Emus live on the Gross-Neveu-Yukawa archipelago

TL;DR

This paper uses an advanced quantum Monte Carlo method to accurately compute critical exponents for the Gross-Neveu-Yukawa chiral Ising transition at N=8, confirming theoretical predictions and overcoming previous lattice simulation obstacles.

Contribution

It introduces the elective-momentum ultra-size (EMUS) QMC method to precisely determine critical exponents for the GNY transition at N=8, aligning lattice results with bootstrap and perturbative approaches.

Findings

Critical exponents match bootstrap and perturbative results

EMUS QMC effectively overcomes finite size effects

Confirmed the GNY transition as a well-defined quantum critical point

Abstract

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.