A Solvable Model of Interacting Fermions in Two Dimensions

TL;DR

This paper presents an exactly solvable two-dimensional fermion model with interspecies magnetic interactions, revealing insights into anyonic theories and topological properties through analytical solutions.

Contribution

It introduces a new solvable 2D fermion model with interspecies magnetic interactions, extending previous 1D models and exploring its topological and transport properties.

Findings

Model reduces to a mean-field form with species-dependent magnetic fields

Analysis of Hall conductivity and wave function overlaps for two species

Model exhibits invariance under charge conjugation and PT symmetry

Abstract

We introduce and study an exactly solvable model of several species of fermions in which particles interact pairwise through a mutual magnetic field; the interaction operates only between particles belonging to different species. After an unitary transformation, the model reduces to one in which each particle sees a magnetic field which depends on the total numbers of particles of all the other species; this may be viewed as the mean-field model for a class of anyonic theories. Our model is invariant under charge conjugation C and the product PT (parity and time reversal). For the special case of two species, we examine various properties of this system, such as the Hall conductivity, the wave function overlap arising from the transfer of one particle from one species to another, and the one-particle off-diagonal density matrix. Our model is a generalization of a recently introduced solvable model in one dimension.