W-representation for multi-character partition function

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-character expansions, which involve a generic number of sets of time variables. We propose integral representations 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 correspondence between the two-color Dyck order in Fredkin spin chain and the tree operator on the ring, we prove that the entanglement scaling of Fredkin spin chain beyond the logarithmic scaling in ordinary critical systems.

mathematical physicsdynamical systemsquantum algebrarepresentation theorysymplectic geometry

Audience: general audience

( slides | video )

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BIMSA Integrable Systems Seminar

Series comments: The aim is to bring together experts in integrable systems and related areas of theoretical and mathematical physics and mathematics. There will be research presentations and overview talks.

Audience: Graduate students and researchers interested in integrable systems and related mathematical structures, such as symplectic and Poisson geometry and representation theory.

The zoom link will be distributed by mail, so please join the mailing list if you are interested in attending the seminar.

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