Inhomogeneous matrix product ansatz and exact steady states of boundary-driven spin chains at large dissipation

Popkov, Vladislav (author), Prosen, Tomaž (author), Zadnik, Lenart (author)

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.

• Language: English
• Keywords: statistical physics, open quantum systems, quantum spin chains
• Typology: 1.01 - Original Scientific Article
• Organization: FMF - Faculty of Mathematics and Physics
• Publication status: Published
• Publication version: Author Accepted Manuscript
• Year: 2020
• Number of pages: Str. 042122-1-042122-10
• Numbering: Vol. 101, iss. 4
• PID: 20.500.12556/RUL-117817
• UDC: 530.145
• ISSN on article: 2470-0045
• DOI: 10.1103/PhysRevE.101.042122
• COBISS.SI-ID: 23761667
• Publication date in RUL: 28.07.2020

Record is a part of a journal

• Title: Physical review
• Shortened title: Phys. rev., E
• Publisher: American Physical Society
• ISSN: 2470-0045
• COBISS.SI-ID: 2048366611

Secondary language

• Language: Slovenian
• Keywords: statistična fizika, odprti kvantni sistemi, kvantne spinske verige

Projects

• Funder: EC - European Commission
• Funding programme: H2020
• Project number: 694544
• Name: Open Many-body Non-Equilibrium Systems
• Acronym: OMNES

• Funder: ARRS - Slovenian Research Agency
• Project number: P1-0402
• Name: Matematična fizika