String-net condensation and topological phases in quantum spin systems
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Physics, 2006.
| Main Author: | |
|---|---|
| Other Authors: | |
| Format: | Thesis |
| Language: | eng |
| Published: |
Massachusetts Institute of Technology
2008
|
| Subjects: | |
| Online Access: | http://dspace.mit.edu/handle/1721.1/36810 http://hdl.handle.net/1721.1/36810 |
| _version_ | 1811068499678724096 |
|---|---|
| author | Levin, Michael Aaron, Ph. D. Massachusetts Institute of Technology |
| author2 | Xiao-Gang Wen. |
| author_facet | Xiao-Gang Wen. Levin, Michael Aaron, Ph. D. Massachusetts Institute of Technology |
| author_sort | Levin, Michael Aaron, Ph. D. Massachusetts Institute of Technology |
| collection | MIT |
| description | Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Physics, 2006. |
| first_indexed | 2024-09-23T07:56:54Z |
| format | Thesis |
| id | mit-1721.1/36810 |
| institution | Massachusetts Institute of Technology |
| language | eng |
| last_indexed | 2024-09-23T07:56:54Z |
| publishDate | 2008 |
| publisher | Massachusetts Institute of Technology |
| record_format | dspace |
| spelling | mit-1721.1/368102019-04-09T15:40:51Z String-net condensation and topological phases in quantum spin systems Levin, Michael Aaron, Ph. D. Massachusetts Institute of Technology Xiao-Gang Wen. Massachusetts Institute of Technology. Dept. of Physics. Massachusetts Institute of Technology. Dept. of Physics. Physics. Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Physics, 2006. Includes bibliographical references (p. 81-86). For many years, it was thought that Landau's theory of symmetry breaking could describe essentially all phases and phase transitions. However, in the last twenty years, it has become clear that at zero temperature, quantum mechanics allows for the possibility of new phases of matter beyond the Landau paradigm. In this thesis, we develop a general theoretical framework for these "exotic phases" analogous to Landau's framework for symmetry breaking phases. We focus on a particular type of exotic phase, known as "topological phases", and a particular physical realization of topological phases - namely frustrated quantum magnets. Our approach is based on a new physical picture for topological phases. We argue that, just as symmetry breaking phases originate from the condensation of particles, topological phases originate from the condensation of extended objects called "string-nets." Using this picture we show that, just as symmetry breaking phases can be classified using symmetry groups, topological phases can be classified using objects known as "tensor categories." (cont.) In addition, just as symmetry breaking order manifests itself in local correlations in a ground state wave function, topological order manifests itself in nonlocal correlations or quantum entanglement. We introduce a new quantity - called "topological entropy" - which measures precisely this nonlocal entanglement. Many of our results are applicable to other (non-topological) exotic phases. by Michael Aaron Levin. Ph.D. 2008-02-28T16:29:02Z 2008-02-28T16:29:02Z 2006 2006 Thesis http://dspace.mit.edu/handle/1721.1/36810 http://hdl.handle.net/1721.1/36810 81896230 eng M.I.T. theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. See provided URL for inquiries about permission. http://dspace.mit.edu/handle/1721.1/36810 http://dspace.mit.edu/handle/1721.1/7582 86 p. application/pdf Massachusetts Institute of Technology |
| spellingShingle | Physics. Levin, Michael Aaron, Ph. D. Massachusetts Institute of Technology String-net condensation and topological phases in quantum spin systems |
| title | String-net condensation and topological phases in quantum spin systems |
| title_full | String-net condensation and topological phases in quantum spin systems |
| title_fullStr | String-net condensation and topological phases in quantum spin systems |
| title_full_unstemmed | String-net condensation and topological phases in quantum spin systems |
| title_short | String-net condensation and topological phases in quantum spin systems |
| title_sort | string net condensation and topological phases in quantum spin systems |
| topic | Physics. |
| url | http://dspace.mit.edu/handle/1721.1/36810 http://hdl.handle.net/1721.1/36810 |
| work_keys_str_mv | AT levinmichaelaaronphdmassachusettsinstituteoftechnology stringnetcondensationandtopologicalphasesinquantumspinsystems |