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Localisation transition in the driven Aubry-Andre model

Localisation transition in the driven Aubry-Andre model
Localisation transition in the driven Aubry-Andre model
A recent experiment by Bordia et al. [P. Bordia et al., Nat. Phys. 13, 5 (2017)] has demonstrated that periodically modulating the potential of a localised many-body quantum system described by the Aubry-André Hamiltonian with on-site interactions can lead to a many-body localisation-delocalisation transition, provided the modulation amplitude is big enough. Here, we consider the noninteracting counterpart of that model in order to explore its phase diagram as a function of the strength of the disordered potential, the driving frequency and its amplitude. We will first of all mimic the experimental procedure of Bordia et al. and use the even-odd sites imbalance as a parameter in order to discern between different phases. Then we compute the Floquet eigenstates and relate the localisation-delocalisation transition to their IPR. Both these approaches show that the delocalisation transition occurs for frequencies that are low compared to the bandwidth of the time independent model. Moreover, in agreement with [P. Bordia et al., Nat. Phys. 13, 5 (2017)] there is an amplitude threshold below which no delocalisation transition occurs. We estimate both the critical values for the frequency and the amplitude.
1434-6060
1-8
Romito, Donato
d4b0ceb2-fe6a-4d15-83d9-0e03a7ad4756
Lobo, Carlos
cde7843a-c00b-4242-a8cd-1abb2dfe0703
Recati, Alessio
ecc995c6-74d3-4169-8362-1c9798dde7cb
Romito, Donato
d4b0ceb2-fe6a-4d15-83d9-0e03a7ad4756
Lobo, Carlos
cde7843a-c00b-4242-a8cd-1abb2dfe0703
Recati, Alessio
ecc995c6-74d3-4169-8362-1c9798dde7cb

Romito, Donato, Lobo, Carlos and Recati, Alessio (2018) Localisation transition in the driven Aubry-Andre model. The European Physical Journal D, 72 (135), 1-8. (doi:10.1140/epjd/e2018-90081-3).

Record type: Article

Abstract

A recent experiment by Bordia et al. [P. Bordia et al., Nat. Phys. 13, 5 (2017)] has demonstrated that periodically modulating the potential of a localised many-body quantum system described by the Aubry-André Hamiltonian with on-site interactions can lead to a many-body localisation-delocalisation transition, provided the modulation amplitude is big enough. Here, we consider the noninteracting counterpart of that model in order to explore its phase diagram as a function of the strength of the disordered potential, the driving frequency and its amplitude. We will first of all mimic the experimental procedure of Bordia et al. and use the even-odd sites imbalance as a parameter in order to discern between different phases. Then we compute the Floquet eigenstates and relate the localisation-delocalisation transition to their IPR. Both these approaches show that the delocalisation transition occurs for frequencies that are low compared to the bandwidth of the time independent model. Moreover, in agreement with [P. Bordia et al., Nat. Phys. 13, 5 (2017)] there is an amplitude threshold below which no delocalisation transition occurs. We estimate both the critical values for the frequency and the amplitude.

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Localisation transition in the driven Aubry-Andr ́e model_manuscript - Accepted Manuscript
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Accepted/In Press date: 1 June 2018
e-pub ahead of print date: 2 August 2018
Published date: August 2018

Identifiers

Local EPrints ID: 422878
URI: https://eprints.soton.ac.uk/id/eprint/422878
ISSN: 1434-6060
PURE UUID: b86572ae-94f4-4781-afb7-4ab2316ca423
ORCID for Carlos Lobo: ORCID iD orcid.org/0000-0001-7060-3905

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Date deposited: 07 Aug 2018 16:30
Last modified: 03 Dec 2019 05:16

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