Thermodynamical properties of a spin-$\frac{1}{2}$ Heisenberg chain coupled to phonons

We performed a finite-temperature quantum Monte Carlo simulation of the one-dimensional spin-$\frac{1}{2}$ Heisenberg model with nearest-neighbor interaction coupled to Einstein phonons. Our method allows us to treat easily up to 100 phonons per site and the results presented are practically free from truncation errors. We studied in detail the magnetic susceptibility, the specific heat, the phonon occupation, the dimerization, and the spin-correlation function for various spin-phonon couplings and phonon frequencies. In particular we give evidence for the transition from a gapless to a massive phase by studying the finite-size behavior of the susceptibility. We also show that the dimerization is proportional to $g^2/\Omega$ for $T<\mathrm{}2J.\mathrm{}$