Exact projected entangled pair ground states with topological Euler invariant
Abstract We report on a class of gapped projected entangled pair states (PEPS) with non-trivial Euler topology motivated by recent progress in band geometry. In the non-interacting limit, these systems have optimal conditions relating to saturation of quantum geometrical bounds, allowing for parent...
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| Format: | Article |
| Language: | English |
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Nature Portfolio
2025-01-01
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| Series: | Nature Communications |
| Online Access: | https://doi.org/10.1038/s41467-024-55484-4 |
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| author | Thorsten B. Wahl Wojciech J. Jankowski Adrien Bouhon Gaurav Chaudhary Robert-Jan Slager |
| author_facet | Thorsten B. Wahl Wojciech J. Jankowski Adrien Bouhon Gaurav Chaudhary Robert-Jan Slager |
| author_sort | Thorsten B. Wahl |
| collection | DOAJ |
| description | Abstract We report on a class of gapped projected entangled pair states (PEPS) with non-trivial Euler topology motivated by recent progress in band geometry. In the non-interacting limit, these systems have optimal conditions relating to saturation of quantum geometrical bounds, allowing for parent Hamiltonians whose lowest bands are completely flat and which have the PEPS as unique ground states. Protected by crystalline symmetries, these states evade restrictions on capturing tenfold-way topological features with gapped PEPS. These PEPS thus form the first tensor network representative of a non-interacting, gapped two-dimensional topological phase, similar to the Kitaev chain in one dimension. Using unitary circuits, we then formulate interacting variants of these PEPS and corresponding gapped parent Hamiltonians. We reveal characteristic entanglement features shared between the free-fermionic and interacting states with Euler topology. Our results hence provide a rich platform of PEPS models that have, unexpectedly, a finite topological invariant, forming the basis for new spin liquids, quantum Hall physics, and quantum information pursuits. |
| format | Article |
| id | doaj-art-3bbda5d7191d443492f0ecdb456f268c |
| institution | Kabale University |
| issn | 2041-1723 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | Nature Portfolio |
| record_format | Article |
| series | Nature Communications |
| spelling | doaj-art-3bbda5d7191d443492f0ecdb456f268c2025-01-05T12:36:57ZengNature PortfolioNature Communications2041-17232025-01-011611910.1038/s41467-024-55484-4Exact projected entangled pair ground states with topological Euler invariantThorsten B. Wahl0Wojciech J. Jankowski1Adrien Bouhon2Gaurav Chaudhary3Robert-Jan Slager4TCM Group, Cavendish Laboratory, Department of PhysicsTCM Group, Cavendish Laboratory, Department of PhysicsTCM Group, Cavendish Laboratory, Department of PhysicsTCM Group, Cavendish Laboratory, Department of PhysicsTCM Group, Cavendish Laboratory, Department of PhysicsAbstract We report on a class of gapped projected entangled pair states (PEPS) with non-trivial Euler topology motivated by recent progress in band geometry. In the non-interacting limit, these systems have optimal conditions relating to saturation of quantum geometrical bounds, allowing for parent Hamiltonians whose lowest bands are completely flat and which have the PEPS as unique ground states. Protected by crystalline symmetries, these states evade restrictions on capturing tenfold-way topological features with gapped PEPS. These PEPS thus form the first tensor network representative of a non-interacting, gapped two-dimensional topological phase, similar to the Kitaev chain in one dimension. Using unitary circuits, we then formulate interacting variants of these PEPS and corresponding gapped parent Hamiltonians. We reveal characteristic entanglement features shared between the free-fermionic and interacting states with Euler topology. Our results hence provide a rich platform of PEPS models that have, unexpectedly, a finite topological invariant, forming the basis for new spin liquids, quantum Hall physics, and quantum information pursuits.https://doi.org/10.1038/s41467-024-55484-4 |
| spellingShingle | Thorsten B. Wahl Wojciech J. Jankowski Adrien Bouhon Gaurav Chaudhary Robert-Jan Slager Exact projected entangled pair ground states with topological Euler invariant Nature Communications |
| title | Exact projected entangled pair ground states with topological Euler invariant |
| title_full | Exact projected entangled pair ground states with topological Euler invariant |
| title_fullStr | Exact projected entangled pair ground states with topological Euler invariant |
| title_full_unstemmed | Exact projected entangled pair ground states with topological Euler invariant |
| title_short | Exact projected entangled pair ground states with topological Euler invariant |
| title_sort | exact projected entangled pair ground states with topological euler invariant |
| url | https://doi.org/10.1038/s41467-024-55484-4 |
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