Phase transitions in definite total spin states of two-component Fermi gases

TL;DR

This paper explores phase transitions in two-component Fermi gases related to non-Abelian permutation symmetry, revealing symmetry-driven thermodynamic changes even in ideal, non-interacting gases.

Contribution

It demonstrates the existence of non-Abelian symmetry-induced phase transitions in spinor Fermi gases, a novel insight into symmetry effects beyond traditional interaction-driven transitions.

Findings

Two distinct phases associated with fermionic and non-Abelian symmetry.

Discontinuous specific heat at the phase transition points.

Transitions occur even in ideal, non-interacting gases.

Abstract

Second-order phase transitions have no latent heat and are characterized by a change in symmetry. In addition to the conventional symmetric and anti-symmetric states under permutations of bosons and fermions, mathematical group-representation theory allows for non-Abelian permutation symmetry. Such symmetry can be hidden in states with defined total spins of spinor gases, which can be formed in optical cavities. The present work shows that the symmetry reveals itself in spin-independent or coordinate-independent properties of these gases, namely as non-Abelian entropy in thermodynamic properties. In weakly interacting Fermi gases, two phases appear associated with fermionic and non-Abelian symmetry under permutations of particle states, respectively. The second-order transitions between the phases are characterized by discontinuities in specific heat. Unlike other phase transitions, the present ones are not caused by interactions and can appear even in ideal gases. Similar effects in Bose gases and strong interactions are discussed.