Novel many-body method in statistical mechanics and strongly correlate…

To calculate the partition function is the most fundamental task in statistical mechanics. The symbolic work is that of Lars Onsager in 1944 for the 2 dimensional Ising model followed by C.N. Yang in 1952. We here develop a new method for including non-integrable systems and 3 dimemsion. The method does not rely on any existing notions such as numerical renormalization group and mean field theories. The idea is "a perturbation in entanglement space". We show the converged and hence exact results, to the precision of 1%, for the specific heat and spontaneous magnetization in 2 and 3 dimensional Ising models. The method is quite simple, general and practically exact, with a tremendous potential of application. Indeed, the method has been succesfully applied to the quantum ground states in 1 dimension, agreeing with the Bethe Ansatz results for the 1 dimensional Hubbard model. Extention to 2 dimension is currently underway, and possibly reported in the talk.