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Communications in Mathematical Physics

, Volume 314, Issue 1, pp 1–56 | Cite as

Exact Solution of a 2D Interacting Fermion Model

  • Jonas de Woul
  • Edwin Langmann
Article

Abstract

We study an exactly solvable quantum field theory (QFT) model describing interacting fermions in 2+1 dimensions. This model is motivated by physical arguments suggesting that it provides an effective description of spinless fermions on a square lattice with local hopping and density-density interactions if, close to half filling, the system develops a partial energy gap. The necessary regularization of the QFT model is based on this proposed relation to lattice fermions. We use bosonization methods to diagonalize the Hamiltonian and to compute all correlation functions. We also discuss how, after appropriate multiplicative renormalizations, all short- and long distance cutoffs can be removed. In particular, we prove that the renormalized two-point functions have algebraic decay with non-trivial exponents depending on the interaction strengths, which is a hallmark of Luttinger-liquid behavior.

Keywords

Fermi Surface Mattis Model Vertex Operator Algebra Lattice Fermion Boson Operator 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag 2012

Authors and Affiliations

  1. 1.Department of Theoretical PhysicsRoyal Institute of Technology (KTH)StockholmSweden

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