Titlebook: An Introduction to Integrable Techniques for One-Dimensional Quantum Systems; Fabio Franchini Book 2017 The Author(s) 2017 Lieb-Liniger mo

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https://doi.org/10.1007/978-3-319-48487-7Lieb-Liniger model; Heisenberg chain; Yang-Baxter equations; Toeplitz determinants; bosonization; XY chai

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An Introduction to Integrable Techniques for One-Dimensional Quantum Systems978-3-319-48487-7Series ISSN 0075-8450 Series E-ISSN 1616-6361

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The XY Chain,stem. Its rich and non-trivial phase-diagram and the possibility of calculating virtually every quantity have rendered it a reference model to understand new effects or to test hypotheses. After a brief introduction in Sects.?. and . we review its standard mapping to free fermions, paying particular

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The Lieb-Liniger Model,tic, although in current experimental realizations the external trapping breaks translational invariance, spoiling integrability (although in some cases the trapping can be accounted for perturbatively). The Lieb-Liniger model is also best suited to illustrate the basic ideas behind the Bethe Ansatz

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The XXZ Chain, Ansatz solution is a “straightforward” generalization of the one employed in the previous chapter, but the classification of complex roots is more involved and the nature of the low energy excitations changes with the anisotropy. After previewing the phase diagram of the chain in Sect.?., we recap

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