The Group-Theoretical Classification of Some Multiparticle States in the Presence of Magnetic Field and Periodic Potential

TL;DR

This paper classifies multiparticle quantum states in magnetic fields and periodic potentials using group theory, revealing degeneracy patterns and symmetry properties, with implications for understanding complex quantum systems.

Contribution

It introduces a group-theoretical framework for classifying multiparticle states, including trions, in magnetic and periodic environments, highlighting gauge independence and symmetry considerations.

Findings

Degeneracy of pair states is N for a given period N.

Three symmetry-adapted bases for trions are proposed.

Results are gauge-independent despite using Landau gauge.

Abstract

The group-theoretical classification of multiparticle states(pairs of particles and charged excitons X^+-) is based on considerations of products of irreducible projective representations of the two-dimensional translation group. The states of a pair particle-antiparticle are non-degenerate, whereas, for a given Born-von Karman period N, degeneracy of pair states is N andthree-particle states are N^2-fold degenerated. The symmetrization of states with respect to particles transposition is considered. Three symmetry adapted bases for trions are considered: (i) the first is obtained from a direct conjugation of three representations; (ii) in the second approach the states of a electrically neutral pair particle-antiparticle are determined in the first step; (iii) the third possibility is to consider a pair of identical particles in the first step. In the discussion presented the Landau gauge A=[0,Hx,0] is used, but it is shown that the results obtained are gauge-independent. In addition the relation between changes of a chosen gauge and local basis transformations are discussed.