量子蒙特卡罗模拟输运数据中的粒子尺寸效应
Finite-size effects in transport data from Quantum Monte Carlo simulations
摘要：
我们研究了正方晶格上哈伯德模型中密度驱动的金属-绝缘体相变的可压缩性、直流电导率、单粒子能隙和Drude重量的行为。这些物理量是通过有限温度下16 × 16格点的量子蒙特卡罗模拟得到的。虽然可压缩性，直流电导率，和间隙是已知的遭受“闭壳”效应，由于在频谱中的人工间隙的存在（由晶格的有限性引起的），我们已经建立，前者跟踪的平均符号的费米子行列式（<sign>），和一个捷径，经常用来计算电导率可能会忽略重要的修正。我们的系统分析还表明，相比之下，Drude重量是不太敏感的有限尺寸效应，更可靠的探针绝缘状态。我们还研究了离散时间间隔（Δτ）对<sign>平均密度（ρ）和双占有率（d）的影响：我们发现，<sign>在远离闭壳层组态的情况下，Δ τ和ρ对Δτ的依赖性更强，但在闭壳层和开壳层组态的情况下，d都遵循Δτ^2的依赖性。
英文摘要：
We have examined the behavior of the compressibility, the dc-conductivity, the single-particle gap, and the Drude weight as probes of the density-driven metal-insulator transition in the Hubbard model on a square lattice. These quantities have been obtained through determinantal quantum Monte Carlo simulations at finite temperatures on lattices up to 16 X 16 sites. While the compressibility, the dc-conductivity, and the gap are known to suffer from `closed-shell' effects due to the presence of artificial gaps in the spectrum (caused by the finiteness of the lattices), we have established that the former tracks the average sign of the fermionic determinant (<sign>), and that a shortcut often used to calculate the conductivity may neglect important corrections. Our systematic analyses also show that, by contrast, the Drude weight is not too sensitive to finite-size effects, being much more reliable as a probe to the insulating state. We have also investigated the influence of the discrete imaginary-time interval (Δτ) on <sign>, on the average density (ρ), and on the double occupancy (d): we have found that <sign> and ρare more strongly dependent on Δτaway from closed-shell configurations, but d follows the Δτ^2 dependence in both closed- and open-shell cases.
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