各向异性海森堡量子链中磁孤子的半经典量子化
Semi-classical quantisation of magnetic solitons in the anisotropic Heisenberg quantum chain
摘要：
利用代数几何方法研究了弱各向异性量子海森堡自旋链中半经典本征态的结构。我们概述了如何经典的非线性自旋波的各向异性朗道-Lifshitz方程产生的相干宏观低能量波动的铁磁基态。特别强调的是致力于最简单类型的解决方案，描述进动运动和椭圆形磁化波。经典自旋波的内部磁振子结构通过使用黎曼-希尔伯特问题方法进行半经典量子化来解决。我们给出了两个半经典本征态重叠的表达式，并讨论了如何在半经典水平上的关联函数从经典相空间平均产生。
英文摘要：
Using the algebro-geometric approach, we study the structure of semi-classical eigenstates in a weakly-anisotropic quantum Heisenberg spin chain. We outline how classical nonlinear spin waves governed by the anisotropic Landau-Lifshitz equation arise as coherent macroscopic low-energy fluctuations of the ferromagnetic ground state. Special emphasis is devoted to the simplest types of solutions, describing precessional motion and elliptic magnetisation waves. The internal magnon structure of classical spin waves is resolved by performing the semi-classical quantisation using the Riemann-Hilbert problem approach. We present an expression for the overlap of two semi-classical eigenstates and discuss how correlation functions at the semi-classical level arise from classical phase-space averaging.
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