Luttinger Model

The First 50 Years and Some New Directions

The Luttinger Model is the only model of many-fermion physics with legitimate claims to be both exactly and completely solvable. In several respects it plays the same role in many-body theory as does the 2D Ising model in statistical physics.

Interest in the Luttinger model has increased steadily ever since its introduction half a century ago. The present volume starts with reprints of the seminal papers in which it was originally introduced and solved, and continues with several contributions setting out the landscape of the principal advances of the last fifty years and of prominent new directions.

Contents:

• The Luttinger Model and Its Solution:

  • An Exactly Soluble Model of a Many-Fermion System (Joaquin M Luttinger)
  • Exact Solution of a Many-Fermion System and Its Associated Boson Field (Daniel C Mattis and Elliott H Lieb)

• Lattice, Dynamical and Nonlinear Effects:

  • Luttinger Model and Luttinger Liquids (Vieri Mastropietro)
  • The Luttinger Liquid and Integrable Models (Jesko Sirker)
  • Long Time Correlations of Nonlinear Luttinger Liquids (Rodrigo G Pereira)
  • An Expanded Luttinger Model (Daniel C Mattis)

• Applications and Experimental Test:

  • 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 (Thierry 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 (Carlo Di Castro and Sergio Caprara)
  • Luttinger Model in Dimensions d > 1 (Daniel C Mattis)

Readership: Physicists and theoretical chemists in condensed matter and/or nuclear-matter physics and graduate students in these fields, mathematical physicists working in the many-body problem, experimentalists in low-dimensional phenomena.