Heparin glycosaminoglycans mediate a range of biological events, including anticoagulation as well as a diversity of cell proliferation and differentiation processes. Heparin saccharides have been shown to act as inhibitors against angiogenesis and metastasis of tumour cells. This thesis describes work developing chemistry towards varying length oligosaccharide sequences with potential to offer variable sulfation patterns. The main synthetic components to this work were contribution to developing scalable syntheses of an orthogonally protected L-Iduronic acid unit and a differentially protected D-glucosamine unit. The synthetic work also evaluated a recently reported diazo transfer reagent, which allowed for earlier placement of azide protection over that of previously developed routes within the group. This provided a cheaper, more atom efficient route towards protected D-glucosamine building blocks. Glycosylation of the developed D-GlcN donor units with the L-Ido acceptor allowed the production of key disaccharides which facilitated an efficient iterative glycosylation strategy towards longer oligosaccharides, ultimately providing a differentially protected pentasaccharide. The project evaluated methods towards generating various dimeric heparin type systems through forming new O4 ether linkages between GlcN residues across various short linker fragments. The most successful of these dimerisations used a methallyl dichloride core which allowed for further derivatisation towards dihydroxylated species, the analysis of which highlighted some interesting proton NMR data. The final aspect of this project began development of chemistry towards non-reducing end-labelled oligosaccharide sequences by implementation of a masked aldehyde unit on the C4 hydroxyl of GlcN synthesised from the allylated GlcN precursor via dihydroxylation chemistry. Incorporation of this moiety (protected as a 1,2-dibenzyl glycol) within both a trisaccharide and a pentasaccharide was achieved. Further development of this chemistry should allow for late step oxidative cleavage to reveal the reactive aldehyde, potentially allowing for attachment of various amine functionalised fluorophores via reductive amination. Radiolabelling of such a species should also be possible through sodium borotritide reduction for example.

This thesis 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.