Prośniak Oskar A, Łącki Mateusz, Damski Bogdan
Jagiellonian University, Institute of Physics, Łojasiewicza 11, 30-348, Kraków, Poland.
Sci Rep. 2019 Jun 18;9(1):8687. doi: 10.1038/s41598-019-44825-9.
We discuss how positions of critical points of the three-dimensional Bose-Hubbard model can be accurately obtained from variance of the on-site atom number operator, which can be experimentally measured. The idea that we explore is that the derivative of the variance, with respect to the parameter driving the transition, has a pronounced maximum close to critical points. We show that Quantum Monte Carlo studies of this maximum lead to precise determination of critical points for the superfluid-Mott insulator transition in systems with mean number of atoms per lattice site equal to one, two, and three. We also extract from such data the correlation-length critical exponent through the finite-size scaling analysis and discuss how the derivative of the variance can be reliably computed from numerical data for the variance. The same conclusions apply to the derivative of the nearest-neighbor correlation function, which can be obtained from routinely measured time-of-flight images.
我们讨论了如何从可通过实验测量的在位原子数算符的方差中准确获得三维玻色-哈伯德模型临界点的位置。我们所探索的想法是，方差相对于驱动相变的参数的导数在临界点附近有一个明显的最大值。我们表明，对该最大值进行量子蒙特卡罗研究可精确确定每个晶格位点平均原子数等于一、二和三的系统中，超流-莫特绝缘体相变的临界点。我们还通过有限尺寸标度分析从这些数据中提取关联长度临界指数，并讨论如何从方差的数值数据中可靠地计算方差的导数。相同的结论也适用于最近邻关联函数的导数，该导数可从常规测量的飞行时间图像中获得。
