Quantum phase transitions of the Dirac oscillator in the Anti-Snyder model

TL;DR

This paper analyzes the Dirac oscillator in a magnetic field under the Anti-Snyder model, revealing that a finite momentum cut-off introduces multiple quantum phase transitions and alters state degeneracies.

Contribution

It provides exact solutions for the Dirac oscillator in the Anti-Snyder model and uncovers how a momentum cut-off modifies quantum phase transitions and degeneracies.

Findings

Finite momentum cut-off introduces additional quantum phase transitions.

The spectrum and degeneracies are significantly modified by the cut-off.

The system exhibits multiple phase transitions unlike the single transition in standard quantum mechanics.

Abstract

We obtain exact solutions of the (2+1) dimensional Dirac oscillator in a homogeneous magnetic field within the Anti-Snyder modified uncertainty relation characterized by a momentum cut-off ($p\leq p_{\text{max}}=1/ \sqrt{\beta}$). In ordinary quantum mechanics ($\beta\to 0$) this system is known to have a single left-right chiral quantum phase transition (QPT). We show that a finite momentum cut-off modifies the spectrum introducing additional quantum phase transitions. It is also shown that the presence of momentum cut-off modifies the degeneracy of the states.