Symmetry-protected topological phases, conformal criticalities, and duality in exactly solvable SO($n$) spin chains
Fuente:
arXiv
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2023
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866913574616563712 |
|---|---|
| author | Chulliparambil, Sreejith Zhang, Hua-Chen Tu, Hong-Hao |
| author_facet | Chulliparambil, Sreejith Zhang, Hua-Chen Tu, Hong-Hao |
| contents | We introduce a family of SO($n$)-symmetric spin chains which generalize the transverse-field Ising chain for $n=1$. These spin chains are defined with Gamma matrices and can be exactly solved by mapping to $n$ species of itinerant Majorana fermions coupled to a static $\mathbb{Z}_2$ gauge field. Their phase diagrams include a critical point described by the $\mathrm{Spin}(n)_{1}$ conformal field theory as well as two distinct gapped phases. We show that one of the gapped phases is a trivial phase and the other realizes a symmetry-protected topological phase when $n \geq 2$. These two gapped phases are proved to be related to each other by a Kramers-Wannier duality. Furthermore, other elegant structures in the transverse-field Ising chain, such as the infinite-dimensional Onsager algebra, also carry over to our models. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2305_03398 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Symmetry-protected topological phases, conformal criticalities, and duality in exactly solvable SO($n$) spin chains Chulliparambil, Sreejith Zhang, Hua-Chen Tu, Hong-Hao Strongly Correlated Electrons Statistical Mechanics High Energy Physics - Theory Mathematical Physics Quantum Physics We introduce a family of SO($n$)-symmetric spin chains which generalize the transverse-field Ising chain for $n=1$. These spin chains are defined with Gamma matrices and can be exactly solved by mapping to $n$ species of itinerant Majorana fermions coupled to a static $\mathbb{Z}_2$ gauge field. Their phase diagrams include a critical point described by the $\mathrm{Spin}(n)_{1}$ conformal field theory as well as two distinct gapped phases. We show that one of the gapped phases is a trivial phase and the other realizes a symmetry-protected topological phase when $n \geq 2$. These two gapped phases are proved to be related to each other by a Kramers-Wannier duality. Furthermore, other elegant structures in the transverse-field Ising chain, such as the infinite-dimensional Onsager algebra, also carry over to our models. |
| title | Symmetry-protected topological phases, conformal criticalities, and duality in exactly solvable SO($n$) spin chains |
| topic | Strongly Correlated Electrons Statistical Mechanics High Energy Physics - Theory Mathematical Physics Quantum Physics |
| url | https://arxiv.org/abs/2305.03398 |