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A new nonlinear integral equation (NLIE) describing the thermodynamics of theHeisenberg spin chain is derived based on the t-W relation of the quantumtransfer matrices. The free energy of the system in a magnetic field is thusobtained by solving the NLIE. This method can be generalized to other latticequantum integrable models. Taking the SU(3)-invariant quantum spin chain as anexample, we construct the corresponding NLIEs and compute the free energy. Thepresent results coincide exactly with those obtained via other methodspreviously.

T-W relation and free energy of the Heisenberg chain at a finite temperature