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Quantum Physics in One Dimension$
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Thierry Giamarchi

Print publication date: 2003

Print ISBN-13: 9780198525004

Published to Oxford Scholarship Online: September 2007

DOI: 10.1093/acprof:oso/9780198525004.001.0001

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Quantum Physics in One Dimension

Thierry Giamarchi

Oxford University Press

This chapter presents some additional complications that arise in addition to the simple Luttinger liquid theory for one-dimensional systems. Examples of pitfalls into which the bosonization beginners can fall are discussed. This chapter also explores one of the most important consequences of the existence of a lattice, namely the possibility for the electrons to give an insulator driven by the interactions known as the Mott insulator. The discussion focuses on what happens when one breaks the spin rotation invariance in a Luttinger liquid with spin, and considers the logarithmic corrections of correlation functions.

Keywords:   long-range interactions, correlation functions, magnetic fields, magnetic anisotropies, Mott transition, Luther-Emery solution, one-dimensional systems

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