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) ⊗ 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 small parameter ϵ with ϵ = 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 ∼ ϵ. 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 weak rotational symmetry breaking on the stability of various RG fixed points.
Highlights
The central outcomes of this study are captured by a representative cut of the global phase diagram, shown in figure 1
By performing a one-loop or leading-order renormalization group (RG) analysis on such an interacting model, controlled by a small parameter with = d − 1, about the lower-critical one spatial dimension (d = 1), we show that the system altogether sustains eight interacting fixed points, see table 1
All the fixed points are located at coupling constants ∼, and can be grouped into following three categories, depending on the emergent chiral symmetry therein
Summary
We show that a collection of isotropically dispersing massless chiral Dirac fermions, interacting via Hubbardlike local or short-range interactions, is described only in terms of four linearly independent four-fermion or quartic terms. At the upper-critical three spatial dimensions we recover the exact mean-field value of the exponent ν = 1/2 [10, 11], from a leading order expansion Some of these fixed points play prominent roles on the global phase diagram of interacting Dirac fermions, a representative cut of which is displayed in figure 1. The fixed points (both critical and bicritical) controlling the continuous quantum phase transitions out of a Dirac semimetal into various broken symmetry phases for finite interactions across different segments of the phase boundary are highlighted in figure 1. We find that the U(1) chiral symmetry of the noninteracting system manifests in the phase diagram as a reflection about the 45◦ diagonal (dashed) line under which the scalar excitonic and pairing masses transform into the pseudoscalar masses. The chiral symmetry among various competing phases, which we demonstrate as an emergent phenomena from a leading-order expansion, is, an exact symmetry, as shown in figure 3
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