Stationary measures for higher spin vertex models on a strip

TL;DR

This paper introduces a higher spin vertex model on a strip, solves for its stationary measure using a matrix product ansatz, and demonstrates a universal phase diagram shared with open ASEP.

Contribution

It generalizes existing models by incorporating higher spin and fused weights, providing a new solution method and revealing universality in phase diagrams.

Findings

Stationary measure characterized via Askey-Wilson process

Shared phase diagram with open ASEP

Universality result for phase behavior

Abstract

We introduce a higher spin vertex model on a strip with fused vertex weights. This model can be regarded as a generalization of both the unfused six-vertex model on a strip [Yan22] and an 'integrable two-step Floquet dynamics' model introduced in [Van18]. We solve for the stationary measure using a fused version of the matrix product ansatz and then characterize it in terms of the Askey-Wilson process. Using this characterization, we obtain the limits of the mean density along an arbitrary down-right path. It turns out that all these models share a common phase diagram, which, after an appropriate mapping, matches the phase diagram of open ASEP, thereby establishing a universality result for this phase diagram.