Abstract
We investigate the asymptotic behaviour of spin–spin correlation functions for the integrable Heisenberg chain. To this end we use the Quantum Transfer Matrix (QTM) technique developed in ref. 1) which results in a set of non-linear integral equations (NLIE). In the case of the largest eigenvalue the solution to these equations yields the free energy and by modifications of the paths of integration the next-leading eigenvalues and hence the correlation lengths are obtained. At finite field h>0 and sufficiently high temperature T the next-leading eigenvalue is unique and given by a 1-string solution to the QTM taking real and negative values thus resulting into exponentially decaying correlations with antiferromagnetic oscillations. At sufficiently low temperatures a different behaviour sets in where the next-leading eigenvalues of the QTM are given by a complex conjugate pair of eigenvalues resulting into incommensurate oscillations. The above scenario is the result of analytical and numerical investigations of the QTM establishing a well defined crossover temperature Tc(h) at which the 1-string eigenvalue to the QTM gets degenerate with the 2-string solution. Among other things we find a simple particle-hole picture for the excitations of the QTM allowing for a description by the dressed charge formulation of CFT.
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Klümper, A., Martínez, J.R.R., Scheeren, C. et al. The Spin-1/2 XXZ Chain at Finite Magnetic Field: Crossover Phenomena Driven by Temperature. Journal of Statistical Physics 102, 937–951 (2001). https://doi.org/10.1023/A:1004811305534
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DOI: https://doi.org/10.1023/A:1004811305534