Classifying phases protected by matrix product operator symmetries using matrix product states
We classify the different ways in which matrix product states (MPSs) can stay invariant under the action of matrix product operator (MPO) symmetries. This is achieved through a local characterization of how the MPSs, that generate a ground space, remain invariant under a global MPO symmetry. This ch...
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| Format: | Article |
| Language: | English |
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Verein zur Förderung des Open Access Publizierens in den Quantenwissenschaften
2023-02-01
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| Series: | Quantum |
| Online Access: | https://quantum-journal.org/papers/q-2023-02-21-927/pdf/ |
| _version_ | 1797901050637713408 |
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| author | José Garre-Rubio Laurens Lootens András Molnár |
| author_facet | José Garre-Rubio Laurens Lootens András Molnár |
| author_sort | José Garre-Rubio |
| collection | DOAJ |
| description | We classify the different ways in which matrix product states (MPSs) can stay invariant under the action of matrix product operator (MPO) symmetries. This is achieved through a local characterization of how the MPSs, that generate a ground space, remain invariant under a global MPO symmetry. This characterization yields a set of quantities satisfying the coupled pentagon equations, associated with a module category over the fusion category that describes the MPO symmetry. Equivalence classes of these quantities provide complete invariants for an MPO symmetry protected phase: they are robust under continuous deformations of the MPS tensor, and two phases with the same equivalence class can be connected by a symmetric gapped path. Our techniques match and extend the known renormalization fixed point classifications and facilitate the numerical study of these systems. For MPO symmetries described by a group, we recover the symmetry protected topological order classification for unique and degenerate ground states. Moreover, we study the interplay between time reversal symmetry and an MPO symmetry and we also provide examples of our classification, together with explicit constructions based on groups. Finally, we elaborate on the connection between our setup and gapped boundaries of two-dimensional topological systems, where MPO symmetries also play a key role. |
| first_indexed | 2024-04-10T08:54:40Z |
| format | Article |
| id | doaj.art-9dcebedbf49d4fcd9d4d1ef7a6e171cd |
| institution | Directory Open Access Journal |
| issn | 2521-327X |
| language | English |
| last_indexed | 2024-04-10T08:54:40Z |
| publishDate | 2023-02-01 |
| publisher | Verein zur Förderung des Open Access Publizierens in den Quantenwissenschaften |
| record_format | Article |
| series | Quantum |
| spelling | doaj.art-9dcebedbf49d4fcd9d4d1ef7a6e171cd2023-02-21T17:02:18ZengVerein zur Förderung des Open Access Publizierens in den QuantenwissenschaftenQuantum2521-327X2023-02-01792710.22331/q-2023-02-21-92710.22331/q-2023-02-21-927Classifying phases protected by matrix product operator symmetries using matrix product statesJosé Garre-RubioLaurens LootensAndrás MolnárWe classify the different ways in which matrix product states (MPSs) can stay invariant under the action of matrix product operator (MPO) symmetries. This is achieved through a local characterization of how the MPSs, that generate a ground space, remain invariant under a global MPO symmetry. This characterization yields a set of quantities satisfying the coupled pentagon equations, associated with a module category over the fusion category that describes the MPO symmetry. Equivalence classes of these quantities provide complete invariants for an MPO symmetry protected phase: they are robust under continuous deformations of the MPS tensor, and two phases with the same equivalence class can be connected by a symmetric gapped path. Our techniques match and extend the known renormalization fixed point classifications and facilitate the numerical study of these systems. For MPO symmetries described by a group, we recover the symmetry protected topological order classification for unique and degenerate ground states. Moreover, we study the interplay between time reversal symmetry and an MPO symmetry and we also provide examples of our classification, together with explicit constructions based on groups. Finally, we elaborate on the connection between our setup and gapped boundaries of two-dimensional topological systems, where MPO symmetries also play a key role.https://quantum-journal.org/papers/q-2023-02-21-927/pdf/ |
| spellingShingle | José Garre-Rubio Laurens Lootens András Molnár Classifying phases protected by matrix product operator symmetries using matrix product states Quantum |
| title | Classifying phases protected by matrix product operator symmetries using matrix product states |
| title_full | Classifying phases protected by matrix product operator symmetries using matrix product states |
| title_fullStr | Classifying phases protected by matrix product operator symmetries using matrix product states |
| title_full_unstemmed | Classifying phases protected by matrix product operator symmetries using matrix product states |
| title_short | Classifying phases protected by matrix product operator symmetries using matrix product states |
| title_sort | classifying phases protected by matrix product operator symmetries using matrix product states |
| url | https://quantum-journal.org/papers/q-2023-02-21-927/pdf/ |
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