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 $N\ge 1$.

References in corpus (68)

• The electronic properties of graphene
• Two-Dimensional Gas of Massless Dirac Fermions in Graphene
• "Deconfined" quantum critical points
• Computational complexity and fundamental limitations to fermionic quantum Monte Carlo simulations
• Continuous Quantum Phase Transitions
• Quantum criticality beyond the Landau-Ginzburg-Wilson paradigm
• The Conformal Bootstrap: Theory, Numerical Techniques, and Applications
• Evidence for deconfined quantum criticality in a two-dimensional Heisenberg model with four-spin interactions
• Interactions and phase transitions on graphene's honeycomb lattice
• Electron fractionalization in two-dimensional graphenelike structures
• Deconfined quantum critical points: symmetries and dualities
• Pinning the order: the nature of quantum criticality in the Hubbard model on honeycomb lattice
• Emergent Photons and New Transitions in the O(3) Sigma Model with Hedgehog Suppression
• Quantum criticality with two length scales
• Nematicity and quantum paramagnetism in FeSe
• A sufficient condition for the absence of the sign problem in the fermionic quantum Monte-Carlo algorithm
• Scaling in the Fan of an Unconventional Quantum Critical Point
• Antiferromagnetic to valence-bond-soild transitions in two-dimensional SU(N) Heisenberg models with multi-spin interactions
• Fermionic quantum criticality in honeycomb and $\pi$-flux Hubbard models: Finite-size scaling of renormalization-group-invariant observables from quantum Monte Carlo
• Universal quantum criticality in the metal-insulator transition of two-dimensional interacting Dirac electrons
• Masses in graphene-like two-dimensional electronic systems: topological defects in order parameters and their fractional exchange statistics
• Solving fermion sign problem in quantum Monte Carlo by Majorana representation
• Emergent $SO(5)$ Symmetry at the Néel to Valence-Bond-Solid Transition
• Deconfined Quantum Criticality, Scaling Violations, and Classical Loop Models
• Four-loop critical exponents for the Gross-Neveu-Yukawa models
• Sign-problem-free quantum Monte Carlo of the onset of antiferromagnetism in metals
• Kekulé valence bond order in an extended Hubbard model on the honeycomb lattice, with possible applications to twisted bilayer graphene
• The phase diagram of the hexagonal lattice quantum dimer model
• Deconfined quantum criticality and Neel order via dimer disorder
• Many-body spin Berry phases emerging from the $\pi$-flux state: antiferromagnetic/valence-bond-solid competition
• A lattice model for the SU(N) Neel-VBS quantum phase transition at large N
• Bridging lattice-scale physics and continuum field theory with quantum Monte Carlo simulations
• Duality between the deconfined quantum-critical point and the bosonic topological transition
• Majorana-time-reversal symmetries: a fundamental principle for sign-problem-free quantum Monte Carlo simulations
• Deconfined criticality flow in the Heisenberg model with ring-exchange interactions
• Fermionic Quantum Critical Point of Spinless Fermions on a Honeycomb Lattice
• Fermion-induced quantum critical points
• Majorana Positivity and the Fermion sign problem of Quantum Monte Carlo Simulations
• Néel to valence-bond solid transition on the honeycomb lattice: Evidence for deconfined criticality
• Sign-Problem-Free Fermionic Quantum Monte Carlo: Developments and Applications
• Bootstrapping the Three-Dimensional Supersymmetric Ising Model
• Dynamical Signature of Fractionalization at the Deconfined Quantum Critical Point
• A tensor product state approach to spin-1/2 square $J_1$-$J_2$ antiferromagnetic Heisenberg model: evidence for deconfined quantum criticality
• Fermion-sign-free Majarana-quantum-Monte-Carlo studies of quantum critical phenomena of Dirac fermions in two dimensions
• Is magic-angle twisted bilayer graphene near a quantum critical point?
• Superconductivity from the Condensation of Topological Defects in a Quantum Spin-Hall Insulator
• Quantum superconducting criticality in graphene and topological insulators
• Dirac Fermions with Competing Orders: Non-Landau Transition with Emergent Symmetry
• Thermal Ising transitions in the vicinity of two-dimensional quantum critical points
• Split orthogonal group: A guiding principle for sign-problem-free fermionic simulations
• A simple fermionic model of deconfined phases and phase transitions
• Symmetric Fermion Mass Generation as Deconfined Quantum Criticality
• Plaquette order and deconfined quantum critical point in the spin-1 bilinear-biquadratic Heisenberg model on the honeycomb lattice
• Mott insulating states and quantum phase transitions of correlated SU(2N) Dirac fermions
• Fermion-induced quantum criticality in two-dimensional Dirac semimetals: Non-perturbative flow equations, fixed points and critical exponents
• Continuous easy-plane deconfined phase transition on the kagome lattice
• Half-filled Landau levels: a continuum and sign-free regularization for 3D quantum critical points
• Fermion bag approach to Hamiltonian lattice field theories in continuous time
• Gauge-field-assisted Kekulé quantum criticality
• Corrections to scaling in the critical theory of deconfined criticality
• Fermion-induced quantum criticality with two length scales in Dirac systems
• Deconfined Quantum Critical Point on the Triangular Lattice
• Fermion-induced quantum critical points in three-dimensional Weyl semimetals
• The quantum valley Hall effect in proximity-induced superconducting graphene: an experimental window for deconfined quantum criticality
• Fermion-induced quantum critical points in two-dimensional Dirac semimetals
• Quantum criticality in the metal-superconductor transition of interacting Dirac fermions on a triangular lattice
• Stochastic series expansion simulation of the $t$-$V$ model
• Finite-temperature valence-bond-solid transitions and thermodynamic properties of interacting SU($2N$) Dirac fermions

Cited by in corpus (12)

• Non-Hermitian strongly interacting Dirac fermions: a quantum Monte-Carlo study
• Dirac electrons in the square lattice Hubbard model with a $d$-wave pairing field: chiral Heisenberg universality class revisited
• Quantum phase transitions in Dirac fermion systems
• Confinement transition in the QED${}_3$-Gross-Neveu-XY universality class
• Emergence of Competing Orders and Possible Quantum Spin Liquid in SU(N) Fermions
• Critical properties of the valence-bond-solid transition in lattice quantum electrodynamics
• Fermion-induced quantum critical point in the Landau-Devonshire model
• 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
• Fermionic criticality with enlarged fluctuations in Dirac semimetals
• Emergent spacetime supersymmetry at 2D fractionalized quantum criticality