Flow Equations for Many-Body Localisation: Dynamics and Dimensionality

Once thought to destroy localisation completely, we now know that adding interactions into disordered quantum matter can lead to the formation of a many-body localised phase. This phase is characterised by an extensive number of local conserved quantities and a failure to thermalise. Consequently it cannot be described by conventional equilibrium quantum statistical mechanics: new theoretical tools are required. Here, we present a semi-analytic flow equation approach that is capable of simulating large system sizes and of computing the real-time dynamics of observables and correlation functions. We employ a continuous unitary transform to diagonalise the Hamiltonian of a gas of interacting spinless fermions, show how local integrals of motion naturally emerge from this method, and go on calculate time evolution and localisation properties in the strongly-disordered regime in both one and two spatial dimensions. We further comment on ongoing work extending the method to incorporate additional features, including spin, as well as three-dimensional systems.

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