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Dynamics of disordered quantum systems using flow equations

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Abstract

In this manuscript, we show how flow equation methods can be used to study localisation in disordered quantum systems, and particularly how to use this approach to obtain the non-equilibrium dynamical evolution of observables. We review the formalism, based on continuous unitary transforms, and apply it to a non-interacting yet non trivial one-dimensional disordered quantum system, the Power-Law Random Banded Matrix model whose dynamics is studied across the localisation-delocalisation transition. We show how this method can be used to compute quench dynamics of simple observables, demonstrate how this formalism provides a natural framework to understand operator spreading and show how to construct complex objects such as correlation functions. We also discuss how the method may be applied to interacting quantum systems, and end with an outlook on unsolved problems and ways in which the method can be further developed in the future. Our goal is to motivate further adoption of the flow equation method, and to equip and encourage others to build on this technique as a means to study localisation phenomena in disordered quantum systems.

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Authors and Affiliations

  1. Institut de Physique Théorique, Université Paris Saclay, CNRS, CEA, 91191, Gif-sur-Yvette, France

    Steven J. Thomson & Marco Schiró

  2. JEIP, USR 3573 CNRS, Collège de France, PSL Research University, 11 Place Marcelin Berthelot, 75321, Paris Cedex 05, France

    Marco Schiró

Authors
  1. Steven J. Thomson
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  2. Marco Schiró
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Correspondence to Steven J. Thomson.

Additional information

Contribution to the Topical Issue “Recent Advances in the Theory of Disordered Systems”, edited by Ferenc Iglói and Heiko Rieger.

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Thomson, S.J., Schiró, M. Dynamics of disordered quantum systems using flow equations. Eur. Phys. J. B 93, 22 (2020). https://doi.org/10.1140/epjb/e2019-100476-3

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