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

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 cutoff ($p\ensuremath{\le}{p}_{\mathrm{max}}=1/\sqrt{\ensuremath{\beta}}$). In ordinary quantum mechanics ($\ensuremath{\beta}\ensuremath{\rightarrow}0$) this system is known to have a single left-right chiral quantum phase transition (QPT). We show that a finite momentum cutoff modifies the spectrum introducing additional quantum phase transitions. It is also shown that the presence of momentum cutoff modifies the degeneracy of the states.