  It is expected that the Gross-Neveu-Yukawa (GNY) chiral Ising transition of
$N$ Majorana (or $N_f=N/4$ four-component Dirac) fermions coupled with scalar
field in (2+1)D will be the first fermionic quantum critical point that various
methods such as conformal bootstrap [1], perturbative renormalization group [2]
and quantum Monte Carlo (QMC) simulations [3], would yield the converged
critical exponents -- serving the same textbook role as the Ising and $O(N)$
models in the statistical and quantum phase transition. However, such
expectation has not been fully realized from the lattice QMC simulations due to
the obstacles introduced by the UV finite size effect. In this work, by means
of the elective-momentum ultra-size (EMUS) QMC method [4], we compute the
critical exponents of the GNY $N=8$ chiral Ising transition on a 2D $\pi$-flux
fermion lattice model between Dirac semimetal and quantum spin Hall insulator
phases [3, 5]. With the matching of fermionic and bosonic momentum transfer and
collective update in momentum space, our QMC results provide the fully
consistent exponents with those obtained from the bootstrap and perturbative
approaches. In this way, the Emus now live happily on the $N=8$ island and
could explore the Gross-Neveu-Yukawa archipelago [1] with ease.
