Flow equations for disordered Floquet systems

Thomson, Steven J.; Magano, Duarte; Schirò, Marco

doi:10.21468/SciPostPhys.11.2.028

SciPost Physics

Flow equations for disordered Floquet systems

Steven J. Thomson, Duarte Magano, Marco Schirò

SciPost Phys. 11, 028 (2021) · published 10 August 2021

doi: 10.21468/SciPostPhys.11.2.028
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Abstract

In this work, we present a new approach to disordered, periodically driven (Floquet) quantum many-body systems based on flow equations. Specifically, we introduce a continuous unitary flow of Floquet operators in an extended Hilbert space, whose fixed point is both diagonal and time-independent, allowing us to directly obtain the Floquet modes. We first apply this method to a periodically driven Anderson insulator, for which it is exact, and then extend it to driven many-body localized systems within a truncated flow equation ansatz. In particular we compute the emergent Floquet local integrals of motion that characterise a periodically driven many-body localized phase. We demonstrate that the method remains well-controlled in the weakly-interacting regime, and allows us to access larger system sizes than accessible by numerically exact methods, paving the way for studies of two-dimensional driven many-body systems.

TY  - JOUR
PB  - SciPost Foundation
DO  - 10.21468/SciPostPhys.11.2.028
TI  - Flow equations for disordered Floquet systems
PY  - 2021/08/10
UR  - https://scipost.org/SciPostPhys.11.2.028
JF  - SciPost Physics
JA  - SciPost Phys.
VL  - 11
IS  - 2
SP  - 028
A1  - Thomson, Steven J.
AU  - Magano, Duarte
AU  - Schirò, Marco
AB  - In this work, we present a new approach to disordered, periodically driven (Floquet) quantum many-body systems based on flow equations. Specifically, we introduce a continuous unitary flow of Floquet operators in an extended Hilbert space, whose fixed point is both diagonal and time-independent, allowing us to directly obtain the Floquet modes. We first apply this method to a periodically driven Anderson insulator, for which it is exact, and then extend it to driven many-body localized systems within a truncated flow equation ansatz. In particular we compute the emergent Floquet local integrals of motion that characterise a periodically driven many-body localized phase. We demonstrate that the method remains well-controlled in the weakly-interacting regime, and allows us to access larger system sizes than accessible by numerically exact methods, paving the way for studies of two-dimensional driven many-body systems.
ER  -

@Article{10.21468/SciPostPhys.11.2.028,
	title={{Flow equations for disordered Floquet systems}},
	author={Steven J. Thomson and Duarte Magano and Marco Schirò},
	journal={SciPost Phys.},
	volume={11},
	pages={028},
	year={2021},
	publisher={SciPost},
	doi={10.21468/SciPostPhys.11.2.028},
	url={https://scipost.org/10.21468/SciPostPhys.11.2.028},
}

Cited by 11

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¹ ² ³ Steven J. Thomson,
¹ ⁴ ⁵ Duarte Magano,
¹ Marco Schirò

Funders for the research work leading to this publication

Agence Nationale de la Recherche [ANR]
Fundação para a Ciência e a Tecnologia (through Organization: Fundação para a Ciência e Tecnologia [FCT])