Entanglement entropy of U(1) quantum spin liquids
We here investigate the entanglement structure of the ground state of a (3+1)-dimensional U(1) quantum spin liquid, which is described by the deconfined phase of a compact U(1) gauge theory. A gapless photon is the only low-energy excitation, with matter existing as deconfined but gapped excitations...
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| Format: | Article |
| Language: | English |
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American Physical Society
2016
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| Online Access: | http://hdl.handle.net/1721.1/104897 https://orcid.org/0000-0001-5013-0186 |
| _version_ | 1811074115002433536 |
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| author | Pretko, Michael Senthil, Todadri |
| author2 | Massachusetts Institute of Technology. Department of Physics |
| author_facet | Massachusetts Institute of Technology. Department of Physics Pretko, Michael Senthil, Todadri |
| author_sort | Pretko, Michael |
| collection | MIT |
| description | We here investigate the entanglement structure of the ground state of a (3+1)-dimensional U(1) quantum spin liquid, which is described by the deconfined phase of a compact U(1) gauge theory. A gapless photon is the only low-energy excitation, with matter existing as deconfined but gapped excitations of the system. It is found that, for a given bipartition of the system, the elements of the entanglement spectrum can be grouped according to the electric flux between the two regions, leading to a useful interpretation of the entanglement spectrum in terms of electric charges living on the boundary. The entanglement spectrum is also given additional structure due to the presence of the gapless photon. Making use of the Bisognano-Wichmann theorem and a local thermal approximation, these two contributions to the entanglement (particle and photon) are recast in terms of boundary and bulk contributions, respectively. Both pieces of the entanglement structure give rise to universal subleading terms (relative to the area law) in the entanglement entropy, which are logarithmic in the system size (log L), as opposed to the subleading constant term in gapped topologically ordered systems. The photon subleading logarithm arises from the low-energy conformal field theory and is essentially local in character. The particle subleading logarithm arises due to the constraint of closed electric loops in the wave function and is shown to be the natural generalization of topological entanglement entropy to the U(1) spin liquid. This contribution to the entanglement entropy can be isolated by means of the Grover-Turner-Vishwanath construction (which generalizes the Kitaev-Preskill scheme to three dimensions). |
| first_indexed | 2024-09-23T09:43:24Z |
| format | Article |
| id | mit-1721.1/104897 |
| institution | Massachusetts Institute of Technology |
| language | English |
| last_indexed | 2024-09-23T09:43:24Z |
| publishDate | 2016 |
| publisher | American Physical Society |
| record_format | dspace |
| spelling | mit-1721.1/1048972022-09-30T16:29:47Z Entanglement entropy of U(1) quantum spin liquids Pretko, Michael Senthil, Todadri Massachusetts Institute of Technology. Department of Physics Pretko, Michael Senthil, Todadri We here investigate the entanglement structure of the ground state of a (3+1)-dimensional U(1) quantum spin liquid, which is described by the deconfined phase of a compact U(1) gauge theory. A gapless photon is the only low-energy excitation, with matter existing as deconfined but gapped excitations of the system. It is found that, for a given bipartition of the system, the elements of the entanglement spectrum can be grouped according to the electric flux between the two regions, leading to a useful interpretation of the entanglement spectrum in terms of electric charges living on the boundary. The entanglement spectrum is also given additional structure due to the presence of the gapless photon. Making use of the Bisognano-Wichmann theorem and a local thermal approximation, these two contributions to the entanglement (particle and photon) are recast in terms of boundary and bulk contributions, respectively. Both pieces of the entanglement structure give rise to universal subleading terms (relative to the area law) in the entanglement entropy, which are logarithmic in the system size (log L), as opposed to the subleading constant term in gapped topologically ordered systems. The photon subleading logarithm arises from the low-energy conformal field theory and is essentially local in character. The particle subleading logarithm arises due to the constraint of closed electric loops in the wave function and is shown to be the natural generalization of topological entanglement entropy to the U(1) spin liquid. This contribution to the entanglement entropy can be isolated by means of the Grover-Turner-Vishwanath construction (which generalizes the Kitaev-Preskill scheme to three dimensions). National Science Foundation (U.S.) (Grant DMR-1305741) Simons Foundation. Simons Investigator Award 2016-10-20T20:23:01Z 2016-10-20T20:23:01Z 2016-09 2016-07 2016-09-08T22:00:22Z Article http://purl.org/eprint/type/JournalArticle 2469-9950 2469-9969 http://hdl.handle.net/1721.1/104897 Pretko, Michael, and T. Senthil. “Entanglement Entropy of U (1) Quantum Spin Liquids.” Physical Review B 94.12 (2016): n. pag. © 2016 American Physical Society https://orcid.org/0000-0001-5013-0186 en http://dx.doi.org/10.1103/PhysRevB.94.125112 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 | Pretko, Michael Senthil, Todadri Entanglement entropy of U(1) quantum spin liquids |
| title | Entanglement entropy of U(1) quantum spin liquids |
| title_full | Entanglement entropy of U(1) quantum spin liquids |
| title_fullStr | Entanglement entropy of U(1) quantum spin liquids |
| title_full_unstemmed | Entanglement entropy of U(1) quantum spin liquids |
| title_short | Entanglement entropy of U(1) quantum spin liquids |
| title_sort | entanglement entropy of u 1 quantum spin liquids |
| url | http://hdl.handle.net/1721.1/104897 https://orcid.org/0000-0001-5013-0186 |
| work_keys_str_mv | AT pretkomichael entanglemententropyofu1quantumspinliquids AT senthiltodadri entanglemententropyofu1quantumspinliquids |