Gapped spin liquid with Z[subscript 2] topological order for the kagome Heisenberg model
We apply the symmetric tensor network state (TNS) to study the nearest-neighbor spin-1/2 antiferromagnetic Heisenberg model on the kagome lattice. Our method keeps track of the global and gauge symmetries in the TNS update procedure and in tensor renormalization group (TRG) calculations. We also int...
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| Format: | Article |
| Language: | English |
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American Physical Society
2017
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| Online Access: | http://hdl.handle.net/1721.1/109742 https://orcid.org/0000-0002-5874-581X |
| _version_ | 1811093242407550976 |
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| author | Mei, Jia-Wei Chen, Ji-Yao He, Huan Wen, Xiao-Gang |
| author2 | Massachusetts Institute of Technology. Department of Physics |
| author_facet | Massachusetts Institute of Technology. Department of Physics Mei, Jia-Wei Chen, Ji-Yao He, Huan Wen, Xiao-Gang |
| author_sort | Mei, Jia-Wei |
| collection | MIT |
| description | We apply the symmetric tensor network state (TNS) to study the nearest-neighbor spin-1/2 antiferromagnetic Heisenberg model on the kagome lattice. Our method keeps track of the global and gauge symmetries in the TNS update procedure and in tensor renormalization group (TRG) calculations. We also introduce a very sensitive probe for the gap of the ground state—the modular matrices, which can also determine the topological order if the ground state is gapped. We find that the ground state of the Heisenberg model on the kagome lattice is a gapped spin liquid with the Z[subscript 2] topological order (or toric code type), which has a long correlation length ξ∼10 unit cells. We justify that the TRG method can handle very large systems with thousands of spins. Such a long ξ explains the gapless behaviors observed in simulations on smaller systems with less than 300 spins or shorter than the length of 10 unit cells. We also discuss experimental implications of the topological excitations encoded in our symmetric tensors. |
| first_indexed | 2024-09-23T15:42:10Z |
| format | Article |
| id | mit-1721.1/109742 |
| institution | Massachusetts Institute of Technology |
| language | English |
| last_indexed | 2024-09-23T15:42:10Z |
| publishDate | 2017 |
| publisher | American Physical Society |
| record_format | dspace |
| spelling | mit-1721.1/1097422022-09-29T15:36:31Z Gapped spin liquid with Z[subscript 2] topological order for the kagome Heisenberg model Gapped spin liquid with Z2 topological order for the kagome Heisenberg model Mei, Jia-Wei Chen, Ji-Yao He, Huan Wen, Xiao-Gang Massachusetts Institute of Technology. Department of Physics Wen, Xiao-Gang We apply the symmetric tensor network state (TNS) to study the nearest-neighbor spin-1/2 antiferromagnetic Heisenberg model on the kagome lattice. Our method keeps track of the global and gauge symmetries in the TNS update procedure and in tensor renormalization group (TRG) calculations. We also introduce a very sensitive probe for the gap of the ground state—the modular matrices, which can also determine the topological order if the ground state is gapped. We find that the ground state of the Heisenberg model on the kagome lattice is a gapped spin liquid with the Z[subscript 2] topological order (or toric code type), which has a long correlation length ξ∼10 unit cells. We justify that the TRG method can handle very large systems with thousands of spins. Such a long ξ explains the gapless behaviors observed in simulations on smaller systems with less than 300 spins or shorter than the length of 10 unit cells. We also discuss experimental implications of the topological excitations encoded in our symmetric tensors. National Science Foundation (U.S.) (Grant DMR-1506475) National Natural Science Foundation (China) (11274192) 2017-06-08T15:32:38Z 2017-06-08T15:32:38Z 2017-06 2017-05 2017-06-05T22:00:04Z Article http://purl.org/eprint/type/JournalArticle 2469-9950 2469-9969 http://hdl.handle.net/1721.1/109742 Mei, Jia-Wei et al. “Gapped Spin Liquid with Z 2 Topological Order for the Kagome Heisenberg Model.” Physical Review B 95.23 (2017): n. pag. © 2017 American Physical Society https://orcid.org/0000-0002-5874-581X en http://dx.doi.org/10.1103/PhysRevB.95.235107 Physical Review B Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use. American Physical Society application/pdf American Physical Society American Physical Society |
| spellingShingle | Mei, Jia-Wei Chen, Ji-Yao He, Huan Wen, Xiao-Gang Gapped spin liquid with Z[subscript 2] topological order for the kagome Heisenberg model |
| title | Gapped spin liquid with Z[subscript 2] topological order for the kagome Heisenberg model |
| title_full | Gapped spin liquid with Z[subscript 2] topological order for the kagome Heisenberg model |
| title_fullStr | Gapped spin liquid with Z[subscript 2] topological order for the kagome Heisenberg model |
| title_full_unstemmed | Gapped spin liquid with Z[subscript 2] topological order for the kagome Heisenberg model |
| title_short | Gapped spin liquid with Z[subscript 2] topological order for the kagome Heisenberg model |
| title_sort | gapped spin liquid with z subscript 2 topological order for the kagome heisenberg model |
| url | http://hdl.handle.net/1721.1/109742 https://orcid.org/0000-0002-5874-581X |
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