粒子间长程相互作用以及晶格中孤立缺陷点对两硬核玻色子在一维晶格势阱中量子行走的影响

Effects of long-range inter-particle interactions and isolated defect on quantum walks of two hard-core bosons in one-dimensional lattices

本文研究了一维晶格势阱中两个硬核玻色子在粒子间长程相互作用下的量子行走.还通过在晶格中的某一个格点加上额外的局域势能,模拟晶格势阱中可能存在的孤立缺陷点对两粒子量子行走的影响.数值计算结果显示粒子间相互作用的范围(长程或短程),相互作用的强度,两粒子初始所处的量子态以及孤立缺陷点的存在对两粒子量子行走结果的影响巨大.在粒子间强长程相互作用下,初始处于非邻近格点的两粒子展现出距离固定步调一致的绑定行走,而在只考虑处于邻近格点粒子间的短程强相互作用下只有初始处于邻近格点的两个粒子才能绑定行走.在引入孤立缺陷点情形下,在粒子间强相互作用下初始处于孤立缺陷点同一侧的两个粒子将保持绑定行走.而初始分别位于孤立缺陷点两侧或者有一个粒子位于孤立缺陷点的两粒子,将停止行走或在孤立缺陷点附近行走,展现出局域化的量子行走行为特点.应用简并量子系统的二阶微扰理论对数值计算结果给予了全面深入的理论分析.研究揭示了在粒子间长程相互作用下两个硬核玻色子在一维没有缺陷点的有序晶格势阱以及具有孤立缺陷点的晶格势阱中量子行走的一些物理规律.

The quantum walk of two hard-core bosons in one-dimensional lattice under the effect of long-range interparticle interaction is studied in detail.We also simulate the influence of an isolated defect that may exist in the lattice on the quantum walk of two particles by adding an additional potential energy to a certain lattice site.Using exact diagonalization method,the continuous-time quantum walk is directly simulated.The numerical simulations show that the range of interaction(long-range or short-range),the strength of the interparticle interaction,the initial state of the two particles and the presence of the isolated defect have great influences on the quantum walk.Under the effect of strong long-range interaction,the particles initially located on the non-adjacent lattice sites have a co-walking behavior,while under the short-range interactions(nearestneighbor interactions)only two particles initially located on the neighboring lattice sites can exhibit co-walking.After introducing the isolated defect into the system with strong interaction,two particles residing on the same side of the isolated defect keep co-walking,while two particles located on either sides of the isolated defect or one particle located on the isolated defect and the other particle staying on the side of the isolated defect,the two particles keep stationary or co-walking near the defect,displaying the characteristics of localization.By using the second-order perturbation theory of degenerate quantum system,a comprehensive theoretical analysis of the above numerical results is given.The theoretical analysis reveals the underlying physical law of quantum walks of two particles in one-dimensional lattice under the effects of strong long-range interaction and isolated defect in the lattice.