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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. 100149. ISSN 00034916

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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 twodimensional topological states, through the bulkboundary 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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