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Models of Quantum Matter - A First Course on Integrability and the Bethe Ansatz (Hardcover)
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Models of Quantum Matter - A First Course on Integrability and the Bethe Ansatz (Hardcover)
Series: Oxford Graduate Texts
Expected to ship within 12 - 17 working days
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An important task of theoretical quantum physics is the building of
idealized mathematical models to describe the properties of quantum
matter. This book provides an introduction to the arguably most
important method for obtaining exact results for strongly
interacting models of quantum matter - the Bethe ansatz. It
introduces and discusses the physical concepts and mathematical
tools used to construct realistic models for a variety of different
fields, including condensed matter physics and quantum optics. The
various forms of the Bethe ansatz - algebraic, coordinate,
multicomponent, and thermodynamic Bethe ansatz, and Bethe ansatz
for finite systems - are then explained in depth and employed to
find exact solutions for the physical properties of the integrable
forms of strongly interacting quantum systems. The Bethe ansatz is
one of the very few methodologies which can calculate physical
properties non-perturbatively. Arguably, it is the only such method
we have which is exact. This means, once the model has been set up,
no further approximations or assumptions are necessary, and the
relevant physical properties of the model can be computed exactly.
Furthermore, an infinite set of conserved quantities can be
obtained. The quantum mechanical model under consideration is fully
integrable. This makes the search for quantum models which are
amenable to an exact solution by the Bethe ansatz, and which are
quantum integrable, so important and rewarding. The exact solution
will provide benchmarks for other models, which do not admit an
exact solution. Bethe ansatz techniques provide valuable insight
into the physics of strongly correlated quantum matter.
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