Generalized Hard-Core Fermions in One Dimension: An Exactly Solvable Luttinger Liquid

G. Gómez-Santos

A model for interacting spinless fermions in one dimension is presented and solved exactly. The solution is shown to be a Luttinger liquid with charge density wave instabilities for well characterized filling factors. Under very plausible assumptions, the exact solution is extended to the spin case with the usual charge-spin separation into two different Luttinger liquids. Required technicalities are almost trivial but the solution is very rich: Periodicity of instabilities and correlation exponents can be chosen at will.

Maxim Khodas, Michael Pustilnik, A. Kamenev +1 more

G. Benfatto, P. Falco, V. Mastropietro

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).

Igor N. Karnaukhov, Alexander A. Ovchinnikov

A family of exactly solvable one-dimensional models with a hard-core repulsive potential is solved by the Bethe ansatz for an arbitrary hard-core radius. The exact ground state phase diagrams in a plane ``electron-density--on-site interaction'' have been studied for several values of a hard-core radius. It is shown that strongly interacting Luttinger liquid can be realized in superconducting state at a high electron density and high value of repulsive on-site Coulomb interaction.

Heinz J. Schulz