Particles in a magnetic field and plasma analogies: doubly periodic boundary conditions

TL;DR

This paper derives an exact form of the N-particle fermion state in a magnetic field with doubly periodic boundaries, linking it to solvable plasma models and predicting universal behavior in Coulomb systems.

Contribution

It introduces a new exact formulation of the fermion state and connects it to solvable plasma models, revealing universal properties of Coulomb systems with periodic boundaries.

Findings

Exact N-particle fermion state in a magnetic field derived

Formulation of solvable plasma and Coulomb gas models

Universal O(1) term in free energy expansion predicted

Abstract

The $N$-particle free fermion state for quantum particles in the plane subject to a perpendicular magnetic field, and with doubly periodic boundary conditions, is written in a product form. The absolute value of this is used to formulate an exactly solvable one-component plasma model, and further motivates the formulation of an exactly solvable two-species Coulomb gas. The large $N$ expansion of the free energy of both these models exhibits the same O(1) term. On the basis of a relationship to the Gaussian free field, this term is predicted to be universal for conductive Coulomb systems in doubly periodic boundary conditions.