Spin dynamics of Sr${\mathrm{Cu}}_2$${\mathrm{O}}_3$ and the Heisenberg ladder

The $S=\frac{1}{2}$ Heisenberg antiferromagnet in the ladder geometry is studied as a model for the spin degrees of freedom of Sr${\mathrm{Cu}}_2$${\mathrm{O}}_3$. The susceptibility and the spin-echo decay rate are calculated using a quantum Monte Carlo technique, and the spin-lattice relaxation rate is obtained by maximum-entropy analytic continuation of imaginary-time correlation functions. All calculated quantities are in reasonable agreement with experimental results for Sr${\mathrm{Cu}}_2$${\mathrm{O}}_3$ if the exchange coupling $J\approx 850$ K. However, for the susceptibility fit an anomalously low factor is required.