Interactions and the θ [theta] term in one-dimensional gapped systems
We study how the θ [theta] term is affected by interactions in certain one-dimensional gapped systems that preserve charge conjugation, parity, and time-reversal invariance. We exploit the relation between the chiral anomaly of a fermionic system and the classical shift symmetry of its bosonized dua...
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| Format: | Article |
| Language: | en_US |
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American Physical Society
2011
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| Online Access: | http://hdl.handle.net/1721.1/65858 |
| _version_ | 1826214353919016960 |
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| author | Mulligan, Michael |
| author2 | Massachusetts Institute of Technology. Center for Theoretical Physics |
| author_facet | Massachusetts Institute of Technology. Center for Theoretical Physics Mulligan, Michael |
| author_sort | Mulligan, Michael |
| collection | MIT |
| description | We study how the θ [theta] term is affected by interactions in certain one-dimensional gapped systems that preserve charge conjugation, parity, and time-reversal invariance. We exploit the relation between the chiral anomaly of a fermionic system and the classical shift symmetry of its bosonized dual. The vacuum expectation value of the dual boson is identified with the value of the θ [theta] term for the corresponding fermionic system. Two (related) examples illustrate the identification. We first consider the massive Luttinger liquid and find the θ [theta] term to be insensitive to the strength of the interaction. Next we study the continuum limit of the Heisenberg XXZ spin-1/2 chain, perturbed by a second nearest-neighbor spin interaction. For a certain range of the XXZ anisotropy, we find that we can tune between two distinct sets of topological phases by varying the second nearest-neighbor coupling. In the first we find the standard vacua at θ=0,π [theta = 0, pi], while the second contains vacua that spontaneously break charge conjugation and parity with fractional θ/π=1/2,3/2 [0/pi = 1/2, 3/2]. We also study quantized pumping in both examples following recent work. |
| first_indexed | 2024-09-23T16:03:43Z |
| format | Article |
| id | mit-1721.1/65858 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T16:03:43Z |
| publishDate | 2011 |
| publisher | American Physical Society |
| record_format | dspace |
| spelling | mit-1721.1/658582022-10-02T06:04:21Z Interactions and the θ [theta] term in one-dimensional gapped systems Mulligan, Michael Massachusetts Institute of Technology. Center for Theoretical Physics Massachusetts Institute of Technology. Laboratory for Nuclear Science Mulligan, Michael Mulligan, Michael We study how the θ [theta] term is affected by interactions in certain one-dimensional gapped systems that preserve charge conjugation, parity, and time-reversal invariance. We exploit the relation between the chiral anomaly of a fermionic system and the classical shift symmetry of its bosonized dual. The vacuum expectation value of the dual boson is identified with the value of the θ [theta] term for the corresponding fermionic system. Two (related) examples illustrate the identification. We first consider the massive Luttinger liquid and find the θ [theta] term to be insensitive to the strength of the interaction. Next we study the continuum limit of the Heisenberg XXZ spin-1/2 chain, perturbed by a second nearest-neighbor spin interaction. For a certain range of the XXZ anisotropy, we find that we can tune between two distinct sets of topological phases by varying the second nearest-neighbor coupling. In the first we find the standard vacua at θ=0,π [theta = 0, pi], while the second contains vacua that spontaneously break charge conjugation and parity with fractional θ/π=1/2,3/2 [0/pi = 1/2, 3/2]. We also study quantized pumping in both examples following recent work. United States. Dept. of Energy (Cooperative research agreement DE-FG0205ER41360) Istituto nazionale di fisica nucleare (INFN) 2011-09-15T19:08:09Z 2011-09-15T19:08:09Z 2011-05 2011-03 Article http://purl.org/eprint/type/JournalArticle 1098-0121 1550-235X http://hdl.handle.net/1721.1/65858 Mulligan, Michael. “Interactions and the Θ [theta] Term in One-dimensional Gapped Systems.” Physical Review B 83.20 (2011) : n. pag. ©2011 American Physical Society en_US http://dx.doi.org/10.1103/PhysRevB.83.205110 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. application/pdf American Physical Society APS |
| spellingShingle | Mulligan, Michael Interactions and the θ [theta] term in one-dimensional gapped systems |
| title | Interactions and the θ [theta] term in one-dimensional gapped systems |
| title_full | Interactions and the θ [theta] term in one-dimensional gapped systems |
| title_fullStr | Interactions and the θ [theta] term in one-dimensional gapped systems |
| title_full_unstemmed | Interactions and the θ [theta] term in one-dimensional gapped systems |
| title_short | Interactions and the θ [theta] term in one-dimensional gapped systems |
| title_sort | interactions and the θ theta term in one dimensional gapped systems |
| url | http://hdl.handle.net/1721.1/65858 |
| work_keys_str_mv | AT mulliganmichael interactionsandtheththetaterminonedimensionalgappedsystems |