基于U(1)对称的无限矩阵乘积态张量网络算法提取Luttinger液体参数K  

Extracting Luttinger liquid parameter K based on U(1) symmetric infinite matrix product states

作　　者：王秀娟 李生好[2,3] Wang Xiu-Juan;Li Sheng-Hao(State Key Laboratory of Power Transmission Equipment and System Security and New Technology,Chongqing University, Chongqing 400044, China;Chongqing Vocational Institute of Engineering, Chongqing 400037, China;Centre for Modern Physics and Department of Physics, Chongqing University, Chongqing 400044, China)

机构地区：[1]重庆大学,输配电装备及系统安全与新技术国家重点实验室,重庆400044 [2]重庆工程职业技术学院,重庆400037 [3]重庆大学,现代物理中心,重庆400044

出　　处：《物理学报》2019年第16期132-141,共10页Acta Physica Sinica

基　　金：国家自然科学基金(批准号:11104362);重庆市基础科学与前沿技术研究专项(批准号:cstc2018jcyjAX0812);重庆市教委科学技术研究项目(批准号:KJQN201801212);陕西省自然科学基金(批准号:2019JM-017)资助的课题~~

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k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.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.

关 键 词：无限矩阵乘积态 Luttinger 液体参数 二分量子涨落 

分 类 号：O151.21[理学—数学]