On the construction and solution of -symmetric models

Rajkumar Roychoudhury, P Roy

Bo-Yu Hou, Mu-Lin Yan, Yu‐Kui Zhou

Mathieu Dabrowski, Loïc Poulain d’Andecy, E. Ragoucy

Abstract We investigate periodic integrable Markov models, constructed from set-theoretical solutions of the Yang–Baxter equation. We first focus on the simplest class of solutions, called Lyubashenko solutions. We show that the resulting models are equivalent to some twisted symmetric simple exclusion process (SSEP), which are usual multi-species periodic SSEP models where a twist is added on a bond of the ring. We also provide various possible interpretations for these Markov models. Then, we study the long time dynamics of the twisted SSEP, characterising its different stationary states and counting them. Allowing the twist to vary, we examine the possible transitions between the different stationary states. Finally, we extend our construction of Markov models to set-theoretical solutions that are more general than Lyubashenko solutions and show that such models are not equivalent to a twisted SSEP in general.

Markus Arndt

Yuji Yamada

We consider solutions to the reflection equation for the critical Z N -symmetric vertex model, which is the trigonometric limit of the elliptic Z N -symmetric R -matrix of Belavin. These critical R -matrices have two parameters u and η. The transfer matrices constructed from this R -matrix R ( u , η) under the cyclic boundary condition are commutative among different u when η is in common, . We prove that an arbitrary solution to the reflection equation is independent of the parameter η.

Yu Wan‐Lun

Based on the fact that the generalized Jaynes-Cummings model can describe two collectively radiation atoms and possesses a super symmetric structure an invariant is constructed from the super symmetric generators in the eigenspace of the super-symmetric generator N'.Thus the invariant method is used to solve this Jaynes-Cummings model.