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.
Highlights
Much attention has been lavished on band structures with symmetry protected nodal points (Dirac and Weyl semimetals) [1,2,3,4,5,6,7] in both two [8,9,10] and three spatial dimensions [11,12,13,14,15]
The paradigmatic example is graphene, where the band touching points are protected by symmetry, and the low-energy dispersion around these points is captured by the massless 2D Dirac equation [16]
We propose a theoretical framework for symmetric mass generation (SMG) broadly as a deconfined quantum critical point, where the physical fermion is fractionalized into bosonic and fermionic partons with emergent gauge interaction
Summary
Much attention has been lavished on band structures with symmetry protected nodal points (Dirac and Weyl semimetals) [1,2,3,4,5,6,7] in both two [8,9,10] and three spatial dimensions [11,12,13,14,15]. We discuss an altogether different mechanism of mass generation for Dirac fermions, which breaks no symmetries and cannot be modeled by a single-particle mass term at the free-fermion level The possibility of such a scenario is informed by recent developments in the theory of interacting fermionic symmetry protected topological (SPT) phases [19,20,21,22,23,24,25,26,27,28,29,30,31,32], relating to the stability of freefermion topological insulators or superconductors to interactions. Numerical simulations of the problem in different models with various microscopic symmetries using different numerical methods [35,40,41,42,47,48,49] seem to uniformly point towards a single continuous SMG transition All these models share one key common property that the weakly interacting semimetal phase should have exactly eight massless Dirac fermions. The remaining option to generate fermion masses without breaking any symmetry is to invoke fermion interactions, such as the charge-4e interaction HI
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
