Book contents
- Frontmatter
- Contents
- Preface
- 1 Introduction to the electron liquid
- 2 The Hartree–Fock approximation
- 3 Linear response theory
- 4 Linear response of independent electrons
- 5 Linear response of an interacting electron liquid
- 6 The perturbative calculation of linear response functions
- 7 Density functional theory
- 8 The normal Fermi liquid
- 9 Electrons in one dimension and the Luttinger liquid
- 10 The two-dimensional electron liquid at high magnetic field
- Appendices
- References
- Index
9 - Electrons in one dimension and the Luttinger liquid
Published online by Cambridge University Press: 05 August 2012
- Frontmatter
- Contents
- Preface
- 1 Introduction to the electron liquid
- 2 The Hartree–Fock approximation
- 3 Linear response theory
- 4 Linear response of independent electrons
- 5 Linear response of an interacting electron liquid
- 6 The perturbative calculation of linear response functions
- 7 Density functional theory
- 8 The normal Fermi liquid
- 9 Electrons in one dimension and the Luttinger liquid
- 10 The two-dimensional electron liquid at high magnetic field
- Appendices
- References
- Index
Summary
Non-Fermi liquid behavior
In this chapter we begin the study of electronic systems that are not Landau Fermi liquids. These systems are like totalitarian societies in which the behavior of the individual is subordinated to the needs of the organization: their low-energy excitations are collective, rather than single-particle-like. A strongly collective behavior is not at all unusual in condensed matter. For example, the low energy excitations of a crystal lattice are acoustic phonons, which are collective oscillations of the atoms about their equilibrium positions. However, such examples are usually associated with a broken symmetry (translational symmetry in this case): when it comes to homogeneous electron liquids, the familiar picture of Landau's quasiparticles is so ingrained that we tend to regard any departure from it as a surprising phenomenon. Nevertheless, departures from the normal Fermi liquid pattern can and do occur in two typical scenarios:
In three- and two-dimensional systems in which the electron liquid is strongly correlated, i.e., when the order of magnitude of the coulomb interaction greatly exceeds the kinetic bandwidth,
In quasi-one-dimensional systems, for any strength of the interaction.
A trivial example of the first scenario is offered by the three-dimensional electron liquid at very low-density. In this case the electrons form a Wigner crystal and their collective behavior arises immediately from the loss of translational symmetry. Amuch more complex example is offered by the two-dimensional electron liquid at high magnetic field. Because the kinetic energy is effectively suppressed by the magnetic field, the structure of the groundstate and the low-lying excitations is entirely controlled by the coulomb interaction.
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- Quantum Theory of the Electron Liquid , pp. 501 - 549Publisher: Cambridge University PressPrint publication year: 2005