One-Dimensional Quantum Liquids

Authored by: Kurt Schönhammer

1 Handbook of Nanophysics

Print publication date:  September  2010
Online publication date:  September  2010

Print ISBN: 9781420075403
eBook ISBN: 9781420075410
Adobe ISBN:

10.1201/9781420075410-13

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Abstract

The low-temperature thermodynamic properties of simple metals, like the alkalis, can be qualitatively understood in terms of the Sommerfeld model [1], which treats the conduction electrons as noninteracting fermions in a box. Typical results obtained using the model are a specific heat linear in temperature and a constant spin susceptibility which are in qualitative agreement with experiments. It took almost 30 years to understand why the low-temperature properties of interacting fermions are qualitatively the same. Landau’s phenomenological Fermi liquid theory [12] rests on the assumption of quasiparticles, which are in a one-to-one correspondence to noninteracting fermions. This leads to a linear specific heat and a constant spin susceptibility but involves renormalized quantities like the effective mass and the quasiparticle interaction parameters [12], which are difficult to calculate microscopically. The consistency of the approach was shown using perturbation theory to infinite order and more recently by renormalization group techniques [23]. Landau’s paper [12] marks the beginning of the general theory of (normal) quantum liquids [17], which are many-body systems in which the indistinguishability of the elementary constituents is important. The description of interacting bosons (liquid Helium 4, or the Bose alkali gases) is another theoretical challenge. These systems can undergo the phenomenon of Bose condensation. The related effect of Cooper pairing can occur in interacting Fermion systems (liquid Helium 3, electrons in the superconducting state).

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