Resolving Quantum Criticality in the Honeycomb Hubbard Model

TL;DR

This study uses large-scale quantum Monte Carlo simulations with a novel algorithm to accurately determine critical exponents of the honeycomb Hubbard model, resolving a decade-long controversy about its quantum criticality.

Contribution

It introduces a new projected submatrix update algorithm enabling high-precision finite-size scaling analysis of quantum critical points in large lattices.

Findings

Critical exponents for the honeycomb Hubbard model are now precisely determined.

Results agree with conformal bootstrap predictions for the related $t$-$V$ model.

The methodology provides a systematic workflow for studying fermionic quantum critical phenomena.

Abstract

Quantum phase transitions driven by electronic correlations are central to understanding the physics of graphene and related two-dimensional materials. A paradigmatic example is the semimetal-to-Mott-insulator transition on the honeycomb lattice, governed by the Gross-Neveu-Heisenberg universality class, yet consensus on its critical exponents has remained elusive for over a decade due to severe finite-size effects and the absence of rigorous conformal bootstrap benchmarks. Here we try to resolve this long-standing controversy by performing projector determinant quantum Monte Carlo simulations on lattices of unprecedented size, reaching 10,368 sites. By developing a novel projected submatrix update algorithm, we achieve a significant algorithmic speedup that enables us to access the thermodynamic limit with high precision. We observe that the fermion anomalous dimension and the correlation length exponent converge rapidly, while the boson anomalous dimension exhibits a systematic size dependence that we resolve via linear extrapolation. To validate our analysis, we perform parallel large-scale simulations of the spinless $t$-$V$ model on the honeycomb lattice, which belongs to the Gross-Neveu-Ising class. Our results for the $t$-$V$ model show agreement with conformal bootstrap predictions, thereby corroborating the robustness of our methodology. Our work provides state-of-the-art critical exponents for the honeycomb Hubbard model and establishes a systematic finite-size scaling workflow applicable to a broad class of strongly correlated quantum systems, paving the way for resolving other challenging fermionic quantum critical phenomena.