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020 _a9783319514581
_9978-3-319-51458-1
024 7 _a10.1007/978-3-319-51458-1
_2doi
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_2bicssc
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082 0 4 _a530.12
_223
100 1 _aNaaijkens, Pieter.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
245 1 0 _aQuantum Spin Systems on Infinite Lattices
_h[electronic resource] :
_bA Concise Introduction /
_cby Pieter Naaijkens.
250 _a1st ed. 2017.
264 1 _aCham :
_bSpringer International Publishing :
_bImprint: Springer,
_c2017.
300 _aXI, 177 p. 6 illus., 1 illus. in color.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aLecture Notes in Physics,
_x0075-8450 ;
_v933
505 0 _aIntroduction -- Operator algebras -- Infinite systems -- Lieb-Robinson bounds -- Local Quantum Physics -- Applications of Lieb-Robinson bounds -- Index.
520 _aThis 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.
650 0 _aQuantum physics.
650 0 _aMathematical physics.
650 0 _aPhysics.
650 1 4 _aQuantum Physics.
_0https://scigraph.springernature.com/ontologies/product-market-codes/P19080
650 2 4 _aMathematical Physics.
_0https://scigraph.springernature.com/ontologies/product-market-codes/M35000
650 2 4 _aMathematical Methods in Physics.
_0https://scigraph.springernature.com/ontologies/product-market-codes/P19013
650 2 4 _aMathematical Applications in the Physical Sciences.
_0https://scigraph.springernature.com/ontologies/product-market-codes/M13120
710 2 _aSpringerLink (Online service)
773 0 _tSpringer Nature eBook
776 0 8 _iPrinted edition:
_z9783319514567
776 0 8 _iPrinted edition:
_z9783319514574
830 0 _aLecture Notes in Physics,
_x0075-8450 ;
_v933
856 4 0 _uhttps://doi.org/10.1007/978-3-319-51458-1
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912 _aZDB-2-SXP
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