Semi-classical quantisation of magnetic solitons in the anisotropic Heisenberg quantum chain
arXiv:2010.07232 · doi:10.21468/SciPostPhys.10.4.086
Abstract
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.
61 pages, 14 figures
References in corpus (14)
- Quantum Quench in the Transverse Field Ising Chain
- Spin transport in a one-dimensional anisotropic Heisenberg model
- Quasilocal conservation laws in XXZ spin-1/2 chains: open, periodic and twisted boundary conditions
- Relaxation dynamics in the gapped XXZ spin-1/2 chain
- Dynamics of the spin-1/2 Heisenberg chain initialized in a domain-wall state
- Domain wall dynamics in the Landau--Lifshitz magnet and the classical-quantum correspondence for spin transport
- Deformed strings in the Heisenberg model
- Relating Field Theories via Stochastic Quantization
- Quantum Stability for the Heisenberg Ferromagnet
- Local correlations in the attractive 1D Bose gas: from Bethe ansatz to the Gross-Pitaevskii equation
- Quantum Crystals and Spin Chains
- Semi-classical analysis of the inner product of Bethe states
- How to calculate correlation functions of Heisenberg chains
- An exact solution to asymptotic Bethe equation