Cyclic spin exchange in cuprate spin ladders

Abstract

We investigate the influence of a cyclic spin exchange ${J}_{\mathrm{cyc}}$ on the one- and two-triplet excitations of an undoped two-leg $S=1/2$ ladder, using the density-matrix renormalization group (DMRG). The dispersion of the $S=0$ two-triplet bound state is dramatically reduced by ${J}_{\mathrm{cyc}}$ due to a repulsion between triplets on neighboring rungs. In $(\mathrm{La},\mathrm{Ca}{)}_{14}{\mathrm{Cu}}_{24}{\mathrm{O}}_{41}$ a consistent description of both the spin gap and the $S$=0 bound state requires ${J}_{\mathrm{cyc}}{/J}_{\ensuremath{\perp}}\ensuremath{\approx}0.20--0.27$ and ${J/J}_{\ensuremath{\perp}}\ensuremath{\approx}1.25--1.35.$ With these coupling ratios the recently developed dynamical DMRG yields an excellent description of the entire $S=0$ excitation spectrum observed in the optical conductivity, including the continuum contribution.