Correlation Lengths in Quantum Spin Ladders

TL;DR

This paper derives analytical expressions for the temperature dependence of correlation lengths in antiferromagnetic spin-1/2 Heisenberg ladders, identifying crossover regimes and validating results with Monte Carlo simulations.

Contribution

It provides the first analytical formulas for correlation length temperature dependence in quantum spin ladders using a finite-size non-linear sigma-model approach.

Findings

Analytical expressions match Monte Carlo results.

Three crossover regimes identified as temperature varies.

Precise approximations formulated for each regime.

Abstract

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.