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.