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This Book contains four studies of the effects of disorder and randomness on
strongly correlated quantum phases of matter. Starting with an itinerant
ferromagnet, I first use an order-by-disorder approach to show that adding
quenched charged disorder to the model generates new quantum fluctuations in
the vicinity of the quantum critical point which lead to the formation of a novel
magnetic phase known as a helical glass.
Switching to bosons, I then employ a momentum-shell renormalisation group
analysis of disordered lattice gases of bosons where I show that disorder breaks
ergodicity in a non-trivial way, leading to unexpected glassy freezing effects. This
work was carried out in the context of ultracold atomic gases, however the same
physics can be realised in dimerised quantum antiferromagnets. By mapping the
antiferromagnetic model onto a hard-core lattice gas of bosons, I go on to show
the importance of the non-ergodic effects to the thermodynamics of the model and
find evidence for an unusual glassy phase known as a Mott glass not previously
thought to exist in this model.
Finally, I use a mean-field numerical approach to simulate current generation
quantum gas microscopes and demonstrate the feasibility of a novel measurement
scheme designed to measure the Edwards-Anderson order parameter, a quantity
which describes the degree of ergodicity breaking and which has never before been
experimentally measured in any strongly correlated quantum system.
Together, these works show that the addition of disorder into strongly
interacting quantum systems can lead to qualitatively new behaviour, triggering
the formation of new phases and new physics, rather than simply leading to
small quantitative changes to the physics of the clean system. They provide new
insights into the underlying physics of the models and make direct connection with
experimental systems which can be used to test the results presented here.
