# Inhomogeneous MPA and exact steady states of boundary driven spin chains at large dissipation

## TL;DR

This paper presents an exact solution for a boundary-driven XYZ spin-1/2 chain with strong dissipation, using novel site-dependent Lax operators and an inhomogeneous matrix product ansatz, revealing complex matrix structures.

## Contribution

It introduces new site-dependent Lax operators and an inhomogeneous MPA for solving the XYZ spin chain in the Zeno limit, expanding understanding of dissipative quantum systems.

## Key findings

- Exact steady state expressed via inhomogeneous MPA
- Matrices cannot be simplified into a tridiagonal form
- Results applicable to open XYZ and eight-vertex models

## Abstract

We find novel site-dependent Lax operators in terms of which we demonstrate exact solvability of a dissipatively driven XYZ spin-1/2 chain in the Zeno limit of strong dissipation, with jump operators polarizing the boundary spins in arbitrary directions. We write the corresponding nonequilibrium steady state using an inhomogeneous MPA, where the constituent matrices satisfy a simple set of linear recurrence relations. Although these matrices can be embedded into an infinite-dimensional auxiliary space, we have verified that they cannot be simultaneously put into a tridiagonal form, not even in the case of axially symmetric (XXZ) bulk interactions and general nonlongitudinal boundary dissipation. We expect our results to have further fundamental applications for the construction of nonlocal integrals of motion for the open XYZ model with arbitrary boundary fields, or the eight-vertex model.