Dualities in One-Dimensional Quantum Lattice Models: Topological Sectors
It has been a long-standing open problem to construct a general framework for relating the spectra of dual theories to each other. Here, we solve this problem for the case of one-dimensional quantum lattice models with symmetry-twisted boundary conditions. In Ref. [PRX Quantum 4, 020357], dualities...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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American Physical Society
2024-03-01
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| Series: | PRX Quantum |
| Online Access: | http://doi.org/10.1103/PRXQuantum.5.010338 |
| _version_ | 1827325020390555648 |
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| author | Laurens Lootens Clement Delcamp Frank Verstraete |
| author_facet | Laurens Lootens Clement Delcamp Frank Verstraete |
| author_sort | Laurens Lootens |
| collection | DOAJ |
| description | It has been a long-standing open problem to construct a general framework for relating the spectra of dual theories to each other. Here, we solve this problem for the case of one-dimensional quantum lattice models with symmetry-twisted boundary conditions. In Ref. [PRX Quantum 4, 020357], dualities are defined between (categorically) symmetric models that only differ in a choice of module category. Using matrix product operators, we construct from the data of module functors explicit symmetry operators preserving boundary conditions as well as intertwiners mapping topological sectors of dual models onto one another. We illustrate our construction with a family of examples that are in the duality class of the spin-1/2 Heisenberg XXZ model. One model has symmetry operators forming the fusion category Rep(S_{3}) of representations of the group S_{3}. We find that the mapping between its topological sectors and those of the XXZ model is associated with the nontrivial braided autoequivalence of the Drinfel’d center of Rep(S_{3}). |
| first_indexed | 2024-03-07T14:12:14Z |
| format | Article |
| id | doaj.art-fd47ee9d587746bca75f7c9f404f3150 |
| institution | Directory Open Access Journal |
| issn | 2691-3399 |
| language | English |
| last_indexed | 2024-03-07T14:12:14Z |
| publishDate | 2024-03-01 |
| publisher | American Physical Society |
| record_format | Article |
| series | PRX Quantum |
| spelling | doaj.art-fd47ee9d587746bca75f7c9f404f31502024-03-06T15:34:26ZengAmerican Physical SocietyPRX Quantum2691-33992024-03-015101033810.1103/PRXQuantum.5.010338Dualities in One-Dimensional Quantum Lattice Models: Topological SectorsLaurens LootensClement DelcampFrank VerstraeteIt has been a long-standing open problem to construct a general framework for relating the spectra of dual theories to each other. Here, we solve this problem for the case of one-dimensional quantum lattice models with symmetry-twisted boundary conditions. In Ref. [PRX Quantum 4, 020357], dualities are defined between (categorically) symmetric models that only differ in a choice of module category. Using matrix product operators, we construct from the data of module functors explicit symmetry operators preserving boundary conditions as well as intertwiners mapping topological sectors of dual models onto one another. We illustrate our construction with a family of examples that are in the duality class of the spin-1/2 Heisenberg XXZ model. One model has symmetry operators forming the fusion category Rep(S_{3}) of representations of the group S_{3}. We find that the mapping between its topological sectors and those of the XXZ model is associated with the nontrivial braided autoequivalence of the Drinfel’d center of Rep(S_{3}).http://doi.org/10.1103/PRXQuantum.5.010338 |
| spellingShingle | Laurens Lootens Clement Delcamp Frank Verstraete Dualities in One-Dimensional Quantum Lattice Models: Topological Sectors PRX Quantum |
| title | Dualities in One-Dimensional Quantum Lattice Models: Topological Sectors |
| title_full | Dualities in One-Dimensional Quantum Lattice Models: Topological Sectors |
| title_fullStr | Dualities in One-Dimensional Quantum Lattice Models: Topological Sectors |
| title_full_unstemmed | Dualities in One-Dimensional Quantum Lattice Models: Topological Sectors |
| title_short | Dualities in One-Dimensional Quantum Lattice Models: Topological Sectors |
| title_sort | dualities in one dimensional quantum lattice models topological sectors |
| url | http://doi.org/10.1103/PRXQuantum.5.010338 |
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