【摘要】 本文数值研究了自旋S=1/2, 1, 2的各向异性量子XXZD模型的Luttinger液体参数K.首先,利用U (1)对称的无限矩阵乘积态算法(iMPS)得到在Luttinger液体相中的基态波函数.通过二分量子涨落F和有限纠缠标度指数κ的关系可以提取出Luttinger液体参数K.对于自旋S=1/2, D=0的量子XXZD模型,本文利用U (1)对称的iMPS的算法得到的数值结果与精确解符合得很好.在参数D≤-2的区域,自旋S=1的XXZD模型的哈密顿量可以被映射到一个自旋S=1/2的有效XXZ模型,本文计算了在这个区域内的Luttinger液体参数K与精确解基本是一致的,相对误差小于1%.此外,在参数?=-0.5, D=0处,本文数值计算的Luttinger液体参数与密度矩阵重整化群(DMRG)的结果也是一致的.这些研究结果表明:当系统具有U (1)对称性时,利用U (1)对称的iMPS的方法可以提取无能隙相中的Luttinger液体参数.本文利用此方法还研究了自旋S=1的XXZD模型在其他参数下的Luttinger液体参数,以及自旋S=2的XXZD模型的Luttinger液体参数.更多还原

【Abstract】 We numerically calculate Luttinger liquid parameter K in the anisotropic spin XXZD models with spin s = 1/2, 1, and 2. In order to obtain groundstate wavefunctions in Luttinger liquid phases, we employ the U(1)symmetric infinite matrix product states algorithm(iMPS). By using relation between the bipartite quantum fluctuations F and the so-called finite-entanglement scaling exponents κ, the Luttinger liquid parameter K can be extracted. For s = 1/2 and D = 0, the numerically extracted Luttinger liquid parameter K is shown to be good agreement with the exact value. On using the fact that the spin-1 XXZD Hamiltonian with D≤-2 can be mapped to an effective spin-1/2 XXZ model, we calculate the Luttinger liquid parameter for the region of D≤-2. It is shown that our numerical value of the Luttinger liquid parameter agree well with the exact values, here, the relative error less than 1%. Also, our Luttinger liquid parameter at ? =-0.5 and D = 0 is shown to be consistent with the result form the density matrix renormalization group(DMRG) method. These results suggest that the U(1) symmetric iMPS method can be applicable to calculate Luttinger liquid parameters if any system has a U(1) symmetry for gapless phases. For instance, we present our Luttinger liquid parameters for the first time for the spin-1 XXZD model under the other parameters and the spin-2 XXZD model with D = 1.5.更多还原