Integral algorithm of exponential observables for interacting fermions in quantum Monte Carlo simulations

作者：Xu Zhang, Gaopei Pan, Bin-Bin Chen, Kai Sun, Zi Yang Meng · 发表于：Physical review. B./Physical review. B · 年份：2024 · DOI：10.1103/physrevb.109.205147 · 被引用次数：18 · 研究领域：Quantum many-body systems、Quantum and electron transport phenomena、Physics of Superconductivity and Magnetism

Exponential observables, formulated as $ln\ensuremath{\langle}{e}^{\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{X}}\ensuremath{\rangle}$ where $\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{X}$ is an extensive quantity, play a critical role in the study of quantum many-body systems, examples of which include the free energy and entanglement entropy. Given that ${e}^{X}$ becomes exponentially large (or small) in the thermodynamic limit, the accurate computation of the expectation value of this exponential quantity presents a significant challenge. In this paper, we propose a comprehensive algorithm to quantify these observables in interacting fermion systems, utilizing the determinant quantum Monte Carlo method. We have applied this algorithm to the two-dimensional square-lattice half-filled Hubbard model and $\ensuremath{\pi}$-flux t-V model. In the Hubbard model case at the strong-coupling limit, our method showcases a significant accuracy improvement on free energy compared to conventional methods that are derived from the internal energy, and in the t-V model, we indicate that the free energy offers a precise determination of the second-order phase transition. We also illustrate that this approach delivers highly efficient and precise measurements of the $n\mathrm{th}$ R\'enyi entanglement entropy. Even more noteworthy is that this improvement comes without incurring increases in computational complexity. This algorithm effectively suppresses exponential fluctuations and can be e...