Description

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.