Symmetric Fermion Mass Generation as Deconfined Quantum Criticality

Abstract

Massless 2+1D Dirac fermions arise in a variety of systems from graphene to the surfaces of topological insulators, where generating a mass is typically associated with breaking a symmetry. However, with strong interactions, a symmetric gapped phase can arise for multiples of eight Dirac fermions. A continuous quantum phase transition from the massless Dirac phase to this massive phase, which we term Symmetric Mass Generation (SMG), is necessarily beyond the Landau paradigm and is hard to describe even at the conceptual level. Nevertheless, such transition has been consistently observed in several numerical studies recently. Here, we propose a theory for the SMG transition which is reminiscent of deconfined criticality and involves emergent non-Abelian gauge fields coupled both to Dirac fermions and to critical Higgs bosons. We motivate the theory using an explicit parton construction and discuss predictions for numerics. Additionally, we show that the fermion Green's function is expected to undergo a zero to pole transition across the critical point.

Figures (4)

• Figure 1: Possible scenarios of transitions from the Dirac semimetal (Dirac SM) to featureless gapped phase. (a) Landau paradigm: an intermediate spontaneous symmetry breaking (SSB) phase sandwiched between the Gross-Neveu and the Wilson-Fisher transitions. (b) A direct continuous transition: the symmetric mass generation (SMG) as a deconfined quantum critical point, with emergent gauge field and fractionalized partons. (c) More exotic (and less likely) scenario: an intermediate Bose semimetal (Bose SM) critical phase between the Higgs and confinement transitions.
• Figure 2: (a) Catching-up energy scales of the bosonic parton gap $\Delta_B$, the fermionic parton gap $\Delta_f$, and the gauge gluon gap $\Delta_a$ on the confinement side of the SMG. (b) Hierarchical length scales of $\xi_B$, $\xi_f$ and $\xi_a$ near the SMG transition.
• Figure 3: The zero-pole transition of the fermion Green's function. Take the one of the $G(k)$ eigenvalues $(\omega-|{\bm{k}}|)/(\omega^2-|{\bm{k}}|^2-|{\bm{M}}|^2)$ for example.
• Figure 4: Diagrams that contributes the the correction of the interaction vertex. Wavy lines are the gauge boson propagators $D(q)_{\mu\nu}^{mn}=16 q^{-1}(\delta_{\mu\nu}-\xi q_\mu q_\nu/q^2)\delta_{mn}$ at the large-$N_f$ fixed point. The arrowed lines are the fermion propagator $G(k)=1/(k_\mu\gamma^\mu)$.