Correlation Lengths in Quantum Spin Ladders

Analytic expressions for the temperature dependences of the correlation length are given for antiferromagnetic spin- $\frac{1}{2}$ Heisenberg ladders using a finite-size nonlinear σ 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.