Spectrum of Relativistic Fermions in a 2d Doped Lattice

TL;DR

This paper investigates the spectrum of Dirac fermions on a randomly doped 2D lattice, revealing a sine-Gordon description, spontaneous symmetry breaking, and mass modifications due to doping effects.

Contribution

It introduces a sine-Gordon model for doped lattice fermions, showing how doping induces quartic interactions and mass changes, and discusses symmetry breaking phenomena.

Findings

Fermions are described by a sine-Gordon action.

Doping leads to quartic interactions and effective mass changes.

The system exhibits spontaneous symmetry breaking with a Goldstone boson.

Abstract

Motivated by some previous work on fermions on random lattices and by suggestions that impurities could trigger parity breaking in 2d crystals, we have analyzed the spectrum of the Dirac equation on a two dimensional square lattice where sites have been removed randomly --- a doped lattice. We have found that the system is well described by a sine-Gordon action. The solitons of this model are the lattice fermions, which pick a quartic interaction due to the doping and become Thirring fermions. They also get an effective mass different from the lagrangian mass. The system seems to exhibit spontaneous symmetry breaking, exactly as it happens for a randomly triangulated lattice. The associated ``Goldstone boson" is the sine-Gordon scalar. We argue, however, that the peculiar behaviour of the chiral condensate is due to finite size effects.