Cascade of phase transitions in a planar Dirac material

TL;DR

This paper explores a model of interacting Dirac fermions in 2+1 dimensions, revealing a sequence of phase transitions and symmetry breakings influenced by mass, temperature, and chemical potential, with complex phase diagrams and exotic phases.

Contribution

It introduces a comprehensive analysis of phase transitions and symmetry breaking patterns in a multi-flavor Dirac fermion model, highlighting novel phases and transitions in the large-N limit.

Findings

Sequence of M first-order phase transitions with symmetry breaking patterns

Rich phase diagram with first and second-order transitions, tricritical points

Existence of exotic symmetry-broken phases such as U(3) to U(1)^3

Abstract

We investigate a model of interacting Dirac fermions in $2+1$ dimensions with $M$ flavors and $N$ colors having the $\mathrm{U}(M)\times \mathrm{SU}(N)$ symmetry. In the large-$N$ limit, we find that the $\mathrm{U}(M)$ symmetry is spontaneously broken in a variety of ways. In the vacuum, when the parity-breaking flavor-singlet mass is varied, the ground state undergoes a sequence of $M$ first-order phase transitions, experiencing $M+1$ phases characterized by symmetry breaking $\mathrm{U}(M)\to \mathrm{U}(M-k)\times \mathrm{U}(k)$ with $k\in\{0,1,2,\cdots,M\}$, bearing a close resemblance to the vacuum structure of three-dimensional QCD. At finite temperature and chemical potential, a rich phase diagram with first and second-order phase transitions and tricritical points is observed. Also exotic phases with spontaneous symmetry breaking of the form as $\mathrm{U}(3)\to \mathrm{U}(1)^3$, $\mathrm{U}(4)\to \mathrm{U}(2)\times \mathrm{U}(1)^2$, and $\mathrm{U}(5)\to \mathrm{U}(2)^2\times \mathrm{U}(1)$ exist. For a large flavor-singlet mass, the increase of the chemical potential $\mu$ brings about $M$ consecutive first-order transitions that separate the low-$\mu$ phase diagram with vanishing fermion density from the high-$\mu$ region with a high fermion density.