Exact renormalization group flow for matrix product density operators

• URL: http://arxiv.org/abs/2410.22696v1
• Date: Wed, 30 Oct 2024 05:09:51 GMT
• Title: Exact renormalization group flow for matrix product density operators
• Authors: Kohtaro Kato,
• Abstract summary: We study a real-space renormalization group transformation of MPDOs represented by a circuit of local quantum channels. Unlike matrix product states (MPS), which always have a well-defined isometric renormalization transformation, we show that general MPDOs do not necessarily admit a converging exact renormalization group flow.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Matrix product density operator (MPDO) provides an efficient tensor network representation of mixed states on one-dimensional quantum many-body systems. We study a real-space renormalization group transformation of MPDOs represented by a circuit of local quantum channels. We require that the renormalization group flow is exact, in the sense that it exactly preserves the correlation between the coarse-grained sites and is therefore invertible by another circuit of local quantum channels. Unlike matrix product states (MPS), which always have a well-defined isometric renormalization transformation, we show that general MPDOs do not necessarily admit a converging exact renormalization group flow. We then introduce a subclass of MPDOs with a well-defined renormalization group flow, and show the structure of the MPDOs in the subclass as a representation of a pre-bialgebra structure. As a result, such MPDOs obey generalized symmetry represented by matrix product operator algebras associated with the pre-bialgebra. We also discuss implications with the classification of mixed-state quantum phases.

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