Yi Hangmo
Department of Physics, Soongsil University, Seoul 156-743, Korea and Institute for Integrative Basic Sciences, Soongsil University, Seoul 156-743, Korea.
Phys Rev E Stat Nonlin Soft Matter Phys. 2015 Jan;91(1):012118. doi: 10.1103/PhysRevE.91.012118. Epub 2015 Jan 9.
I study the properties of the quantum critical point of the transverse-field quantum Ising model on various fractal lattices such as the Sierpiński carpet, Sierpiński gasket, and Sierpiński tetrahedron. Using a continuous-time quantum Monte Carlo simulation method and finite-size scaling analysis, I identify the quantum critical point and investigate its scaling properties. Among others, I calculate the dynamic critical exponent and find that it is greater than one for all three structures. The fact that it deviates from one is a direct consequence of the fractal structures not being integer-dimensional regular lattices. Other critical exponents are also calculated. The exponents are different from those of the classical critical point and satisfy the quantum scaling relation, thus confirming that I have indeed found the quantum critical point. I find that the Sierpiński tetrahedron, of which the dimension is exactly 2, belongs to a different universality class than that of the two-dimensional square lattice. I conclude that the critical exponents depend on more details of the structure than just the dimension and the symmetry.
我研究了横场量子伊辛模型在各种分形晶格（如谢尔宾斯基地毯、谢尔宾斯基垫圈和谢尔宾斯基四面体）上的量子临界点性质。通过使用连续时间量子蒙特卡罗模拟方法和有限尺寸标度分析，我确定了量子临界点并研究了其标度性质。其中，我计算了动态临界指数，发现对于所有这三种结构，该指数都大于1。其偏离1这一事实是分形结构不是整数维规则晶格的直接结果。还计算了其他临界指数。这些指数不同于经典临界点的指数，并满足量子标度关系，从而证实我确实找到了量子临界点。我发现维度恰好为2的谢尔宾斯基四面体属于与二维正方形晶格不同的普适类。我得出结论，临界指数取决于结构的更多细节，而不仅仅是维度和对称性。
