The 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).

Edwin Langmann A

Antônio Sérgio Teixeira Pires

Kridsanaphong Limtragool, Zhidong Leong, Philip Phillips

We investigate the validity of Luttinger’s theorem (or Luttinger sum rule) in two scale-invariant fermionic models. We find that, in general, Luttinger’s theorem does not hold in a system of fermions with power-law Green functions which do not necessarily preserve particle-hole symmetry. However, Ref. [1,2] showed that Luttinger liquids, another scale-invariant fermionic model, respect Luttinger’s theorem. To understand the difference, we examine the spinless Luttinger liquid model. We find two properties which make the Luttinger sum rule valid in this model: particle-hole symmetry and lmG(\omega=0,-\infty)=0 l m G ( ω = 0 , − ∞ ) = 0 . We conjecture that these two properties represent sufficient, but not necessary, conditions for the validity of the Luttinger sum rule in condensed matter systems.

Uwe K. Albertin, Michael G. Cleveland, Tim Pritchett

The standard solution of the Luttinger model (1963) is compared with recent formulations of the Thirring model used in describing Thirring strings. These models may in turn be described by compactified boson models of particular radii. An interesting discrepancy is noted between the apparent radius of the bosons in the Luttinger model and those in the Thirring model. This difference manifests itself in different conformal weights for the fermion fields. The authors resolve this discrepancy by performing an additional rescaling of the Luttinger model bosons. They then examine the enhanced symmetry points that occur in the boson theory at particular values of the radii. In particular, for the Thirring model with two families of spinors, which corresponds to a conformal theory with central extension c=2, one finds an enhanced SU(3) L *SU(3) R symmetry for certain values of the boson radii. This theory is equivalent to the Luttinger model with spin. By examining the response functions for the Luttinger model it is found that the point of SU(3) L *SU(3) R symmetry lies on the Luttinger model phase transition lines.

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