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000888526 1001_ $$00000-0001-7641-8030$$aOstmeyer, Johann$$b0$$eCorresponding author
000888526 245__ $$aSemimetal–Mott insulator quantum phase transition of the Hubbard model on the honeycomb lattice
000888526 260__ $$aWoodbury, NY$$bInst.$$c2020
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000888526 520__ $$aWe take advantage of recent improvements in the grand canonical Hybrid Monte Carlo algorithm, to performa precision study of the single-particle gap in the hexagonal Hubbard model, with on-site electron-electron interactions. Aftercarefully controlled analyses of the Trotter error, the thermodynamic limit, and finite-size scaling with inverse temperature, we find acritical coupling of $U_c/\kappa=3.834(14)$ and the critical exponent $z\nu=1.185(43)$. Under the assumption that this corresponds to the expected anti-ferromagnetic Mott transition, weare also able to provide a preliminary estimate $\beta=1.095(37)$ for the critical exponent of the order parameter. We consider our findings in viewof the $SU(2)$ Gross-Neveu, or chiral Heisenberg, universality class. We also discuss the computational scaling of the Hybrid Monte Carlo algorithm, and possible extensions of our work to carbon nanotubes, fullerenes, and topological insulators.
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