Z_{2} topologically ordered phases on a simple hyperbolic lattice
In this paper, we consider 2D Z_{2} topologically ordered phases (Z_{2} toric code and the modified surface code) on a simple hyperbolic lattice. Introducing a 2D lattice consisting of the product of a 1D Cayley tree and a 1D conventional lattice, we investigate two topological quantities of the Z_{...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
American Physical Society
2022-11-01
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| Series: | Physical Review Research |
| Online Access: | http://doi.org/10.1103/PhysRevResearch.4.043099 |
| _version_ | 1797210552461688832 |
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| author | Hiromi Ebisu Bo Han |
| author_facet | Hiromi Ebisu Bo Han |
| author_sort | Hiromi Ebisu |
| collection | DOAJ |
| description | In this paper, we consider 2D Z_{2} topologically ordered phases (Z_{2} toric code and the modified surface code) on a simple hyperbolic lattice. Introducing a 2D lattice consisting of the product of a 1D Cayley tree and a 1D conventional lattice, we investigate two topological quantities of the Z_{2} topologically ordered phases on this lattice: the ground state degeneracy on a closed surface and the topological entanglement entropy. We find that both quantities depend on the number of branches and the generation of the Cayley tree. We attribute these results to a huge number of superselection sectors of anyons. |
| first_indexed | 2024-04-24T10:12:25Z |
| format | Article |
| id | doaj.art-0097aa6df6924145a1282713b7b39762 |
| institution | Directory Open Access Journal |
| issn | 2643-1564 |
| language | English |
| last_indexed | 2024-04-24T10:12:25Z |
| publishDate | 2022-11-01 |
| publisher | American Physical Society |
| record_format | Article |
| series | Physical Review Research |
| spelling | doaj.art-0097aa6df6924145a1282713b7b397622024-04-12T17:26:02ZengAmerican Physical SocietyPhysical Review Research2643-15642022-11-014404309910.1103/PhysRevResearch.4.043099Z_{2} topologically ordered phases on a simple hyperbolic latticeHiromi EbisuBo HanIn this paper, we consider 2D Z_{2} topologically ordered phases (Z_{2} toric code and the modified surface code) on a simple hyperbolic lattice. Introducing a 2D lattice consisting of the product of a 1D Cayley tree and a 1D conventional lattice, we investigate two topological quantities of the Z_{2} topologically ordered phases on this lattice: the ground state degeneracy on a closed surface and the topological entanglement entropy. We find that both quantities depend on the number of branches and the generation of the Cayley tree. We attribute these results to a huge number of superselection sectors of anyons.http://doi.org/10.1103/PhysRevResearch.4.043099 |
| spellingShingle | Hiromi Ebisu Bo Han Z_{2} topologically ordered phases on a simple hyperbolic lattice Physical Review Research |
| title | Z_{2} topologically ordered phases on a simple hyperbolic lattice |
| title_full | Z_{2} topologically ordered phases on a simple hyperbolic lattice |
| title_fullStr | Z_{2} topologically ordered phases on a simple hyperbolic lattice |
| title_full_unstemmed | Z_{2} topologically ordered phases on a simple hyperbolic lattice |
| title_short | Z_{2} topologically ordered phases on a simple hyperbolic lattice |
| title_sort | z 2 topologically ordered phases on a simple hyperbolic lattice |
| url | http://doi.org/10.1103/PhysRevResearch.4.043099 |
| work_keys_str_mv | AT hiromiebisu z2topologicallyorderedphasesonasimplehyperboliclattice AT bohan z2topologicallyorderedphasesonasimplehyperboliclattice |