Super-extended noncommutative Landau problem and conformal symmetry

TL;DR

This paper explores a supersymmetric spin-1/2 particle in a noncommutative plane under various magnetic fields, revealing phase-dependent symmetries and boundary behaviors linked to conformal and exotic Newton-Hooke structures.

Contribution

It introduces a detailed analysis of the super-extended noncommutative Landau problem, identifying phase-dependent symmetry structures and boundary critical phenomena.

Findings

Three distinct phases depending on magnetic field strength

Supercritical phase exhibits so(3) symmetry with frozen spins

Boundary critical phase relates to zero-energy eigensubspace

Abstract

A supersymmetric spin-1/2 particle in the noncommutative plane, subject to an arbitrary magnetic field, is considered, with particular attention paid to the homogeneous case. The system has three different phases, depending on the magnetic field. Due to supersymmetry, the boundary critical phase which separates the sub- and super-critical cases can be viewed as a reduction to the zero-energy eigensubspace. In the sub-critical phase the system is described by the superextension of exotic Newton-Hooke symmetry, combined with the conformal so(2,1) ~ su(1,1) symmetry; the latter is changed into so(3) ~ su(2) in the super-critical phase. In the critical phase the spin degrees of freedom are frozen and supersymmetry disappears.