横场中具有周期性各向异性的一维XY模型的量子相变  

Quantum phase transitions of one-dimensional period-two anisotropic XY models in a transverse field

作　　者：宋加丽 钟鸣[1] 童培庆[1,2] Song Jia-Li Zhong Ming Tong Pei-Qing(Department of Physics and Institute of Theoretical Physics, Nanjing Normal University, Nanjing 210023, China Jiangsu Key Laboratory for Numerical Simulation of Large Scale Complex Systems, Nanjing Normal University, Nanjing 210023, China)

机构地区：[1]南京师范大学物理科学与技术学院,南京210023 [2]江苏省大规模复杂系统数值模拟重点实验室,南京210023

出　　处：《物理学报》2017年第18期47-54,共8页Acta Physica Sinica

基　　金：国家自然科学基金(批准号:11575087)资助的课题~~

摘　　要：通过解析和数值计算的方法研究了横场中具有周期性各向异性的一维XY自旋模型的量子相变和量子纠缠.主要讨论了周期为二的情况,即各向异性参数交替地取比值为α的两个值.结果表明,与横场中均匀XY模型相比,α=-1所对应的模型在参数空间的相图存在着明显的不同.原来的Ising相变仍然存在,没有了沿x和y方向的各向异性铁磁(FM_x,FM_y)相,即各向异性相变消失,出现了一个新的相,并且该相内沿x和y方向的长程关联函数相等且大于零,我们称新相为各向同性铁磁(FM_(xx))相.这是由于系统新的对称性所导致的.解析结果还说明系统在FM_(xx)相中的单粒子能谱有两个零点,是一个无能隙的相.最后,利用冯·诺依曼熵数值地研究了系统在新相内各点的量子纠缠,发现该相内每一点的冯·诺依曼熵的标度行为与均匀XY模型在各向异性相变处的相似,即S_L～1/3㏒_2L+Const.The quantum phase transitions of one-dimensional period-two anisotropic XY models in a transverse field with the Hamiltonian H=N∑（i=1）[-J/2（（1 ＋ γ_i）/2σ_i^xσ_（i＋1）~x＋（1-y_i）/2σ_i^yσ_（i＋1）~y）-1/2hσ_i^z] ,where the anisotropy parameters γ_i take γ and αγ alternately, are studied. The Hamiltonian can be reduced to the diagonal form by Jordan-Wigner and Bogoliubov transformations. The long-range correlations C^x and C^y are calculated numerically. The phase with C^x Cy≠0（or C^y C^x≠ 0） is referred to as the ferromagnetic（FM） phase along the x（or y） direction, while the phase with C^x= C^y= 0 is the paramagnetic（PM） phase. It is found that the phase diagrams with the ratio α≠-1 and α =-1 are different obviously.For the case with α ≠-1, the line h = h_（c1） =（1-[γ（1-α）/2]~2）^（1/2） separates an FM phase from a PM phase, while the line γ = 0 is the boundary between a ferromagnetic phase along the x direction（FM_x） and a ferromagnetic phase along the y direction（FM_y）. These are similar to those of the uniform XY chains in a transverse field（i.e., α = 1）.When α =-1, the FM_x and FM_y phases disappear and there appears a new FM phase. The line h = h_（c2） =（1-γ~2）^（1/2） separates this new FM phase from the PM phase. The new phase is gapless with two zeros in single particle energy spectrum. This is due to the new symmetry in the system with α =-1, i.e., the Hamiltonian is invariant under the transformation σ_（2i）~x→ σ_（2i＋1）~y, σ_（2i）~y→ σ_（2i＋1）~x. The correlation function between the 2i-1 and 2i lattice points along the x（y） direction is equal to that between the 2i and 2i＋1 lattice points along the y（x） direction. As a result, the long-range correlation functions along two directions are equivalent. In order to facilitate the description, we call this gapless phase the isotropic ferromagnetic（FM_（xx）） phase.Finally, the relationship between quantum entanglement

关 键 词：周期性各向异性XY模型 量子相变 各向同性铁磁相 冯·诺依曼熵 

分 类 号：O469[理学—凝聚态物理]