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We present quantum Monte Carlo simulations for the chiral Heisenberg Gross-Neveu-Yukawa quantum phase transition of relativistic fermions with $N=4$ Dirac spinor components subject to a repulsive, local four fermion interaction in 2+1$d$. Here we employ a two dimensional lattice Hamiltonian with a single, spin-degenerate Dirac cone, which exactly reproduces a linear energy-momentum relation for all finite size lattice momenta in the absence of interactions. This allows us to significantly reduce finite size corrections compared to the widely studied honeycomb and $\pi$-flux lattices. A Hubbard term dynamically generates a mass beyond a critical coupling of ${U_c = 6.76(1)}$ as the system acquires antiferromagnetic order and SU(2) spin rotational symmetry is spontaneously broken. At the quantum phase transition we extract a self-consistent set of critical exponents ${\nu = 0.98(1)}$, ${\eta_{\phi} = 0.53(1)}$, ${\eta_{\psi} = 0.18(1)}$, ${\beta = 0.75(1)}$. We provide evidence for the continuous degradation of the quasi-particle weight of the fermionic excitations as the critical point is approached from the semimetallic phase. Finally we study the effective "speed of light" of the

Author

Lang, Thomas C.; Läuchli, Andreas M.

Published

2018

Language

EN