Topological degeneracy and pairing in a one-dimensional gas of spinless fermions
We revisit the low-energy physics of one-dimensional spinless fermion liquids, showing that with sufficiently strong interactions the conventional Luttinger liquid can give way to a strong-pairing phase. While the density fluctuations in both phases are described by a gapless Luttinger liquid, singl...
| Main Authors: | , |
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| Other Authors: | |
| Format: | Article |
| Language: | English |
| Published: |
American Physical Society
2018
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| Online Access: | http://hdl.handle.net/1721.1/114707 |
| _version_ | 1826194169725452288 |
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| author | Altman, Ehud Ruhman, Yehonatan |
| author2 | Massachusetts Institute of Technology. Department of Physics |
| author_facet | Massachusetts Institute of Technology. Department of Physics Altman, Ehud Ruhman, Yehonatan |
| author_sort | Altman, Ehud |
| collection | MIT |
| description | We revisit the low-energy physics of one-dimensional spinless fermion liquids, showing that with sufficiently strong interactions the conventional Luttinger liquid can give way to a strong-pairing phase. While the density fluctuations in both phases are described by a gapless Luttinger liquid, single fermion excitations are gapped only in the strong-pairing phase. Smooth spatial Interfaces between the two phases lead to topological degeneracies in the ground-state and low-energy spectrum of the density fluctuations. Using a concrete microscopic model, with both single-particle and pair hopping, we show that the strong-pairing state is established through emergence of a new low-energy fermionic mode. We characterize the two phases with numerical calculations using the density matrix renormalization group. In particular we find enhancement of the central charge from c=1 in the two Luttinger liquid phases to c=3/2 at the critical point, which gives direct evidence for an emergent critical Majorana mode. Finally, we confirm the existence of topological degeneracies in the low-energy phonon spectrum, associated with spatial interfaces between the two phases. |
| first_indexed | 2024-09-23T09:52:01Z |
| format | Article |
| id | mit-1721.1/114707 |
| institution | Massachusetts Institute of Technology |
| language | English |
| last_indexed | 2024-09-23T09:52:01Z |
| publishDate | 2018 |
| publisher | American Physical Society |
| record_format | dspace |
| spelling | mit-1721.1/1147072022-09-30T17:21:01Z Topological degeneracy and pairing in a one-dimensional gas of spinless fermions Altman, Ehud Ruhman, Yehonatan Massachusetts Institute of Technology. Department of Physics Ruhman, Yehonatan We revisit the low-energy physics of one-dimensional spinless fermion liquids, showing that with sufficiently strong interactions the conventional Luttinger liquid can give way to a strong-pairing phase. While the density fluctuations in both phases are described by a gapless Luttinger liquid, single fermion excitations are gapped only in the strong-pairing phase. Smooth spatial Interfaces between the two phases lead to topological degeneracies in the ground-state and low-energy spectrum of the density fluctuations. Using a concrete microscopic model, with both single-particle and pair hopping, we show that the strong-pairing state is established through emergence of a new low-energy fermionic mode. We characterize the two phases with numerical calculations using the density matrix renormalization group. In particular we find enhancement of the central charge from c=1 in the two Luttinger liquid phases to c=3/2 at the critical point, which gives direct evidence for an emergent critical Majorana mode. Finally, we confirm the existence of topological degeneracies in the low-energy phonon spectrum, associated with spatial interfaces between the two phases. Gordon and Betty Moore Foundation (Grant GBMF4303) 2018-04-13T16:34:25Z 2018-04-13T16:34:25Z 2017-08 2017-05 2017-11-14T22:46:48Z Article http://purl.org/eprint/type/JournalArticle 2469-9950 2469-9969 http://hdl.handle.net/1721.1/114707 Ruhman, Jonathan and Ehud Altman. "Topological degeneracy and pairing in a one-dimensional gas of spinless fermions." Physical Review B 96, 8 (August 2017): 085133 © 2017 American Physical Society en http://dx.doi.org/10.1103/PhysRevB.96.085133 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 | Altman, Ehud Ruhman, Yehonatan Topological degeneracy and pairing in a one-dimensional gas of spinless fermions |
| title | Topological degeneracy and pairing in a one-dimensional gas of spinless fermions |
| title_full | Topological degeneracy and pairing in a one-dimensional gas of spinless fermions |
| title_fullStr | Topological degeneracy and pairing in a one-dimensional gas of spinless fermions |
| title_full_unstemmed | Topological degeneracy and pairing in a one-dimensional gas of spinless fermions |
| title_short | Topological degeneracy and pairing in a one-dimensional gas of spinless fermions |
| title_sort | topological degeneracy and pairing in a one dimensional gas of spinless fermions |
| url | http://hdl.handle.net/1721.1/114707 |
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