A Two-dimensional Model with Chiral Condensates and Cooper Pairs having QCD-like Phase Structure

TL;DR

This paper introduces a two-dimensional O(N) symmetric model with chiral and superconducting phases, analytically solvable at large N, which mimics QCD phase structure and can inform studies of heavy ion collisions and neutron star interiors.

Contribution

The authors develop a solvable two-dimensional model with QCD-like phase structure, including detailed phase diagrams and a renormalization group invariant parameter, expanding understanding of phase transitions in similar systems.

Findings

Model exhibits chiral symmetry breaking and Cooper pair phases at large N.

Phase diagram features first- and second-order transitions, including a tricritical point.

Mimics QCD phase structure, relevant for heavy ion and neutron star physics.

Abstract

We generalize our previous model to an O(N) symmetric two-dimensional model which possesses chiral symmetry breaking and superconducting (Cooper pair condensates) phases at large-N. At zero temperature and density, the model can be solved analytically in the large-N limit. We perform the renormalization explicitly and obtain a closed form expression of the effective potential. There exists a renormalization group invariant parameter $\delta$ that determines which of the condensates exist in the vacuum. At finite temperatures and densities, we map out the phase structure of the model by a detailed numerical analysis of the renormalized effective potential. For $\delta$ positive and sufficiently large, the phase diagram in the $\mu$-$T$ (chemical potential-temperature) plane exactly mimics the features expected for QCD with two light flavors of quarks. At low temperatures there exists low-$\mu$ chiral symmetry breaking and high-$\mu$ Cooper pair condensate regions which are separated by a first-order phase transition. At high $\mu$, when the temperature is raised, the system undergoes a second-order phase transition from the superconducting phase to an unbroken phase in which both condensates vanish. For a range of values of $\delta$ the theory possesses a tricritical point ($\mu_{tc}$ and $T_{tc}$); for $\mu > \mu_{tc}$ ($\mu < \mu_{tc}$) the phase transition from the low temperature chiral symmetry breaking phase to unbroken phase is first-order (second-order). For the range of $\delta$ in which the system mimics QCD, we expect the model to be useful for the investigation of dynamical aspects of nonequilibrium phase transitions, and to provide information relevant to the study of relativistic heavy ion collisions and the dense interiors of neutron stars.