Quantum phase transitions of the Dirac oscillator in a minimal length scenario

TL;DR

This paper derives exact solutions for the (2+1)D Dirac oscillator under a minimal length scenario, revealing an infinite series of quantum phase transitions and new states absent in standard quantum mechanics.

Contribution

It introduces the impact of a minimal length on the Dirac oscillator, showing the emergence of multiple quantum phase transitions and novel states not present in classical quantum mechanics.

Findings

Infinite quantum phase transitions induced by minimal length

Modification of state degeneracies due to minimal length

Existence of new states absent in ordinary quantum mechanics

Abstract

We obtain exact solutions of the (2+1) dimensional Dirac oscillator in a homogeneous magnetic field within a minimal length ($\Delta x_0=\hbar \sqrt{\beta}$), or generalised uncertainty principle (GUP) scenario. This system in ordinary quantum mechanics has a single left-right chiral quantum phase transition (QPT). We show that a non zero minimal length turns on a infinite number of quantum phase transitions which accumulate towards the known QPT when $\beta \to 0$. It is also shown that the presence of the minimal length modifies the degeneracy of the states and that in this case there exist a new class of states which do not survive in the ordinary quantum mechanics limit $\beta \to 0$.