Bethe ansatz solution for crossover scaling functions of the asymmetric XXZ chain and the Kardar-Parisi-Zhang-type growth model.
Bethe ansatz solution for crossover scaling functions of the asymmetric XXZ chain and the Kardar-Parisi-Zhang-type growth model.
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DOI：
10.1103/physreve.52.3512
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发表时间：
1995-03
期刊：
影响因子：
--
通讯作者：
Kim
中科院分区：
文献类型：
--
作者：
Kim
发展了一种微扰方法来计算非对称XXZ哈密顿量在随机线附近低能态的有限尺寸修正。根据普适的交叉标度函数确定了质量隙从各向同性到各向异性的Kardar - Parisi - Zhang（KPZ）标度的交叉。在随机线处，非对称XXZ哈密顿量描述了一维单步或体心固 - 固生长模型的时间演化。找到了生长模型的质量隙作为生长速率和基底斜率的函数。还计算了对生长模型质量隙的高阶修正，以得到在零斜率区域大参数展开中KPZ到Edward - Wilkinson交叉标度函数的首项。
A perturbative method is developed to calculate the finite size corrections of the low lying energies of the asymmetric XXZ hamiltonian near the stochastic line. The crossover from isotropic to anisotropic, Kardar-Parisi-Zhang (KPZ) scaling of the mass gaps is determined in terms of universal crossover scaling functions. At the stochastic line, the asymmetric XXZ hamiltonian describes the time evolution of the single-step or body-centered solid-on-solid growth model in one dimension. The mass gaps of the growth model are found as a function of the growth rate and the substrate slope. Higher order corrections to the growth model mass gaps are also calculated to obtain the first terms of the KPZ to Edward-Wilkinson crossover scaling function in the large argument expansion in the zero slope sector.