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Criticality, the Area Law, and the Computational Power of Projected Entangled Pair States

Verstraete, F. and Wolf, M. M. and Perez-Garcia, D. and Cirac, J. I. (2006) Criticality, the Area Law, and the Computational Power of Projected Entangled Pair States. Physical Review Letters, 96 (22). Art. No. 220601. ISSN 0031-9007. https://resolver.caltech.edu/CaltechAUTHORS:VERprl06b

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Abstract

The projected entangled pair state (PEPS) representation of quantum states on two-dimensional lattices induces an entanglement based hierarchy in state space. We show that the lowest levels of this hierarchy exhibit a very rich structure including states with critical and topological properties. We prove, in particular, that coherent versions of thermal states of any local 2D classical spin model correspond to such PEPS, which are in turn ground states of local 2D quantum Hamiltonians. This correspondence maps thermal onto quantum fluctuations, and it allows us to analytically construct critical quantum models exhibiting a strict area law scaling of the entanglement entropy in the face of power law decaying correlations. Moreover, it enables us to show that there exist PEPS which can serve as computational resources for the solution of NP-hard problems.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.1103/PhysRevLett.96.220601DOIUNSPECIFIED
Additional Information:©2006 The American Physical Society (Received 27 January 2006; published 6 June 2006) Work supported by the Gordon and Betty Moore Foundation, European projects, der Bayerischen Staatsregierung and MEC MTM2005-00082.
Subject Keywords:quantum entanglement; lattice theory; critical points
Issue or Number:22
Record Number:CaltechAUTHORS:VERprl06b
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:VERprl06b
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:3589
Collection:CaltechAUTHORS
Deposited By: Archive Administrator
Deposited On:18 Jun 2006
Last Modified:02 Oct 2019 23:04

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