Related papers: Parent Lindbladians for Matrix Product Density Operators

Parent Lindbladians for Matrix Product Density Operators

URL: http://arxiv.org/abs/2501.10552v1
Date: Fri, 17 Jan 2025 20:56:06 GMT
Title: Parent Lindbladians for Matrix Product Density Operators
Authors: Yuhan Liu, Alberto Ruiz-de-Alarcón, Georgios Styliaris, Xiao-Qi Sun, David Pérez-García, J. Ignacio Cirac,
Abstract summary: We analytically construct parent Lindbladians for MPDO RFPs. We find that parent Lindbladians possess a rich structure, including non-commutativity for certain classes of RFPs.
Score: 11.988185405531286
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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) which are RFPs are believed to encapsulate mixed-state phases of matter in one dimension. However, it remains an open question whether, by analogy, 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, including non-commutativity for certain classes of RFPs, distinguishing them from their Hamiltonian counterparts.

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