Non-equilibrium processes and ergodicity-breaking in isolated quantum systems

Abstract

In this thesis we consider isolated quantum systems influenced by disorder and external driving, and explore aspects of localisation and ergodicity-breaking in three different models.

We first consider the XYZ spin chain in a disordered magnetic field; this system breaks the U(1) symmetry of the XXZ model and therefore violates the conservation of the z component of the total magnetisation. We identify a quantum phase transition between an ergodic phase and a many-body localised phase at a finite disorder strength that is strongly dependent on the size of the U(1) symmetry-breaking term. We also investigate the breakdown of thermalisation by studying the matrix elements of local operators in the basis of the system's eigenstates, and we find suggestive evidence of subdiffusive energy transport at disorder strengths preceding the localisation transition.

We then consider a two-level time-dependent quantum system that is influenced by a fluctuating classical noise term. We show that the noise does not fully randomise the quantum state if the fluctuations of every noise parameter coupled to the system are perfectly correlated; the state of the system instead becomes distributed over a finite subset of the full state space.

Lastly we consider a one-dimensional Anderson-localised system that is affected by randomly fluctuating onsite potentials. We explore how the spatiotemporal correlations between these onsite potentials affect the delocalisation of a particle initially localised on a single site.