Exact solutions of few-magnon problems in the spin-S periodic XXZ chain
Exact solutions of few-magnon problems in the spin-S periodic XXZ chain
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自旋-S周期XXZ链中少磁振子问题的精确解
DOI：
10.1103/physrevb.105.064419
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发表时间：
2022
影响因子：
3.7
通讯作者：
Xi-Wen Guan
中科院分区：
文献类型：
--
作者：
Ning Wu;Hosho Katsura;Sheng-Wen Li;Xiaoming Cai;Xi-Wen Guan
We solve few-magnon problems for afinite-sizespin-periodic Heisenberg XXZ chain with single-ion anisotropy through constructing sets ofexactBloch states achieving block diagonalization of the system. Concretely, the two-magnon (three-magnon) problem is converted to a single-particle one on a one-dimensional (two-dimensional) effective lattice whose size depends linearly (quadratically) on the total number of sites. For parameters lying within certain ranges, various types of multimagnon bound states are manifested and shown to correspond to edge states on the effective lattices. In the absence of the single-ion anisotropy, we reveal the condition under which exact zero-energy states emerge. As applications of the formalism, we calculate the transverse dynamic structure factor for a higher-spin chain near saturation magnetization and find signatures of the multimagnon bound states. We also calculate the real-time three-magnon dynamics from certain localized states, which are relevant to cold-atom quantum simulations, by simulating single-particle quantum walks on the effective lattices. This provides a physically transparent interpretation of the observed dynamics in terms of propagation of bound state excitations. Our method can be directly applied to more general spin or itinerant particle systems possessing translational symmetry.
