Emergent chiral symmetry in a three-dimensional interacting Dirac liquid

TL;DR

This paper investigates how strong local electronic interactions influence three-dimensional Dirac fermions, revealing emergent chiral symmetry at certain quantum critical points through a renormalization group analysis.

Contribution

It introduces a lattice model for chiral Dirac fermions and demonstrates emergent chiral symmetry at RG fixed points in an interacting 3D Dirac liquid.

Findings

Emergent chiral symmetry at RG fixed points

Multiple quantum critical and bicritical points identified

Restoration of chiral and pseudospin symmetries at phase transitions

Abstract

We compute the effects of strong Hubbardlike local electronic interactions on three-dimensional four-component massless Dirac fermions, which in a noninteracting system possess a microscopic global U(1)$\otimes$SU(2) chiral symmetry. A concrete lattice realization of such chiral Dirac excitations is presented, and the role of electron-electron interactions is studied by performing a field theoretic renormalization group (RG) analysis, controlled by a \emph{small} parameter $\epsilon$ with $\epsilon=d-1$, about the lower-critical one spatial dimension. Besides the noninteracting Gaussian fixed point, the system supports four quantum critical and four bicritical points at nonvanishing interaction couplings $\sim \epsilon$. Even though the chiral symmetry is absent in the interacting model, it gets restored (either partially or fully) at various RG fixed points as emergent phenomena. A representative cut of the global phase diagram displays a confluence of scalar and pseudoscalar excitonic and superconducting (such as the $s$-wave and $p$-wave) mass ordered phases, manifesting restoration of (a) chiral U(1) symmetry between two excitonic masses for repulsive interactions and (b) pseudospin SU(2) symmetry between scalar or pseudoscalar excitonic and superconducting masses for attractive interactions. Finally, we perturbatively study the effects of \emph{weak} rotational symmetry breaking on the stability of various RG fixed points.