1994/05/14 by J. C. Talstra, F. D. M. Haldane · 1 citation
Physics and Astronomy · #Advanced Condensed Matter Physics #Magnetic properties of thin films #Physics of Superconductivity and Magnetism #cond-mat
paper · pdf · doi:10.1103/physrevb.50.6889
29 pages, REVTEX v3.0, including 6 PostScript figures
arxiv created 1994/05/14 · openalex publication_date 1994/09/01 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
We present a selection rule for matrix elements of local spin operators in the S=1/2 Haldane-Shastry model. Based on this rule we extend a recent exact calculation by Haldane and Zirnbauer of the ground-state dynamical spin correlation function Sab(n,t)=〈0\ensuremath\VertSa(n,t)Sb(0,0)\ensuremath\Vert0〉 and its Fourier transform Sab(Q,E) of this model to a finite magnetic field. In zero field, only two-spinon excitations contribute to the spec tral function; in the (positively) partially spin-polarized case, there are two types of elementary excitations: spinons (\ensuremathΔSz=\ifmmode±\else\textpm\fi1/2) and magnons (\ensuremathΔSz=-1). The magnons are divided into left- or right-moving branches. The only classes of excited states contributing to the spectral functions are (I) two spinons, (II) two spinons+one magnon, (IIIa) two spinons+two magnons (moving in opposite directions), and (IIIb) one magnon. The contributions to the various correlations are S^\mathrm\ensuremath-+: (I); Szz: (I)+(II); S^+\mathrm\ensuremath-: (I)+(II)+(III). In the zero-field limit there are no magnons, while in the fully polarized case, there are no spinons. We discuss the relation of the spectral functions to correlations of the Calogero-Sutherland model at coupling \ensuremathλ=2.