Quantum mechanics is central to the understanding of condensed matter systems, particularly at temperatures smaller than the characteristic energy scales set by interactions or by the chemical potential. The mathematical framework used to describe collective quantum phenomena varies greatly according to the systems being studied. Some of the mathematical ideas are very close to those being employed in string theory and particle physics, and being studied by the Strings and Particles CRT; and both fields use the language and results of quantum field theory. At higher temperatures, the behaviour of matter becomes more classical- some of the most interesting high-T phenomena occur in biological systems (see the Complex Systems CRT).

Two central problems in quantum condensed matter physics are (i) the physics of the strongly-correlated lattice electrons, particularly for lower-dimensional systems; and (ii) the physics of large-scale quantum phenomena, ranging from macroscopic superpositions of collective states to the study of solid-state qubits. These topics are closely linked physically, and mathematically- the basic models describing, eg., decoherence, are similar to those used in describing strongly-correlated electrons (and to models in string and particle theory). For example, the theory of flux phases in high-T_c systems can be mapped to models of dissipative open strings and Ө-vacua, to lattice gauge theories, and to the composite fermion theory of the fractional Hall effect. These in turn are related to models in quantum gravity, to the Schmid or spin-boson models in quantum dissipation and decoherence theory, and to models of junctions of quantum wires.

To study strongly-correlated electrons we have a core group whose focus is on models of 2-d interacting fermions like the Hubbard model, and/or on phenomenological models intended to describe the low-energy propeties of 2-d fermions. Some of these models have metal-insulator transitions, and there are complex relations between them involving topology and symmetries of different kinds. Some of the work also involves new computational approaches to the Hubbard model. Many different 'quantum materials' are described by such models, and so the work involves ideas from fields as varied as string theory and topology to quantum chemistry, and links to experimental work in North America and Japan are important.

Large-scale quantum phenomena are being studied in superconducting devices, "spin nets" of nanomagnetic molecules, and quantum wires. The theory involves the correlations in these systems, and how decoherence affects them. Models that are studied range from 'quantum impurity' models like spin-boson model or the central spin model, describing qubits coupled to quantum environments, to 'lattice anyon' models of quantum computation. Similar models are used to discuss 1- and 2-dimensional interacting fermions. The theoretical work involves solid state theory as well as quantum information theory. Again, this theoretical work requires extensive dialogue with experimental groups, notably those working in quantum nanomagnetism, in nanoelectronics, and on SQUID qubits.