The spin-1/2 XXZ chain at finite magnetic field: Crossover phenomena driven by temperature

We investigate the asymptotic behaviour of spin-spin correlation functions for the integrable Heisenberg chain. To this end we use the Quantum Transfe r Matrix (QTM) technique developed in ref. ii which results in a set of non -linear integral equations (NLIE). In the case of the largest eigenvalue th e solution to these equations yields the Free energy and by modifications o f the paths of integration the next-leading eigenvalues and hence the corre lation lengths are obtained. At finite field h > 0 and sufficiently high te mperature T the next-leading eigenvalue is unique and given by a 1-string s olution to the QTM taking real and negative values thus resulting into expo nentially decaying correlations with antiferromagnetic oscillations. At suf ficiently low temperatures a different behaviour sets in where the next-lea ding eigenvalues of the QTM are given by a complex conjugate pair of eigenv alues resulting into incommensurate oscillations. The above scenario is the result of analytical and numerical investigations of the QTM establishing a well defined crossover temperature T-c(h) at which the 1-string eigenvalu e to the QTM gels degenerate with the 2-string solution. Among other things we find a simple particle-hole picture for the excitations of the QTM allo wing for a description by the dressed charge formulation of CFT.