Correlation Lengths in Quantum Spin Ladders

Analytic expressions for the correlation length temperature dependences are given for antiferromagnetic spin-1/2 Heisenberg ladders using a finite-size non-linear sigma-model approach. These calculations rely on identifying three successive crossover regimes as a function of temperature. In each of these regimes, precise and controlled approximations are formulated. The analytical results are found to be in excellent agreement with Monte Carlo simulations for the Heisenberg Hamiltonian.