Jeyaretnam, Jared Anand;
(2023)
Ergodicity breaking and stabilisation of quantum order.
Doctoral thesis (Ph.D), UCL (University College London).
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Abstract
At zero temperature, symmetry-protected topological (SPT) order can encode quantum information in an edge strong zero mode, robust to perturbations respecting some symmetry. On the other hand, phenomena like many-body localisation (MBL) and quantum scarring can arrest the approach to thermal equilibrium, contrary to the ergodic dynamics expected of generic quantum systems. This raises the possibility that by combining SPT order with such ergodicity breaking phenomena, one might be able to construct a quantum memory that is robust at finite temperature. However, MBL is threatened by thermal avalanches due to rare low-disorder grains, while the survival of quantum scars in the thermodynamic limit is still uncertain beyond certain finely-tuned models. To this end, we study the interaction between ergodicity breaking and novel quantum order in spin chains. First, we look at an interacting spin-½ chain hosting SPT order and protected edge modes, identify quantum scars responsible for long-lived coherence in the bulk of the system, and show that these scars exhibit signatures of SPT order even at finite energy density. Secondly, we study a topological transition between two MBL phases with different topological order. Through a renormalisation group approach, we identify many-body resonances between the localised states; close to the transition these proliferate, link together into an extensive network, and cause delocalisation. Additionally, we characterise the SPT strong zero mode in the ordered phase. This has important implications for the stability of MBL and transitions between MBL phases with different topological orders. Finally, we investigate a model known for its use in a proof of MBL, finding that the localised phase is destabilised by proximity to an SPT critical point even though the system itself has no symmetries. This thesis therefore provides important insight into the stability of quantum order at finite temperatures.
| Type: | Thesis (Doctoral) |
|---|---|
| Qualification: | Ph.D |
| Title: | Ergodicity breaking and stabilisation of quantum order |
| Open access status: | An open access version is available from UCL Discovery |
| Language: | English |
| Additional information: | Copyright © The Author 2023. Original content in this thesis is licensed under the terms of the Creative Commons Attribution 4.0 International (CC BY 4.0) Licence (https://creativecommons.org/licenses/by/4.0/). Any third-party copyright material present remains the property of its respective owner(s) and is licensed under its existing terms. Access may initially be restricted at the author’s request. |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Physics and Astronomy |
| URI: | https://discovery-pp.ucl.ac.uk/id/eprint/10184332 |
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