Entanglement convertibility by sweeping through the quantum phases of the alternating bonds XXZ chain
We study the entanglement structure and the topological edge states of the ground state of the spin-1/2 XXZ model with bond alternation. We employ parity-density matrix renormalization group with periodic boundary conditions. The finite-size scaling of Rényi entropies S2 and S∞ are used to construct...
| Main Authors: | , , , , |
|---|---|
| Other Authors: | |
| Format: | Journal Article |
| Language: | English |
| Published: |
2018
|
| Subjects: | |
| Online Access: | https://hdl.handle.net/10356/81203 http://hdl.handle.net/10220/46616 |
| _version_ | 1811678350010220544 |
|---|---|
| author | Tzeng, Yu-Chin Dai, Li Chung, Ming-Chiang Amico, Luigi Kwek, Leong-Chuan |
| author2 | Institute of Advanced Studies |
| author_facet | Institute of Advanced Studies Tzeng, Yu-Chin Dai, Li Chung, Ming-Chiang Amico, Luigi Kwek, Leong-Chuan |
| author_sort | Tzeng, Yu-Chin |
| collection | NTU |
| description | We study the entanglement structure and the topological edge states of the ground state of the spin-1/2 XXZ model with bond alternation. We employ parity-density matrix renormalization group with periodic boundary conditions. The finite-size scaling of Rényi entropies S2 and S∞ are used to construct the phase diagram of the system. The phase diagram displays three possible phases: Haldane type (an example of symmetry protected topological ordered phases), Classical Dimer and Néel phases, the latter bounded by two continuous quantum phase transitions. The entanglement and non-locality in the ground state are studied and quantified by the entanglement convertibility. We found that, at small spatial scales, the ground state is not convertible within the topological Haldane dimer phase. The phenomenology we observe can be described in terms of correlations between edge states. We found that the entanglement spectrum also exhibits a distinctive response in the topological phase: the effective rank of the reduced density matrix displays a specifically large “susceptibility” in the topological phase. These findings support the idea that although the topological order in the ground state cannot be detected by local inspection, the ground state response at local scale can tell the topological phases apart from the non-topological phases. |
| first_indexed | 2024-10-01T02:51:51Z |
| format | Journal Article |
| id | ntu-10356/81203 |
| institution | Nanyang Technological University |
| language | English |
| last_indexed | 2024-10-01T02:51:51Z |
| publishDate | 2018 |
| record_format | dspace |
| spelling | ntu-10356/812032022-02-16T16:26:11Z Entanglement convertibility by sweeping through the quantum phases of the alternating bonds XXZ chain Tzeng, Yu-Chin Dai, Li Chung, Ming-Chiang Amico, Luigi Kwek, Leong-Chuan Institute of Advanced Studies DRNTU::Science::Physics Quantum Phase Transition Entanglement Convertibility We study the entanglement structure and the topological edge states of the ground state of the spin-1/2 XXZ model with bond alternation. We employ parity-density matrix renormalization group with periodic boundary conditions. The finite-size scaling of Rényi entropies S2 and S∞ are used to construct the phase diagram of the system. The phase diagram displays three possible phases: Haldane type (an example of symmetry protected topological ordered phases), Classical Dimer and Néel phases, the latter bounded by two continuous quantum phase transitions. The entanglement and non-locality in the ground state are studied and quantified by the entanglement convertibility. We found that, at small spatial scales, the ground state is not convertible within the topological Haldane dimer phase. The phenomenology we observe can be described in terms of correlations between edge states. We found that the entanglement spectrum also exhibits a distinctive response in the topological phase: the effective rank of the reduced density matrix displays a specifically large “susceptibility” in the topological phase. These findings support the idea that although the topological order in the ground state cannot be detected by local inspection, the ground state response at local scale can tell the topological phases apart from the non-topological phases. NRF (Natl Research Foundation, S’pore) MOE (Min. of Education, S’pore) Published version 2018-11-09T04:43:05Z 2019-12-06T14:23:32Z 2018-11-09T04:43:05Z 2019-12-06T14:23:32Z 2016 Journal Article Tzeng, Y.-C., Dai, L., Chung, M.-C., Amico, L., & Kwek, L.-C. (2016). Entanglement convertibility by sweeping through the quantum phases of the alternating bonds XXZ chain. Scientific Reports, 6, 26453-. doi:10.1038/srep26453 https://hdl.handle.net/10356/81203 http://hdl.handle.net/10220/46616 10.1038/srep26453 27216970 en Scientific Reports © 2016 The Authors (Nature Publishing Group). This work is licensed under a Creative Commons Attribution 4.0 International License. The images or other third party material in this article are included in the article’s Creative Commons license, unless indicated otherwise in the credit line; if the material is not included under the Creative Commons license, users will need to obtain permission from the license holder to reproduce the material. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/ 13 p. application/pdf |
| spellingShingle | DRNTU::Science::Physics Quantum Phase Transition Entanglement Convertibility Tzeng, Yu-Chin Dai, Li Chung, Ming-Chiang Amico, Luigi Kwek, Leong-Chuan Entanglement convertibility by sweeping through the quantum phases of the alternating bonds XXZ chain |
| title | Entanglement convertibility by sweeping through the quantum phases of the alternating bonds XXZ chain |
| title_full | Entanglement convertibility by sweeping through the quantum phases of the alternating bonds XXZ chain |
| title_fullStr | Entanglement convertibility by sweeping through the quantum phases of the alternating bonds XXZ chain |
| title_full_unstemmed | Entanglement convertibility by sweeping through the quantum phases of the alternating bonds XXZ chain |
| title_short | Entanglement convertibility by sweeping through the quantum phases of the alternating bonds XXZ chain |
| title_sort | entanglement convertibility by sweeping through the quantum phases of the alternating bonds xxz chain |
| topic | DRNTU::Science::Physics Quantum Phase Transition Entanglement Convertibility |
| url | https://hdl.handle.net/10356/81203 http://hdl.handle.net/10220/46616 |
| work_keys_str_mv | AT tzengyuchin entanglementconvertibilitybysweepingthroughthequantumphasesofthealternatingbondsxxzchain AT daili entanglementconvertibilitybysweepingthroughthequantumphasesofthealternatingbondsxxzchain AT chungmingchiang entanglementconvertibilitybysweepingthroughthequantumphasesofthealternatingbondsxxzchain AT amicoluigi entanglementconvertibilitybysweepingthroughthequantumphasesofthealternatingbondsxxzchain AT kwekleongchuan entanglementconvertibilitybysweepingthroughthequantumphasesofthealternatingbondsxxzchain |