Transition of the uniform statistical field anyon state to the nonuniform one ar low particle densities

TL;DR

This paper predicts a phase transition in a gas of spinless fermions from a uniform to a nonuniform magnetic field state at low particle densities, based on an exact analysis of their motion in a nonhomogeneous magnetic field.

Contribution

It provides an exact description of fermion motion in a specific nonhomogeneous magnetic field and predicts a density-dependent phase transition.

Findings

At low densities, the nonuniform field state has lower energy.

A transition from uniform to nonuniform magnetic field state occurs as density decreases.

The transition depends on the critical density (B, elta).

Abstract

Using results of our exact description of the spinless fermion motion in a nonhomogeneous magnetic field \( {\bf B} = B( 0, 0, 1/cosh^{2}( \frac{x-x_{0}}{ \delta })) \) we study a gas of these particles moving in this field. For lower densities \( \nu < \nu_{c}(B, \delta ) \) the corresponding total energy is lower than that of the uniform field state. Thus when the density of anyons decreases a transition from the uniform statistical field state to the nonhomogeneous field state is predicted.