{
  "id": "1905.09273",
  "version": "v1",
  "published": "2019-05-22T17:59:03.000Z",
  "updated": "2019-05-22T17:59:03.000Z",
  "title": "Inhomogeneous matrix product ansatz and exact steady states of boundary driven spin chains at large dissipation",
  "authors": [
    "Vladislav Popkov",
    "Tomaž Prosen",
    "Lenart Zadnik"
  ],
  "comment": "5 pages main text, 5 pages supplemental material, 3 figures",
  "categories": [
    "cond-mat.stat-mech",
    "math-ph",
    "math.MP"
  ],
  "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 matrix product ansatz, 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.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-05-22T17:59:03.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "inhomogeneous matrix product ansatz",
      "boundary driven spin chains",
      "exact steady states",
      "large dissipation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 5,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}