Abstract

We discuss several results on work in collaboration (with V.Mishnyakov, A.Popolitov, F.Liu,R.Wang and with B. Kang, K.Wu, W.Z. Zhao). We construct W-representations for multi-characterexpansions, which involve a generic number of sets of time variables. We propose integralrepresentations for such kind of partition functions which are given by tensor models and multi-matrix models with multi-trace couplings. In addition, we present the W-representation for a two-tensor model with order-3. We derive the compact expressions of correlators from the W.representation, and analyze the free energy in the large N limit. By establishing the correspondencebetween the two-color Dyck order in Fredkin spin chain and the tree operator on the ring, we provethat the entanglement scaling of Fredkin spin chain beyond the logarithmic scaling in ordinarycritical systems.