Fermion-induced quantum critical point in Dirac semimetals: a sign-problem-free quantum Monte Carlo study

Abstract

According to Landau criterion, a phase transition should be first order when cubic terms of order parameters are allowed in its effective Ginzburg-Landau free energy. Recently, it was shown by renormalization group (RG) analysis that continuous transition can happen at putatively first-order $Z_3$ transitions in 2D Dirac semimetals and such non-Landau phase transitions were dubbed "fermion-induced quantum critical points" (FIQCP) [Li et al., Nature Communications 8, 314 (2017)]. The RG analysis, controlled by the 1/$N$ expansion with $N$ the number of flavors of four-component Dirac fermions, shows that FIQCP occurs for $N\ge N_c$. Previous QMC simulations of a microscopic model of SU($N$) fermions on the honeycomb lattice showed that FIQCP occurs at the transition between Dirac semimetals and Kekule-VBS for $N\ge 2$. However, precise value of the lower bound $N_c$ has not been established. Especially, the case of $N=1$ has not been explored by studying microscopic models so far. Here, by introducing a generalized SU($N$) fermion model with $N=1$ (namely spinless fermions on the honeycomb lattice), we perform large-scale sign-problem-free Majorana quantum Monte Carlo simulations and find convincing evidence of FIQCP for $N=1$. Consequently, our results suggest that FIQCP can occur in 2D Dirac semimetals for all positive integers $N\ge 1$.

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Cited by in corpus (7)

• Non-Hermitian strongly interacting Dirac fermions: a quantum Monte-Carlo study
• Emergence of Competing Orders and Possible Quantum Spin Liquid in SU(N) Fermions
• SO(4) multicriticality of two-dimensional Dirac fermions
• Nonequilibrium Dynamics of Dirac Quantum Criticality in Imaginary Time
• Emergent soft-gap Anderson models at quantum criticality in a lattice Hamiltonian within dynamical mean field theory
• Emergent spacetime supersymmetry at 2D fractionalized quantum criticality
• Fermionic criticality with enlarged fluctuations in Dirac semimetals