Exact solution of a 2D interacting fermion model

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.

59 pages, 3 figures, v2: further references added; additional subsections elaborating mathematical details; additional appendix with details on the relation to lattice fermions

References in corpus (2)

• Partially gapped fermions in 2D
• Luttinger liquid fixed point for a 2D flat Fermi surface

Cited by in corpus (6)

• Steady states and universal conductance in a quenched Luttinger model
• Correlation Energy of a Weakly Interacting Fermi Gas
• Construction by bosonization of a fermion-phonon model
• Fermions in two dimensions, bosonization, and exactly solvable models
• Exact operator Hamiltonians and interactions in the droplet bosonization method
• Gauge invariance, correlated fermions, and photon mass in 2+1 dimensions