Gross-Neveu Heisenberg criticality: dynamical generation of quantum spin Hall masses

Abstract

We consider fermions on a honeycomb lattice supplemented by a spin invariant interaction that dynamically generates a quantum spin Hall insulator. This lattice model provides an instance of Gross-Neveu Heisenberg criticality, as realized for example by the Hubbard model on the honeycomb lattice. Using auxiliary field quantum Monte Carlo simulations we show that we can compute with unprecedented precision susceptibilities of the order parameter. In O(N) Gross-Neveu transitions, the anomalous dimension of the bosonic mode grows as a function of N such that in the large-N limit it is of particular importance to consider susceptibilities rather than equal time correlations so as to minimize contributions from the background. For the N=3 case, we obtain $1/\nu =1.11(4)$, ${\eta }_{\varphi }=0.80(9)$, and ${\eta }_{\psi }=0.29(2)$ for respectively the correlation length exponent, bosonic and fermionic anomalous dimensions.

11 pages,13 figures

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Cited by in corpus (16)

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• Disorder Operator and Rényi Entanglement Entropy of Symmetric Mass Generation
• Gross-Neveu-Heisenberg criticality from $2+\mathbf{\epsilon }$ expansion
• Wilson-Fisher fixed points in presence of Dirac fermions
• $SO(8)$ unification and the large-N theory of superconductor-insulator transition of two-dimensional Dirac fermions
• Relativistic Mott transitions and finite-temperature effects of quantum criticality in Dirac semimetals
• Topological Gap Opening without Symmetry Breaking from Dynamical Quantum Correlations
• 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
• Chiral Heisenberg Gross-Neveu-Yukawa criticality: Honeycomb vs. SLAC fermions
• Alteration of Topology in Quantum Phase Transitions via Symmetry Enrichment
• Critical structure and emergent symmetry of Dirac fermion systems
• Thermodynamic and Dynamical Signatures of a Quantum Spin-Hall Insulator to Superconductor Transition
• Dirac quantum criticality in twisted double bilayer transition metal dichalcogenides
• Lattice Field Theory Analysis of the Chiral Heisenberg Model