Emergent chiral symmetry in a three-dimensional interacting Dirac liquid

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.

Coulomb Instabilities of a Three-Dimensional Higher-Order Topological Insulator

“…Concomitant with the topological phase transition from second-order to topological insulator, time-reversal symmetry and inversion symmetry emerge. The previous works has shown the possibility of emergent Lorentz symmetry [63][64][65][66][67][68][69][70], emergent chiral symmetry [71][72][73], and even emergent supersymmetry [74][75][76][77][78][79][80][81][82][83][84][85]. Here, by providing the concrete example, we show that emergent symmetries could happen for the discrete time-reversal and inversion symmetries, which enrich the family of emergent symmetries [86].…”

Extended Hubbard model in undoped and doped monolayer and bilayer graphene: Selection rules and organizing principle among competing orders

“…, 9 and j = s, t. To shed light on the structure of the global phase dia-gram of interacting two-dimensional Dirac and Luttinger fermions, we perform Wilsonian momentum shell RG analysis at zero, as well as finite temperature (T ) and chemical potential (µ). We already established the scaling of the coupling constants to be g j µ = z − d, which pins the lower critical dimension of the corresponding theories at d = z and facilitates an expansion around the marginal dimensionality with = d − z [98][99][100]. Notice that the physical values of are 1 and 0 for twodimensional Dirac and Luttinger fermions, respectively.…”

Correlated interaction effects in three-dimensional semi-Dirac semimetal

“…, we can get the properties of the fixed point. A negative (positive) eigenvalue is corresponding to a stable (unstable) eigendirection [32,34]. There is one unstable direction for QCP, and there are two and three unstable directions for bicritical point (BCP) and tricritical point (TCP) respectively.…”

“…There are eight kinds of four-fermion couplings. However, not all of them are linearly independent, due to the constraint by Fierz identity [31,33,34].…”

“…The correlation effects in Dirac and Weyl fermion systems are extensively studied, and are well understood relatively [23][24][25][26][27][28][29][30][31][32][33][34]. The influence of many-body interaction on unconventional fermion systems also attracted much interest and is an important topic.…”