“Not- A”, representation symmetry-protected topological, and Potts phases in an S3 -invariant chain
We analyze in depth an S 3 -invariant nearest-neighbor quantum chain in the region of a U ( 1 ) -invariant self-dual multicritical point. We find four distinct proximate gapped phases. One has three-state Potts order, corresponding to topological order in a parafermionic formulation. Another has “...
| Main Authors: | , , |
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| Format: | Journal article |
| Language: | English |
| Published: |
American Physical Society
2020
|
| _version_ | 1797094098451038208 |
|---|---|
| author | O’Brien. E Vernier, E Fendley, P |
| author_facet | O’Brien. E Vernier, E Fendley, P |
| author_sort | O’Brien. E |
| collection | OXFORD |
| description | We analyze in depth an
S
3
-invariant nearest-neighbor quantum chain in the region of a
U
(
1
)
-invariant self-dual multicritical point. We find four distinct proximate gapped phases. One has three-state Potts order, corresponding to topological order in a parafermionic formulation. Another has “representation” symmetry-protected topological (RSPT) order, while its dual exhibits an unusual “not-
A
” order, where the spins prefer to align in two of the three directions. Within each of the four phases, we find a frustration-free point with exact ground state(s). The exact ground states in the not-
A
phase are product states, each an equal-amplitude sum over all states where one of the three spin states on each site is absent. Their dual, the RSPT ground state, is a matrix product state similar to that of Affleck-Kennedy-Lieb-Tasaki. A field-theory analysis shows that all transition lines are in the universality class of the critical three-state Potts model. They provide a lattice realization of a flow from a free-boson field theory to the Potts conformal field theory. |
| first_indexed | 2024-03-07T04:09:24Z |
| format | Journal article |
| id | oxford-uuid:c7537573-c2ec-4cf1-a48c-7ff1161b179b |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T04:09:24Z |
| publishDate | 2020 |
| publisher | American Physical Society |
| record_format | dspace |
| spelling | oxford-uuid:c7537573-c2ec-4cf1-a48c-7ff1161b179b2022-03-27T06:44:11Z“Not- A”, representation symmetry-protected topological, and Potts phases in an S3 -invariant chainJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:c7537573-c2ec-4cf1-a48c-7ff1161b179bEnglishSymplectic ElementsAmerican Physical Society2020O’Brien. EVernier, EFendley, PWe analyze in depth an S 3 -invariant nearest-neighbor quantum chain in the region of a U ( 1 ) -invariant self-dual multicritical point. We find four distinct proximate gapped phases. One has three-state Potts order, corresponding to topological order in a parafermionic formulation. Another has “representation” symmetry-protected topological (RSPT) order, while its dual exhibits an unusual “not- A ” order, where the spins prefer to align in two of the three directions. Within each of the four phases, we find a frustration-free point with exact ground state(s). The exact ground states in the not- A phase are product states, each an equal-amplitude sum over all states where one of the three spin states on each site is absent. Their dual, the RSPT ground state, is a matrix product state similar to that of Affleck-Kennedy-Lieb-Tasaki. A field-theory analysis shows that all transition lines are in the universality class of the critical three-state Potts model. They provide a lattice realization of a flow from a free-boson field theory to the Potts conformal field theory. |
| spellingShingle | O’Brien. E Vernier, E Fendley, P “Not- A”, representation symmetry-protected topological, and Potts phases in an S3 -invariant chain |
| title | “Not- A”, representation symmetry-protected topological, and Potts phases in an S3 -invariant chain |
| title_full | “Not- A”, representation symmetry-protected topological, and Potts phases in an S3 -invariant chain |
| title_fullStr | “Not- A”, representation symmetry-protected topological, and Potts phases in an S3 -invariant chain |
| title_full_unstemmed | “Not- A”, representation symmetry-protected topological, and Potts phases in an S3 -invariant chain |
| title_short | “Not- A”, representation symmetry-protected topological, and Potts phases in an S3 -invariant chain |
| title_sort | not a representation symmetry protected topological and potts phases in an s3 invariant chain |
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