Thermodynamics of the Anisotropic Spin-1/2 Heisenberg Chain and Related Quantum Chains

The free energy and correlation lengths of the spin-1/2 $XYZ$ chain are studied at finite temperature. We use the quantum transfer matrix approach and derive non-linear integral equations for all eigenvalues. Analytic results are presented for the low-temperature asymptotics, in particular for the critical $XXZ$ chain in an external magnetic field. These results are compared to predictions by conformal field theory. The integral equations are solved numerically for the non-critical $XXZ$ chain and the related spin-1 biquadratic chain at arbitrary temperature.