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

Physical Review Letters

Generalization of a Fermi Liquid to a Liquid with Fractional Exclusion Statistics in Arbitrary Dimensions: Theory of a Haldane Liquid

Kazumoto Iguchi

Published Feb 23, 1998• 18 citations
Publisher

Abstract

A liquid of interacting quasiparticles with Haldane-Wu (fractional exclusion) statistics in arbitrary dimensions is discussed in terms of Fermi-liquid theory. The universal properties of this Haldane liquid are investigated.
DOI
10.1103/physrevlett.80.1698

Related papers

Haldane liquid with mutual exclusion statistics

Kazumoto Iguchi

I study basic properties of a Haldane liquid with mutual exclusion statistics (MES), which is a liquid of quasiparticles interacting only through the MES that are assumed to be parameters as usually done in the definition of Haldane statistics. By this approximation for the statistics, I obtain the following: The ground state of the system has multiple pseudo--Fermi surfaces for all species of quasiparticles when $T=0,$ where the pseudo--Fermi surface for each species exhibits the particle-hole asymmetry. I define the dressed energies so as to satisfy the Sutherland-Wu (SW) functional equations that are the defining relations for the MES, from which the elementary excitations near the ground state are given. And finally, I show that the SW equations have an unusual type of duality such as spin-charge duality in the system.

Physical review. B, Condensed matter•May 15, 2000•7 citations

Generalization of Tomonaga–Luttinger Liquids and the Calogero–Sutherland Model: Microscopic Models for the Haldane Liquids

Kazumoto Iguchi

We discuss the quantum many-body system interacting with a separately symmetric two-body potential in higher dimensions as a generalization of the Calogero–Sutherland model in one dimension. This system exhibits the properties of a Haldane liquid such as Haldane–Wu (i.e., fractional exclusion) statistics, broken particle–hole symmetry and the existence of pseudo-Fermi surface as a generalization of the cencept of Tomonaga–Luttinger liquids in one dimension.

Modern Physics Letters B•Jul 10, 1998•1 citation

Quantum Statistical Mechanics of an Ideal Gas with Fractional Exclusion Statistics in Arbitrary Dimensions

Kazumoto Iguchi

The quantum statistical mechanics of an ideal gas with fractional exclusion (i.e., Haldane-Wu) statistics in arbitrary dimensions is discussed. The general formulation for pressure and density of the system is obtained in a closed form in terms of the $D$-dimensional momentum representation, which can be regarded as a natural generalization of the classic results for Fermi and Bose gases. Using this, it is shown that ideal gases with fractional exclusion statistics can be regarded as composites of fermions and bosons, and that no condensation occurs at low temperature except for the pure boson case.

Physical Review Letters•Apr 28, 1997•33 citations

Comment on “Generalization of a Fermi Liquid to a Liquid with Fractional Exclusion Statistics in Arbitrary Dimensions: Theory of a Haldane Liquid”

J. M. P. Carmelo, Peter Horsch, Alexander A. Ovchinnikov +3 more

A Comment on the Letter by Kazumoto Iguchi, Phys. Rev. Lett. 80, 1698 (1998).Received 15 April 1998DOI:https://doi.org/10.1103/PhysRevLett.81.489©1998 American Physical Society

Physical Review Letters•Jul 13, 1998•8 citations

The Fermi liquid theory with fractional exclusion statistics

Dragoş-Victor Anghel

The Fermi liquid theory may provide a good description of the thermodynamic properties of an interacting particle system when the interaction between the particles contributes to the total energy of the system with a quantity which may depend on the total particle number, but does not depend on the temperature. In such a situation, the ideal part of the Hamiltonian, i.e. the energy of the system without the interaction energy, also provides a good description of the system's thermodynamics. If the total interaction energy of the system, being a complicated function of the particle populations, is temperature dependent, then the Landau's quasiparticle gas cannot describe accurately the thermodynamics of the system. A general solution to this problem is presented in this paper, in which the quasiparticle energies are redefined in such a way that the total energy of the system is identical to the sum of the energies of the quasiparticles. This implies also that the thermodynamic properties of the system and those of the quasiparticle gas are identical. By choosing a perspective in which the quasiparticle energies are fixed while the density of states along the quasiparticle axis vary, we transform our quasiparticle system into an ideal gas which obey fractional exclusion statistics.

arXiv:1204.4064•Apr 18, 2012•1 citation

Luttinger liquids, Fermi liquids, and fractional statistics

Jon Magne Leinaas

We discuss how one-dimensional interacting fermion systems, which in the low-energy approximation are described by Luttinger liquid theory, can be reformulated as systems of weakly interacting particles with fractional charge and statistics. Our approach is to use Landau's phenomenological approach to Fermi liquid theory, where the quasiparticles are interpreted as adiabatically dressed fermions. In an earlier publication, the local charge carried by these excitations has been shown to be fractional. We focus here on the statistics of the quasiparticles and show that by a change of momentum variables the Landau parameters of the generalized Fermi fluid can be transformed to zero. This change in interaction is compensated by a change of the entropy function, which is consistent with the interpretation of the quasiparticles as satisfying generalized exclusion statistics.

arXiv:1612.07585•Physical review. B./Physical review. B•Apr 19, 2017•2 citations
I study basic properties of a Haldane liquid with mutual exclusion statistics (MES), which is a liquid of quasiparticles interacting only through the MES that are assumed to be parameters as usually done in the definition of Haldane statistics. By this approximation for the statistics, I obtain the following: The ground state of the system has multiple pseudo--Fermi surfaces for all species of quasiparticles when T=0,T=0,T=0, where the pseudo--Fermi surface for each species exhibits the particle-hole asymmetry. I define the dressed energies so as to satisfy the Sutherland-Wu (SW) functional equations that are the defining relations for the MES, from which the elementary excitations near the ground state are given. And finally, I show that the SW equations have an unusual type of duality such as spin-charge duality in the system.
The quantum statistical mechanics of an ideal gas with fractional exclusion (i.e., Haldane-Wu) statistics in arbitrary dimensions is discussed. The general formulation for pressure and density of the system is obtained in a closed form in terms of the DDD-dimensional momentum representation, which can be regarded as a natural generalization of the classic results for Fermi and Bose gases. Using this, it is shown that ideal gases with fractional exclusion statistics can be regarded as composites of fermions and bosons, and that no condensation occurs at low temperature except for the pure boson case.
The Fermi liquid theory may provide a good description of the thermodynamic properties of an interacting particle system when the interaction between the particles contributes to the total energy of the system with a quantity which may depend on the total particle number, but does not depend on the temperature. In such a situation, the ideal part of the Hamiltonian, i.e. the energy of the system without the interaction energy, also provides a good description of the system's thermodynamics. If the total interaction energy of the system, being a complicated function of the particle populations, is temperature dependent, then the Landau's quasiparticle gas cannot describe accurately the thermodynamics of the system. A general solution to this problem is presented in this paper, in which the quasiparticle energies are redefined in such a way that the total energy of the system is identical to the sum of the energies of the quasiparticles. This implies also that the thermodynamic properties of the system and those of the quasiparticle gas are identical. By choosing a perspective in which the quasiparticle energies are fixed while the density of states along the quasiparticle axis vary, we transform our quasiparticle system into an ideal gas which obey fractional exclusion statistics.
We discuss how one-dimensional interacting fermion systems, which in the low-energy approximation are described by Luttinger liquid theory, can be reformulated as systems of weakly interacting particles with fractional charge and statistics. Our approach is to use Landau's phenomenological approach to Fermi liquid theory, where the quasiparticles are interpreted as adiabatically dressed fermions. In an earlier publication, the local charge carried by these excitations has been shown to be fractional. We focus here on the statistics of the quasiparticles and show that by a change of momentum variables the Landau parameters of the generalized Fermi fluid can be transformed to zero. This change in interaction is compensated by a change of the entropy function, which is consistent with the interpretation of the quasiparticles as satisfying generalized exclusion statistics.