Parent Lindbladians for matrix product density operators
Year: 2026
Type: article
Abstract: Understanding quantum phases of matter is a fundamental goal in physics. For pure states, the representatives of phases are the ground states of locally interacting Hamiltonians, which are also renormalization fixed points (RFPs). These RFP states are exactly described by tensor networks. Extending this framework to mixed states, matrix product density operators (MPDOs) that are RFPs are believed to encapsulate mixed-state phases of matter in one dimension, where nontrivial topological phases have already been shown to exist. However, to better motivate the physical relevance of those states, and in particular the physical relevance of the recently found non trivial phases, it remains an open question whether such MPDO RFPs can be realized as steady states of local Lindbladians. In this work, we resolve this question by analytically constructing parent Lindbladians for MPDO RFPs. These Lindbladians are local, frustration free, and exhibit minimal steady-state degeneracy. Interestingly, we find that parent Lindbladians possess a rich structure that distinguishes them from their Hamiltonian counterparts. In particular, we uncover an intriguing connection between the noncommutativity of the Lindbladian terms and the fact that the corresponding MPDO RFP belongs to a nontrivial phase.
Source: Physical Review Research
DOI: 10.1103/1qyd-59z7
Language: English
Topic: Quantum many-body systems
Subfield: Atomic and Molecular Physics, and Optics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $2,625
Funders: Alexander von Humboldt-Stiftung, Comunidad de Madrid, Government of Canada, European Commission, Deutsche Forschungsgemeinschaft, Bundesministerium für Bildung und Forschung, Universidad Complutense de Madrid, Ministerio de Ciencia e Innovación, Institut Périmètre de physique théorique, Ministry of Colleges and Universities, Munich Center for Quantum Science and Technology, Agencia Estatal de Investigación
Awards: G1175115578, G121809054, G1768993395, G1855990336, G1908868068, G210041235, G2262748287, G2309174360, G2601397997, G2660406951, G2756433129, G279363373, G2960115771, G300979063, G34346518, G3480869486, G3681454997, G379951279, G4042783231, G4192779913, G425668148, G430777504, G455862292, G4710139657, G4886082077, G5080475149, G5195188938, G5421974903, G5768859344, G5805502524, G7084143925, G712370837, G866891011, EXC 2111: Munich Center for Quantum Science and Technology (MCQST), G897484643, G99296377
OpenAlex ID: W4406692398