Critical Entanglement and Exotic Quantum Phase Transition

Gross-Neveu-Yukawa theory of SO(2N)→SO(N)×SO(N) spontaneous symmetry breaking

In this talk, we will discuss the relativistic Gross-Neveu-Yukawa field theory for the SO(2N) real symmetric second-rank tensor order parameter coupled to N_f flavors of 4N-component Majorana fermions in 2+1 dimensions. Such a tensor order parameter unifies all Lorentz-invariant mass-gap orders for N two-component Dirac fermions in two dimensions except for the SO(2N)-singlet anomalous quantum Hall state. The value N_f=1 corresponds to the canonical Gross-Neveu model. Within the leading-order ε-expansion around the upper critical dimension of 3+1 the field theory exhibits a critical fixed point in its renormalization group flow which describes spontaneous symmetry breaking to SO(N)×SO(N) for the number of flavors of Majorana fermions higher than a critical value N_f,c2≈2N. For N_f,c1<N_f<N_f,c2 , with N_f,c1≈N the critical fixed point resides in the unstable region of the theory where the effective potential is unbounded from below, whereas for N_f<N_f,c1 there is no real critical fixed point, and the flow runs away. In either case, for N_f<N_f,c2 the transition should become fluctuation-induced first-order, and we discuss the dependence of its size on the parameters N and N_f in the theory. One-loop critical exponents for the universality class at N_f,c2<N_f are computed and the flow diagram in various regimes is discussed.