Quantum criticality in the metal-superconductor transition of interacting Dirac fermions on a triangular lattice

Abstract

We investigate a semimetal-superconductor phase transition of two-dimensional Dirac electrons at zero temperature by large-scale and essentially unbiased quantum Monte Carlo simulations for the half-filled attractive Hubbard model on the triangular lattice, in the presence of alternating magnetic $\pi$-flux, that is introduced to construct two Dirac points in the one-particle bands at the Fermi level. This phase transition is expected to describe quantum criticality of the chiral XY class in the framework of the Gross-Neveu model, where, in the ordered phase, the $U(1)$ symmetry is spontaneously broken and a mass gap opens in the excitation spectrum. We compute the order parameter of the s-wave superconductivity and estimate the quasiparticle weight from the long-distance behavior of the single-particle Green's function. These calculations allow us to obtain the critical exponents of this transition in a reliable and accurate way. Our estimate for the critical exponents is in good agreement with those obtained for a transition to a Kekulé valence bond solid, where an emergent $U(1)$ symmetry is proposed [Z.-X. Li et al., Nat. Commun. 8, 314 (2017)].

9 pages, 7 figures

References in corpus (12)

• Tunable gauge potential for neutral and spinless particles in driven lattices
• Quantum spin-liquid emerging in two-dimensional correlated Dirac fermions
• Interactions and phase transitions on graphene's honeycomb lattice
• Absence of a Spin Liquid Phase in the Hubbard Model on the Honeycomb Lattice
• Theory of interacting electrons on the honeycomb lattice
• Fermionic quantum criticality in honeycomb and $\pi$-flux Hubbard models: Finite-size scaling of renormalization-group-invariant observables from quantum Monte Carlo
• Four-loop critical exponents for the Gross-Neveu-Yukawa models
• Fermionic Quantum Critical Point of Spinless Fermions on a Honeycomb Lattice
• Large $N$ critical exponents for the chiral Heisenberg Gross-Neveu universality class
• Gauge-field-assisted Kekulé quantum criticality
• Mott physics in the half-filled Hubbard model on a family of vortex-full square lattices
• Quantum paramagnet in a $\pi$ flux triangular lattice Hubbard model

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• Fermion-induced quantum critical point in Dirac semimetals: a sign-problem-free quantum Monte Carlo study
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• Benchmark study of an auxiliary-field quantum Monte Carlo technique for the Hubbard model with shifted-discrete Hubbard-Stratonovich transformations
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• A numerically exact study of Weyl superconductivity
• Quantum criticality of magnetic catalysis in two-dimensional correlated Dirac fermions
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• Nonequilibrium Dynamics of Dirac Quantum Criticality in Imaginary Time
• Bandwidth controlled quantum phase transition between an easy-plane quantum spin Hall state and an s-wave superconductor
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