Coherent states and phase transitions in quantum spin systems

It has been known from the work of Berezin and Lieb from early 1970s that the free energy of quantum spin systems converges, in the limit of large spin, to the free energy of the corresponding classical model. Unfortunately, this alone does not give any information about phase transitions in the quantum system. I will show how one can enhance the Berezin-Lieb upper bound into an inequality for matrix elements (relative to the overcomplete basis of coherent states) which, for models that permit the use of chessboard estimates, allow proofs of phase transitions by direct comparison with the classical counterpart.

In some cases (anisotropic Heissenberg antiferromagnet) this offers an alternative to "exponential localization" developed by Frohlich and Lieb; in other cases (models with temperature driven transitions or highly degenerate ground states) this yields proofs of phase transitions that have not been accessible heretofore. Based on joint work with L. Chayes and S. Starr.