Laboratoire de Physique Théorique
Toulouse - UMR 5152

The interplay between many-body interactions and quenched disorder in quantum systems can result in rich dynamical phenomena far from equilibrium. When the disorder is strong enough to prevent thermalisation, this can lead to phases of matter with no equilibrium analogue, such as many-body localisation (MBL). In combination with periodic drive, MBL can even allow for the existence of exotic states such as time crystals. Crucially, in MBL systems the eigenstate thermalisation hypothesis - which underpins the use of equilibrium statistical mechanics in isolated quantum systems - dramatically fails : new theoretical approaches are needed.

In this talk, I will outline how the flow equation method can be used to directly obtain the emergent local integrals of motion that characterise MBL matter, and show how this allows us to compute both static and dynamical quantities of strongly disordered systems on larger scales than those accessible with any other technique, including in two dimensions [1]. I will show how long-range couplings can lead to the breakdown of many-body localisation [2,3], and how periodically driven (Floquet) systems can be treated within the same general formalism [4], paving the way for future studies of time crystals in two-dimensional systems.

[1] - S. J. Thomson & M. Schiró, Phys. Rev. B 97, 060201(R) (2018)

[2] - S. J. Thomson & M. Schiró, Eur. Phys. J. B 93, 22 (2020)

[3] - S. J. Thomson & M. Schiró, Phys. Rev. Research 2, 043368 (2020)

[4] - S. J. Thomson, D. Magano & M. Schiró, arXiv:2009.03186