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We are interested in exploring the interplay of low dimensionality, strong correlations and quantum fluctuations giving rise to novel emergent states of matter in quantum condensed matter systems. By "emergence", we mean that in a many-body system whose constituents interact with one another, we often find complex collective behaviour that is qualitatively different from the behaviour of the constituent parts upon changing energy scales. The theoretical analysis of such phenomena is often made challenging by the absence of any obvious small coupling constant in the problem: when the competing tendencies for a quantum particle to either localise in space (due to inter-particle correlations, scattering from disorder or lattice vibrations) or to spread out its wavefunction (due to its kinetic energy) match one another, any theoretical description typically faces restrictions on its validity and powers of prediction. In addition, critical phenomena in low-dimensional systems are often at zero-temperature and driven by quantum fluctuations arising from the competition between different quantum orders.