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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

The bosonization technique is useful for solving the interacting problem and for extracting a certain number of properties such as power law behavior of the correlation functions. However, this derivation is, strictly speaking, based on a linearization of the spectrum close to the Fermi energy. One can thus wonder what will remain of the results of the previous chapter when it is impossible to stay confined close to the Fermi level, for example, when the interactions become strong. In order to answer this question, it is necessary to rederive the bosonization formulas, in a more phenomenological but more general way. This chapter demonstrates that a similar concept as Fermi liquids exists in one dimension. This concept, called Luttinger liquid, encompasses most of the physics of simple one-dimensional systems and will be the starting point for the study more complex situations. The concept of Luttinger liquids is explained using very low level techniques.

Keywords:   Luttinger liquids, bosonization, statistical mechanics, conformal theory, elastic systems, physical interpretations, one-dimensional systems

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