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

CRC Press eBooks

One-Dimensional Quantum Liquids

Klaus D. Sattler

Published Sep 17, 2010• 1 citation
Publisher

Abstract

Fortunately even with only little background in the quantum many-body problem, the emergence of the Luttinger liquid (LL) picture can be understood. What is needed is a fresh look at the statistical mechanics of noninteracting fermions in one dimension and a comparison with the physics of the harmonic chain. ese simple systems are treated in textbooks on solid state physics and statistical mechanics [1,18].

DOI
10.1201/9781420075410-17

Related papers

Physics in one dimension: theoretical concepts for quantum many-body systems

Kurt Schönhammer

Various sophisticated approximation methods exist for the description of quantum many-body systems. It was realized early on that the theoretical description can simplify considerably in one-dimensional systems and various exact solutions exist. The focus in this introductory paper is on fermionic systems and the emergence of the Luttinger liquid concept.

arXiv:1212.1632•Journal of Physics Condensed Matter•Dec 5, 2012•15 citations

Luttinger Model

Vieri Mastropietro, Daniel Charles Mattis

The Luttinger Model and Its Solution: An Exactly Soluble Model of a Many-Fermion System (J M Luttinger) Exact Solution of a Many-Fermion System and its Associated Boson Field (Daniel C Mattis and Elliott H Lieb) Lattice, Dynamical and Non Linear Effects: Luttinger Model and Luttinger Liquids (Vieri Mastropietro) The Luttinger Liquid and Integrable Models (J Sirker) Long Time Correlations of Nonlinear Luttinger Liquids Rodrigo (G Pereira) An Expanded Luttinger Model (Daniel C Mattis) Applications and Experimental Tests: Quantum Hall Edge Physics and Its One-Dimensional Luttinger Liquid Description (Orion Ciftja) A Luttinger Liquid Core Inside Helium-4 Filled Nanopores (Adrian Del Maestro) Some Experimental Tests of Tomonaga - Luttinger Liquids (T Giamarchi) Bosonization and Its Application to Transport in Quantum Wires (Feifei Li) Generalizations to Higher Dimensions: Fermions in Two Dimensions, Bosonization, and Exactly Solvable Models (Jonas De Woul and Edwin Langmann) Luttinger Liquid, Singular Interaction and Quantum Criticality in Cuprate Materials (C Di Castro and S Caprara) Luttinger Model in Dimensions d > 1 (Daniel C Mattis).

Series on directions in condensed matter physics•Jun 18, 2013•11 citations

Luttinger Liquid in Two Dimensions--Fermionic Backflow and Transfer of Statistics (Low Dimensional Field Theories and Condensed Matter Physics(Proceedings of the 4th Yukawa International Seminar))

G. Baskaran

Progress of Theoretical Physics•May 1, 1992•0 citations

‘Luttinger liquid theory’ of one-dimensional quantum fluids: I. Properties of the Luttinger model and their extension to the general 1D interacting spinless Fermi gas

F. D. M. Haldane

WORLD SCIENTIFIC eBooks•Dec 1, 1994•6 citations

The Luttinger liquid concept for interacting electrons in one dimension

Kurt Schönhammer

The theoretical description of interacting fermions in one spatial dimension is simplified by the fact that the low-energy spectrum of noninteracting fermions is identical to the one for a harmonic chain. This allows us to describe interacting fermions as a system of coupled oscillators. The exact solution of the Tomonaga-Luttinger model is discussed and results for the momentum distribution and spectral functions are presented. The general Luttinger liquid phenomenology is briefly discussed and various attempts at the experimental verification of the theoretical predictions are examined. Extended defects in semiconductors might also be candidate systems.

•Jan 1, 2002•0 citations

The Luttinger liquid concept for interacting electrons in one dimension

K Sch nhammer

The theoretical description of interacting fermions in one spatial dimension is simplified by the fact that the low-energy spectrum of noninteracting fermions is identical to the one for a harmonic chain. This allows us to describe interacting fermions as a system of coupled oscillators. The exact solution of the Tomonaga–Luttinger model is discussed and results for the momentum distribution and spectral functions are presented. The general Luttinger liquid phenomenology is briefly discussed and various attempts at the experimental verification of the theoretical predictions are examined. Extended defects in semiconductors might also be candidate systems.

Journal of Physics Condensed Matter•Nov 22, 2002•21 citations
Fortunately even with only little background in the quantum many-body problem, the emergence of the Luttinger liquid (LL) picture can be understood. What is needed is a fresh look at the statistical mechanics of noninteracting fermions in one dimension and a comparison with the physics of the harmonic chain. ese simple systems are treated in textbooks on solid state physics and statistical mechanics [1,18].
The Luttinger Model and Its Solution: An Exactly Soluble Model of a Many-Fermion System (J M Luttinger) Exact Solution of a Many-Fermion System and its Associated Boson Field (Daniel C Mattis and Elliott H Lieb) Lattice, Dynamical and Non Linear Effects: Luttinger Model and Luttinger Liquids (Vieri Mastropietro) The Luttinger Liquid and Integrable Models (J Sirker) Long Time Correlations of Nonlinear Luttinger Liquids Rodrigo (G Pereira) An Expanded Luttinger Model (Daniel C Mattis) Applications and Experimental Tests: Quantum Hall Edge Physics and Its One-Dimensional Luttinger Liquid Description (Orion Ciftja) A Luttinger Liquid Core Inside Helium-4 Filled Nanopores (Adrian Del Maestro) Some Experimental Tests of Tomonaga - Luttinger Liquids (T Giamarchi) Bosonization and Its Application to Transport in Quantum Wires (Feifei Li) Generalizations to Higher Dimensions: Fermions in Two Dimensions, Bosonization, and Exactly Solvable Models (Jonas De Woul and Edwin Langmann) Luttinger Liquid, Singular Interaction and Quantum Criticality in Cuprate Materials (C Di Castro and S Caprara) Luttinger Model in Dimensions d > 1 (Daniel C Mattis).
The theoretical description of interacting fermions in one spatial dimension is simplified by the fact that the low-energy spectrum of noninteracting fermions is identical to the one for a harmonic chain. This allows us to describe interacting fermions as a system of coupled oscillators. The exact solution of the Tomonaga-Luttinger model is discussed and results for the momentum distribution and spectral functions are presented. The general Luttinger liquid phenomenology is briefly discussed and various attempts at the experimental verification of the theoretical predictions are examined. Extended defects in semiconductors might also be candidate systems.
The theoretical description of interacting fermions in one spatial dimension is simplified by the fact that the low-energy spectrum of noninteracting fermions is identical to the one for a harmonic chain. This allows us to describe interacting fermions as a system of coupled oscillators. The exact solution of the Tomonaga–Luttinger model is discussed and results for the momentum distribution and spectral functions are presented. The general Luttinger liquid phenomenology is briefly discussed and various attempts at the experimental verification of the theoretical predictions are examined. Extended defects in semiconductors might also be candidate systems.