Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Fermi Liquid Theory

Henrik Bruus, Karsten Flensberg

Published Sep 2, 2004• 1 citation
Publisher

Abstract

Abstract The concept of Fermi liquid theory was developed by Landau in 1957–59 and later refined by others. The basic conclusion is that a gas of interacting particles can be described by a system of almost non-interacting “quasiparticles.” These quasi particles are approximate excitations of the system at sufficiently short time scales. What we mean by “sufficiently short” of course has to be quantified, and this condition will set the limits for the applicability of the theory.

DOI
10.1093/oso/9780198566335.003.0015

Related papers

Fermi liquid theory

K. Yamada

We will consider the normal state of interacting Fermi particles without any longrange order. The normal state at low temperatures is called the Fermi liquid and is considered to be the system of free quasi-particles that is continuously connected with free Fermi gas. The concept of the Fermi liquid was introduced and developed by L. D. Landau. Landau's Fermi liquid theory, which concentrates rich contents into a simple theory, is a good example to solve many-body problems. In this chapter, we introduce the basis and main contents of the Fermi liquid. Principle of continuity The basis of the Fermi liquid theory is the principle of adiabatic continuity, which connects free Fermi gas with the Fermi liquid by introducing gradually an interaction among particles. There is a one-to-one correspondence between two states before and after the introduction of the interaction. States belonging to the same symmetry do not cross each other, and new states with the interaction can be represented by the old quantum number. Since the distribution of free Fermi gas is given by the Fermi distribution function n( k ) , that of the Fermi liquid is also written n ( k ). The state denoted by k , σ in the Fermi liquid is called the quasi-particle. For the system to be described by quasi-particles, the following condition is necessary. Let us consider the basis of the Fermi liquid theory following the explanation of the Landau theory given by Nozières and Anderson.

Cambridge University Press eBooks•Sep 23, 2004•1 citation

Microscopic Theories of the Electron Liquid

David Pines, Philippe Nozières

The macroscopic theory of Fermi liquids we have developed in the preceding chapters possesses the advantage of being exact for any normal liquid, irrespective of its density or law of interaction, so long as the temperature is sufficiently low and the phenomena under discussion involve both long wavelengths and low frequencies. It is, of course, incomplete, since it can provide no account of microscopic phenomena involving short wavelengths and large excitation energies, or of equilibrium properties such as the ground state energy and pair distribution function. In contrast, microscopic theories are able to describe both macroscopic and microscopic phenomena. They are, however, subject to one of the following limitations: They are exact for only a limited range of particle density or interaction, one which rarely corresponds to physical reality. The extent to which they provide an approximate account of a real physical system can rarely be estimated with any precision.

CRC Press eBooks•Mar 5, 2018•1 citation

Landau’s Theory of a Fermi Liquid

John B. Ketterson

Abstract This chapter analyses Landau’s Fermi liquid theory. A fundamental postulate of Landau’s Fermi liquid theory is that quasiparticle energies are a function of the momentum, p, and that the momentum, pF, corresponding to the Fermi energy continues to be given by a free particle expression. Thus, the quasiparticle states are in one-to-one correspondence with those of an ideal Fermi gas and each quasiparticle has a spin quantum number, σ ± 1/2. The remainder of the chapter deals with the quasiparticle interaction function; sum rules; and collisionless collective modes, which are defined as a collective mode as a time- (or frequency) and space- (or wave vector) dependent oscillation of the fluid involving a coordinated motion of its constituent particles. Sample problems are also provided at the end of the chapter.

•Sep 8, 2016•0 citations

Luttinger many-fermion model

Ladislav Šamaj, Zoltán Bajnok

Low-temperature properties of 3D interacting fermion systems are well described by Landau's theory of Fermi liquids; for reviews see, e.g. [183, 184]. It involves only excitations of the system around the Fermi surface on energy scales small compared to the Fermi energy. Excitations are well described by quasi-particles which are in one-to-one correspondence with the bare particles. The bare-particle interaction does not break the qualitative picture of non-interacting system, but renormalizes the dynamical characteristics (the effective mass and the pair interaction) of quasi-particles. Within the microscopic Green function formalism, the existence of quasi-particles is equivalent to assuming that the self-energy correction Σ( k , ω) is regular (has only short-range contributions in time and space) close to the Fermi surface. The lifetime of quasi-particles τ α(ε k −ε F ) −2 is long enough to consider them as well-defined eigenstates over long time-scales. The momentum occupation number of the bare particles exhibits a sharp discontinuity when crossing the Fermi momentum. The charge and spin degrees of freedom of quasi-particle always travel together. The Landau theory breaks down in 1D systems of interacting fermions which have a very specific Fermi surface consisting of two points ± k F . In such systems, the self-energy Σ( k , ω) no longer possesses the analytic properties required for introducing quasi-particles. In contrast to Fermi liquids, the momentum occupation number of the bare particles in the ground state is continuous at the Fermi momentum. Moreover, the charge and spin excitations are separated.

Cambridge University Press eBooks•May 16, 2013•0 citations

What is a quasi-particle?

J. R. Schrieffer

The concept of a quasi-particle excitation in an interacting many-body system will be discussed from both the physical and the math e matical points of vi e w.Th e physi cal origin of mass enhancement, wave fun ction re normalization, interac tio ns betwee n quasi-particles, etc. will be presented.Landau's Fermi liquid theory, including th e quasi-particle kinetic equation, will be reviewed.Finally, the domain of validity of the quasi-particl e approximation will be discuss ed.

Journal of Research of the National Bureau of Standards Section A Physics and Chemistry•Jul 1, 1970•6 citations

Fermi liquids, and their phase transitions

Subir Sachdev A

The Fermi liquid is perhaps the most familiar quantum many-body state of solid state physics; we met it briefly in Section 16.2.2. It is the generic state of fermions at nonzero density, and is found in all metals. Its basic characteristics can already be understood in a simple free fermion picture. Noninteracting fermions occupy the lowest energy single-particle states, consistent with the exclusion principle. This leads to the fundamental concept of the Fermi surface: a surface in momentum space separating the occupied and empty single fermion states. The lowest energy excitations then consist of quasiparticle excitations which are particle-like outside the Fermi surface, and hole-like inside the Fermi surface. Landau's Fermi liquid theory is a careful justification for the stability of this simple picture in the presence of interactions between fermions. Just as we found in Chapters 5 and 7 for the quantum Ising and rotor models, interaction corrections modify the wavefunction of the quasiparticle and so introduce a quasiparticle residue A ; however, they do not destabilize the integrity of the quasiparticle, as we review in Section 18.1. The purpose of this chapter is to describe two paradigms of symmetry breaking quantum transitions in Fermi liquids. In the first class, studied in Section 18.2, the broken symmetry is related to the point-group symmetry of the crystal, while translational symmetry is preserved; consequently, the order parameter resides at zero wavevector. In the second class, studied in Section 18.3, the order parameter is at a finite wavevector, and so translational symmetry is also broken.

Cambridge University Press eBooks•Apr 7, 2011•1 citation
Abstract The concept of Fermi liquid theory was developed by Landau in 1957–59 and later refined by others. The basic conclusion is that a gas of interacting particles can be described by a system of almost non-interacting “quasiparticles.” These quasi particles are approximate excitations of the system at sufficiently short time scales. What we mean by “sufficiently short” of course has to be quantified, and this condition will set the limits for the applicability of the theory.
We will consider the normal state of interacting Fermi particles without any longrange order. The normal state at low temperatures is called the Fermi liquid and is considered to be the system of free quasi-particles that is continuously connected with free Fermi gas. The concept of the Fermi liquid was introduced and developed by L. D. Landau. Landau's Fermi liquid theory, which concentrates rich contents into a simple theory, is a good example to solve many-body problems. In this chapter, we introduce the basis and main contents of the Fermi liquid. Principle of continuity The basis of the Fermi liquid theory is the principle of adiabatic continuity, which connects free Fermi gas with the Fermi liquid by introducing gradually an interaction among particles. There is a one-to-one correspondence between two states before and after the introduction of the interaction. States belonging to the same symmetry do not cross each other, and new states with the interaction can be represented by the old quantum number. Since the distribution of free Fermi gas is given by the Fermi distribution function n( k ) , that of the Fermi liquid is also written n ( k ). The state denoted by k , σ in the Fermi liquid is called the quasi-particle. For the system to be described by quasi-particles, the following condition is necessary. Let us consider the basis of the Fermi liquid theory following the explanation of the Landau theory given by Nozières and Anderson.
The macroscopic theory of Fermi liquids we have developed in the preceding chapters possesses the advantage of being exact for any normal liquid, irrespective of its density or law of interaction, so long as the temperature is sufficiently low and the phenomena under discussion involve both long wavelengths and low frequencies. It is, of course, incomplete, since it can provide no account of microscopic phenomena involving short wavelengths and large excitation energies, or of equilibrium properties such as the ground state energy and pair distribution function. In contrast, microscopic theories are able to describe both macroscopic and microscopic phenomena. They are, however, subject to one of the following limitations: They are exact for only a limited range of particle density or interaction, one which rarely corresponds to physical reality. The extent to which they provide an approximate account of a real physical system can rarely be estimated with any precision.
Abstract This chapter analyses Landau’s Fermi liquid theory. A fundamental postulate of Landau’s Fermi liquid theory is that quasiparticle energies are a function of the momentum, p, and that the momentum, pF, corresponding to the Fermi energy continues to be given by a free particle expression. Thus, the quasiparticle states are in one-to-one correspondence with those of an ideal Fermi gas and each quasiparticle has a spin quantum number, σ ± 1/2. The remainder of the chapter deals with the quasiparticle interaction function; sum rules; and collisionless collective modes, which are defined as a collective mode as a time- (or frequency) and space- (or wave vector) dependent oscillation of the fluid involving a coordinated motion of its constituent particles. Sample problems are also provided at the end of the chapter.
Low-temperature properties of 3D interacting fermion systems are well described by Landau's theory of Fermi liquids; for reviews see, e.g. [183, 184]. It involves only excitations of the system around the Fermi surface on energy scales small compared to the Fermi energy. Excitations are well described by quasi-particles which are in one-to-one correspondence with the bare particles. The bare-particle interaction does not break the qualitative picture of non-interacting system, but renormalizes the dynamical characteristics (the effective mass and the pair interaction) of quasi-particles. Within the microscopic Green function formalism, the existence of quasi-particles is equivalent to assuming that the self-energy correction Σ( k , ω) is regular (has only short-range contributions in time and space) close to the Fermi surface. The lifetime of quasi-particles τ α(ε k −ε F ) −2 is long enough to consider them as well-defined eigenstates over long time-scales. The momentum occupation number of the bare particles exhibits a sharp discontinuity when crossing the Fermi momentum. The charge and spin degrees of freedom of quasi-particle always travel together. The Landau theory breaks down in 1D systems of interacting fermions which have a very specific Fermi surface consisting of two points ± k F . In such systems, the self-energy Σ( k , ω) no longer possesses the analytic properties required for introducing quasi-particles. In contrast to Fermi liquids, the momentum occupation number of the bare particles in the ground state is continuous at the Fermi momentum. Moreover, the charge and spin excitations are separated.
The Fermi liquid is perhaps the most familiar quantum many-body state of solid state physics; we met it briefly in Section 16.2.2. It is the generic state of fermions at nonzero density, and is found in all metals. Its basic characteristics can already be understood in a simple free fermion picture. Noninteracting fermions occupy the lowest energy single-particle states, consistent with the exclusion principle. This leads to the fundamental concept of the Fermi surface: a surface in momentum space separating the occupied and empty single fermion states. The lowest energy excitations then consist of quasiparticle excitations which are particle-like outside the Fermi surface, and hole-like inside the Fermi surface. Landau's Fermi liquid theory is a careful justification for the stability of this simple picture in the presence of interactions between fermions. Just as we found in Chapters 5 and 7 for the quantum Ising and rotor models, interaction corrections modify the wavefunction of the quasiparticle and so introduce a quasiparticle residue A ; however, they do not destabilize the integrity of the quasiparticle, as we review in Section 18.1. The purpose of this chapter is to describe two paradigms of symmetry breaking quantum transitions in Fermi liquids. In the first class, studied in Section 18.2, the broken symmetry is related to the point-group symmetry of the crystal, while translational symmetry is preserved; consequently, the order parameter resides at zero wavevector. In the second class, studied in Section 18.3, the order parameter is at a finite wavevector, and so translational symmetry is also broken.