Topic: Shor-Movassagh chain leads to unusual integrable model

Speaker: Assoc. Prof. Kun Hao

Coordinates:  PCFT C1124, 16:00, Thursday, Nov. 4

Abstract: The ground state of the Shor-Movassagh chain can be analytically described by the Motzkin paths. There is no analytical description of the excited states. The model is not solvable.We prove the integrability of the model without interacting part [free Shor-Movassagh].Since the model does not have crossing unitarity, the integrable open chain can not be constructed by the reflection equation (boundary Yang-Baxter equation). Our Lax pair construction directly demonstrates the quantum integrability of the model, described by the Yang-Baxter algebra.The free Shor-Movassagh chain with periodic boundary conditions has also been studied. Based on some intrinsic properties of the R-matrix, we derive the functional relations of the transfer matrix. Together with the asymptotic behavior, these relations allow us to construct a generalized T-Q relation and the associated Bethe Ansatz equations. There are new structures in this T-Q relation. Their pattern can be described by the Moebius function in number theory.