SU}(2)$ to ${\rm U}(1)$ with one type-B Goldstone mode, featuring that the highest weight state is entangled at quarter filling, but there is always a choice to keep the highest weight state unentangled away from quarter filling. It is found that the ground-state degeneracies under both periodic and open boundary conditions constitute essentially the Fibonacci sequences, behaving asymptotically as the golden spiral - a self-similar geometric object. A set of orthonormal basis states are generated from the repeated action of the lowering operator of the symmetry group ${\rm SU}(2)$ on the highest weight state at a specific filling. In particular, it is possible to construct the orthonormal basis states reflecting an abstract fractal underlying the ground-state subspace, which are permutation-invariant away from quarter filling, but not at quarter filling. As a consequence, there exists a singularity that accounts for the emergence of the saturated flat-band ferromagnetism at quarter filling. We perform a systematic finite system-size scaling analysis of the entanglement entropy, thus confirming that it scales logarithmically with the block size in the thermodynamic limit, with the prefactor being half the number of type-B Goldstone modes, for the orthonormal basis states at and away from quarter filling. |
| title | Entanglement entropy for the one-dimensional flat-band ferromagnetic Tasaki model: spontaneous symmetry breaking with one type-B Goldstone mode |
| topic | Strongly Correlated Electrons |
| url | https://arxiv.org/abs/2412.15724 |