Abstract
A unified theory of quantum critical points beyond the conventional Landau–Ginzburg–Wilson paradigm remains unknown. According to Landau cubic criterion, phase transitions should be first-order when cubic terms of order parameters are allowed by symmetry in the Landau–Ginzburg free energy. Here, from renormalization group analysis, we show that second-order quantum phase transitions can occur at such putatively first-order transitions in interacting two-dimensional Dirac semimetals. As such type of Landau-forbidden quantum critical points are induced by gapless fermions, we call them fermion-induced quantum critical points. We further introduce a microscopic model of SU(N) fermions on the honeycomb lattice featuring a transition between Dirac semimetals and Kekule valence bond solids. Remarkably, our large-scale sign-problem-free Majorana quantum Monte Carlo simulations show convincing evidences of a fermion-induced quantum critical points for N = 2, 3, 4, 5 and 6, consistent with the renormalization group analysis. We finally discuss possible experimental realizations of the fermion-induced quantum critical points in graphene and graphene-like materials.
Highlights
A unified theory of quantum critical points beyond the conventional Landau– Ginzburg–Wilson paradigm remains unknown
The Landau cubic criterion states that continuous phase transitions are forbidden when cubic terms of order parameters are allowed by symmetry in the Landau–Ginzburg (LG) free energy
We discover an intriguing scenario violating the Landau cubic criterion; namely fermion-induced quantum critical points (FIQCP) are second-order quantum phase transitions induced by coupling gapless fermions to fluctuations of order parameters whose cubic terms appear in the Landau–Ginzburg theory
Summary
We begin by constructing the low-energy field theory describing the quantum phase transition. At low-energy and long-distance near the transition, the system can be described by Dirac fermions, fluctuating order parameters, and their couplings: S = Sψ + Sφ + Sψφ. The most general but symmetry constrained action describing the order-parameter fluctuations up to the fourth order is given by. The action in Eq (2) describes an effective field theory of quantum three-state Potts model, which supports a weakly first-order quantum phase transition in 2 + 1 dimensions[12, 30, 31]. As we shall show below, the coupling between the gapless Dirac fermions and order-parameter fluctuations will dramatically change this scenario by rendering the putative first-order transition into a continuous one. We employ dimensionless coupling constants ~r; ~g2; ~b2; u~
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