\lambda-transition in low dimensional systems with SU_q(2) symmetry

TL;DR

This paper demonstrates that one- and two-dimensional systems with SU_q(2) symmetry undergo a Bose-Einstein condensation at a critical temperature when q>1, revealing a quantum phase transition with unique thermodynamic properties.

Contribution

It introduces the occurrence of a lambda-transition in low-dimensional SU_q(2) symmetric systems, highlighting the effects of quantum deformation on phase transitions.

Findings

Bose-Einstein condensation occurs for q>1 in 1D and 2D systems.

Critical temperature and heat capacity gap increase with q deviations from 1.

Entropy at low temperatures is lower than that of an ideal Bose gas for q>1.

Abstract

We show that $SU_q(2)$ invariant systems in one and two dimensions exhibit Bose-Einstein condensation for $q >1$. For these systems there is a $\lambda$-transition at the critical temperature. The critical temperature and the gap in the heat capacity increase more rapidly for small deviations from the standard value $q=1$, and they become approximately constant for large values of $q$. For low temperatures and $q>1$ the entropy is lower than the entropy of an ideal Bose gas.