EAN: 9783319514567

QUANTUM SPIN SYSTEMS ON INFINITE LATTICES - PIE...

This course-based primer offers readers a concise introduction to the description of quantum
mechanical systems with infinitely many degrees of freedom - and quantum spin systems in
particular - using the operator algebraic approach. Here  the observables are modeled using
elements of some operator algebra  usually a C*-algebra. This text introduces readers to the
framework and the necessary mathematical tools without assuming much mathematical background 
making it more accessible than advanced monographs. The book also highlights the usefulness of
the so-called thermodynamic limit of quantum spin systems  which is the limit of infinite
system size. For example  this makes it possible to clearly distinguish between local and
global properties  without having to keep track of the system size. Together with Lieb-Robinson
bounds  which play a similar role in quantum spin systems to that of the speed of light in
relativistic theories  this approach allows ideas from relativistic field theories to be
implemented in a quantum spin system. Several related cases are discussed  demonstrating the
merits of the operator algebraic approach. Featuring representative worked-out examples and
many exercises  this text is primarily targeted at graduate students and advanced
undergraduates in theoretical physics or mathematics with a keen interest in mathematical
physics. The material provides the necessary background and pointers to start exploring the
recent literature. As such  it will also be useful for active researchers seeking a quick and
comparatively self-contained introduction to the operator algebraic approach to quantum spin
systems.

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