Semi-classical spectrum of the continuous Heisenberg spin chain

Vladyslav O. Cheranovskii

Hiroyuki Mashiyama

The relaxation function and the spectral shape are investigated theoretically for a classical Heisenberg magnetic chain. In order to reproduce the spectrum, moments of the spin correlation function are calculated rigorously up to the eighth order for the magnetic chain. Proper continuations are introduced in the continued fraction expansion of spin-pair correlation function.

Jonathan P. Keating, Noah Linden, H. J. Wells

Hans C. Fogedby

The continuous Heisenberg chain is quantised semiclassically. The spectrum consists of unit spin bosons (magnons) and integer spin bosons (solitons) with dispersion laws E=JS(ka) 2 and E n =16JS 3 sin 2 (ka/4S)/n (n=1...) respectively. It is proposed that the n=1 soliton is the magnon and that the spectrum is exact, including all quantum corrections. For S= 1 / 2 the spectrum agrees with results for the discrete chain and it is inferred that the soliton is a multi-magnon bound state.

Yuan Miao, Enej Ilievski, Oleksandr Gamayun

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.

Z. Slanič, Harvey Gould, Jan Tobochnik