Simulation of solitons in an Ising-like S=(1/2 antiferromagnet on a linear chain

Abstract

The dynamics of quantum solitons in an Ising-like S=(1/2 antiferromagnet on finite linear chains with spins N (\ensuremath{\le}15) is studied by integrating the Schr\"odinger equation of motion. Space-time correlation functions ${S}^{\mathrm{zz}}$(r,t) and their Fourier transforms, i.e., dynamical structure factor ${S}^{\mathrm{zz}}$(q,\ensuremath{\omega}), are calculated for both even and odd N. A slow but large oscillation of ${S}^{\mathrm{zz}}$(r,t) is seen, which gives a direct evidence of the occurrence of propagating domain walls, i.e., solitons. The oscillation leads to a low-energy component of ${S}^{\mathrm{zz}}$(q,\ensuremath{\omega}) whose line shape greatly depends on whether N is even or odd and on the temperature. We analyze in detail the dependence of soliton number in the line shape and give a plausible conjecture that ${S}^{\mathrm{zz}}$(q,\ensuremath{\omega}) for N=\ensuremath{\infty} should exhibit a very broad double maximum at low temperatures. We estimate ${S}^{\mathrm{zz}}$(q,\ensuremath{\omega}) at various temperatures. Our results reproduce experimental observations of ${S}^{\mathrm{zz}}$(q,\ensuremath{\omega}) on ${\mathrm{CsCoCl}}_{3}$ and ${\mathrm{CsCoBr}}_{3}$ very well over a wide temperature range.