狄拉克量子临界性的有限温度量子蒙特卡洛研究：算法进展与综合分析

中文摘要 AI 辅助

我们利用有限温度辅助场量子蒙特卡洛（AFQMC）模拟，对蜂窝晶格哈伯德模型中从狄拉克半金属到反铁磁莫特绝缘体的量子相变进行了系统性研究。鉴于临界点处的动力学临界指数$z=1$，我们将逆温度$\beta$与线性系统尺寸$L$按比例缩放，即$\beta t=L$（其中$t$为跳跃振幅），以同时逼近热力学极限和零温极限。在算法方面，我们将路径传播中的快速傅里叶变换推广到多子格系统，并在构型更新中采用延迟更新技术以加速AFQMC模拟。这些进展使我们能够访问前所未有的系统尺寸，最大达3528个格点（$L=42$且$\beta t=42$）。此外，我们采用扭曲平均边界条件以减少所计算观测量中的有限尺寸效应。在物理方面，我们通过对自旋关联和非对角单粒子格林函数的有限尺寸标度分析确定了狄拉克量子临界性，并将临界点定位于$U_c/t=3.731(4)$，临界指数为$\nu=1.097(7)$，$\eta_{\phi}=0.72(2)$和$\eta_{\psi}=0.155(6)$。我们进一步通过检查若干相关量来佐证临界点，包括准粒子权重、费米液体参数、电荷压缩率、双占据的$U$导数以及保真度磁化率。我们的工作为蜂窝哈伯德模型中的手性海森堡Gross-Neveu-Yukawa临界性建立了独立的基准，为之前的基态模拟提供了互补的视角。

英文摘要

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.

发表机构

• Institute of Modern Physics, Northwest University（西北大学现代物理研究所）
• Hefei National Laboratory（合肥国家实验室）
• School of Physics, Northwest University（西北大学物理学院）
• Shaanxi Key Laboratory for Theoretical Physics Frontiers（陕西理论物理前沿重点实验室）
• Fundamental Discipline Research Center for Quantum Science and Technology of Shaanxi Province（陕西省量子科学与技术基础学科研究中心）

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23 pages, 18 figures