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- Publisher Website: 10.1103/PhysRevB.106.094415
- Scopus: eid_2-s2.0-85138177016
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Article: Topological disorder parameter: A many-body invariant to characterize gapped quantum phases
Title | Topological disorder parameter: A many-body invariant to characterize gapped quantum phases |
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Authors | |
Issue Date | 2022 |
Citation | Physical Review B, 2022, v. 106, n. 9, article no. 094415 How to Cite? |
Abstract | We introduce a many-body topological invariant, called the topological disorder parameter (TDP), to characterize gapped quantum phases with global internal symmetry in 2+1 dimensions. TDP is defined as the constant correction that appears in the ground-state expectation value of a partial symmetry transformation applied to a connected spatial region M, the absolute value of which scales generically as exp(-αl+γ) where l is the perimeter of M and γ is the TDP. Motivated by a topological quantum field theory interpretation of the operator, we show that eγ can be related to the quantum dimension of the symmetry defect, and provide a general formula for γ when the entanglement Hamiltonian of the topological phase can be described by a (1+1)-dimensional conformal field theory (CFT). A special case of TDP is equivalent to the topological Rényi entanglement entropy when the symmetry is the cyclic permutation of the replica of the gapped phase. We then investigate several examples of lattice models of topological phases, both analytically and numerically, in particular when the assumption of having a CFT edge theory is not satisfied. We also consider an example of partial translation symmetry in Wen's plaquette model and show that the result can be understood using the edge CFT. Our results establish an alternative tool to detect quantum topological order. |
Persistent Identifier | http://hdl.handle.net/10722/330854 |
ISSN | 2023 Impact Factor: 3.2 2023 SCImago Journal Rankings: 1.345 |
ISI Accession Number ID |
DC Field | Value | Language |
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dc.contributor.author | Chen, Bin Bin | - |
dc.contributor.author | Tu, Hong Hao | - |
dc.contributor.author | Meng, Zi Yang | - |
dc.contributor.author | Cheng, Meng | - |
dc.date.accessioned | 2023-09-05T12:15:16Z | - |
dc.date.available | 2023-09-05T12:15:16Z | - |
dc.date.issued | 2022 | - |
dc.identifier.citation | Physical Review B, 2022, v. 106, n. 9, article no. 094415 | - |
dc.identifier.issn | 2469-9950 | - |
dc.identifier.uri | http://hdl.handle.net/10722/330854 | - |
dc.description.abstract | We introduce a many-body topological invariant, called the topological disorder parameter (TDP), to characterize gapped quantum phases with global internal symmetry in 2+1 dimensions. TDP is defined as the constant correction that appears in the ground-state expectation value of a partial symmetry transformation applied to a connected spatial region M, the absolute value of which scales generically as exp(-αl+γ) where l is the perimeter of M and γ is the TDP. Motivated by a topological quantum field theory interpretation of the operator, we show that eγ can be related to the quantum dimension of the symmetry defect, and provide a general formula for γ when the entanglement Hamiltonian of the topological phase can be described by a (1+1)-dimensional conformal field theory (CFT). A special case of TDP is equivalent to the topological Rényi entanglement entropy when the symmetry is the cyclic permutation of the replica of the gapped phase. We then investigate several examples of lattice models of topological phases, both analytically and numerically, in particular when the assumption of having a CFT edge theory is not satisfied. We also consider an example of partial translation symmetry in Wen's plaquette model and show that the result can be understood using the edge CFT. Our results establish an alternative tool to detect quantum topological order. | - |
dc.language | eng | - |
dc.relation.ispartof | Physical Review B | - |
dc.title | Topological disorder parameter: A many-body invariant to characterize gapped quantum phases | - |
dc.type | Article | - |
dc.description.nature | link_to_subscribed_fulltext | - |
dc.identifier.doi | 10.1103/PhysRevB.106.094415 | - |
dc.identifier.scopus | eid_2-s2.0-85138177016 | - |
dc.identifier.volume | 106 | - |
dc.identifier.issue | 9 | - |
dc.identifier.spage | article no. 094415 | - |
dc.identifier.epage | article no. 094415 | - |
dc.identifier.eissn | 2469-9969 | - |
dc.identifier.isi | WOS:000903820500001 | - |