A Study of the S=1/2 Alternating Chain using Multiprecision Methods

.A.Tennant In thispaperwepresentresultsfortheground state and low-lying excitationsofthe S = 1 = 2 alternating H eisenberg antiferrom agnetic chain.O urm ore conventionaltechniquesinclude perturbation theory about the dim er lim it and num ericaldiagonalization ofsystem s ofup to 28 spins. A novel application ofm ultipleprecision num ericaldiagonalization allowsusto determ ineanalyticalpertur-bation series to high order;the results found using thisapproach include ninth-orderperturbation seriesforthe ground state energy and one m agnon gap,which were previously known only to third order. W e also give the (cid:12)fth-orderdispersion relation and third-orderexclusive neutron scattering structure factorforone-m agnon m odesand num ericaland analyticalbinding energiesof S = 0 and S = 1 two-m agnon bound states.