Finite-temperature quantum Monte Carlo study of Dirac quantum criticality: Algorithmic advances and comprehensive analysis
Abstract
We present a systematic study of the quantum phase transition from a Dirac semimetal to an antiferromagnetic Mott insulator in the honeycomb-lattice Hubbard model, using finite-temperature auxiliary-field quantum Monte Carlo (AFQMC) simulations. Given the dynamical critical exponent z=1 at criticality, we scale the inverse temperature β with the linear system size L, i.e., βt=L (with t as the hopping amplitude), to approach the thermodynamic and zero-temperature limits simultaneously. On the algorithmic front, we generalize the fast Fourier transform in path propagation to multi-sublattice systems and employ the delayed update technique in configuration updates to accelerate the AFQMC simulations. These advances enable us to access unprecedented system sizes of up to $3528$ sites (with L=42 and βt = 42). We additionally use twist-averaged boundary conditions to reduce the finite-size effects in computed observables. On the physical side, we determine the Dirac quantum criticality via finite-size scaling analysis of the spin correlations and off-diagonal single-particle Green's function, and locate the critical point at Uc/t=3.731(4) with the critical exponents ν=1.097(7), ηϕ=0.72(2) and ηψ=0.155(6). We further corroborate the critical point by examining several relevant quantities, including the quasiparticle weight, Fermi-liquid parameter, charge compressibility, U-derivative of double occupancy, and fidelity susceptibility. Our work establishes an independent benchmark for the chiral Heisenberg Gross-Neveu-Yukawa criticality in the honeycomb Hubbard model, offering a complementary perspective to previous ground-state simulations.
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BibTeX
@misc{du2026finitetemperature,
title = {{Finite-temperature quantum Monte Carlo study of Dirac quantum criticality: Algorithmic advances and comprehensive analysis}},
author = {Hou-Min Du and Qian Sun and Yuan-Yao He},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.14668},
eprint = {2609.14668},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.14668},
}
RIS
TY - UNPB
TI - Finite-temperature quantum Monte Carlo study of Dirac quantum criticality: Algorithmic advances and comprehensive analysis
AU - Hou-Min Du
AU - Qian Sun
AU - Yuan-Yao He
PY - 2026
DA - 2026/09/13
PB - arXiv
DO - 10.48550/arxiv.2609.14668
UR - https://arxiv.org/abs/2609.14668
AB - We present a systematic study of the quantum phase transition from a Dirac semimetal to an antiferromagnetic Mott insulator in the honeycomb-lattice Hubbard model, using finite-temperature auxiliary-field quantum Monte Carlo (AFQMC) simulations. Given the dynamical critical exponent z=1 at criticality, we scale the inverse temperature β with the linear system size L, i.e., βt=L (with t as the hopping amplitude), to approach the thermodynamic and zero-temperature limits simultaneously. On the algorithmic front, we generalize the fast Fourier transform in path propagation to multi-sublattice systems and employ the delayed update technique in configuration updates to accelerate the AFQMC simulations. These advances enable us to access unprecedented system sizes of up to $3528$ sites (with L=42 and βt = 42). We additionally use twist-averaged boundary conditions to reduce the finite-size effects in computed observables. On the physical side, we determine the Dirac quantum criticality via finite-size scaling analysis of the spin correlations and off-diagonal single-particle Green's function, and locate the critical point at U_c/t=3.731(4) with the critical exponents ν=1.097(7), η_ϕ=0.72(2) and η_ψ=0.155(6). We further corroborate the critical point by examining several relevant quantities, including the quasiparticle weight, Fermi-liquid parameter, charge compressibility, U-derivative of double occupancy, and fidelity susceptibility. Our work establishes an independent benchmark for the chiral Heisenberg Gross-Neveu-Yukawa criticality in the honeycomb Hubbard model, offering a complementary perspective to previous ground-state simulations.
ER -