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Matrix product density operators: Renormalization fixed points and boundary theories

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Cirac, J. I. and Pérez García, David and Schuch, N. and Verstraete, F. (2017) Matrix product density operators: Renormalization fixed points and boundary theories. Annals of physics, 378 . pp. 100-149. ISSN 0003-4916

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Official URL: http://www.sciencedirect.com/science/article/pii/S0003491616303013


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Abstract

We consider the tensors generating matrix product states and density operators in a spin chain. For pure states, we revise the renormalization procedure introduced in (Verstraete et al., 2005) and characterize the tensors corresponding to the fixed points. We relate them to the states possessing zero correlation length, saturation of the area law, as well as to those which generate ground states of local and commuting Hamiltonians. For mixed states, we introduce the concept of renormalization fixed points and characterize the corresponding tensors. We also relate them to concepts like finite correlation length, saturation of the area law, as well as to those which generate Gibbs states of local and commuting Hamiltonians. One of the main result of this work is that the resulting fixed points can be associated to the boundary theories of two-dimensional topological states, through the bulk-boundary correspondence introduced in (Cirac et al., 2011).


Item Type:Article
Uncontrolled Keywords:Boundary theory; Matrix product state; Renormalization fixed point; Tensor network state; Topological order
Subjects:Sciences > Mathematics > Functional analysis and Operator theory
ID Code:42065
Deposited On:05 Apr 2017 10:15
Last Modified:05 Apr 2017 10:42

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