Static and Dynamic Features of non-Hermitian Many-Body Localisation

Abstract

The investigation of ergodicity and its breaking in quantum systems is important both from a foundational viewpoint and for applications. Theoretical and experimental studies over the past decade have seen many-body localisation (MBL) emerge as a non-ergodic phase of matter in closed interacting quantum systems evolving unitarily. Notably, an MBL system does not reach thermal equilibrium and retains memory of its initial conditions. Although MBL is predominantly a closed-system phenomenon, realistic quantum systems, which can be experimentally investigated, are inevitably open and their evolution is non-unitary.

Motivated by this, in this Thesis we investigate the stability of MBL in the presence of non-Hermitian perturbations which break unitarity. The latter are not only theoretically interesting, but are gaining direct relevance, as recent experimental advances provide access to non-Hermitian effects in quantum physics. Specifically, we study the interacting Hatano-Nelson Hamiltonian, which describes particles asymmetrically hopping on a lattice in the presence of nearest-neighbour interactions and on-site disorder; the unequal magnitudes of the left and right hopping amplitudes makes the model non-Hermitian. By using exact diagonalisation, we extract the midspectrum eigenstates and eigenenergies, and establish the phase diagram. In our finite-size numerical study we find an intermediate region of the phase diagram which opens up as the interaction strength is tuned away from zero. Moreover, we explore the role that complex eigenvalues, arising due to non-Hermiticity, play in the relaxation dynamics of physical observables. We show that the time to reach the steady state behaves very differently in the ergodic and the localised phases. We also provide an interpretation for the phase diagram in terms of dynamics. Finally, we conclude with directions for future research.

Date of Award	1 Jul 2024
Original language	English
Awarding Institution	King's College London
Supervisor	affiliated academic (Supervisor) & Joe Bhaseen (Supervisor)