Universality class of integer quantum spin chains: S=2 case study

The density-matrix renormalization-group technique is employed to show explicitly that S = 2 quantum spin chains belong to the same universality class as S = 1 spin chains. The dispersion of the single-magnon band for periodic chains is shown to be root Delta(2) + omega(q)(2), where Delta is the Haldane gap and omega(q) = upsilon\sin(pi-q)\ with upsilon = Delta xi, xi as the correlation length, pi-q = 2 pi n/L, L as the chain length, and n as an integer. Moreover, the existence of spin-1/2 topological excitations due to the breaking of one singlet bond is demonstrated by finite-size scaling of correlation functions decaying as exp(-r/xi)/root L. These stringent numerical tests, as well as the repulsive interactions between magnons, provide strong evidence in favor of the existence of a universality class for integer quantum spin chains conjectured by Haldane.