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PEPS as ground states: degeneracy and topology

Schuch, Norbert and Pérez García, David and Cirac, Ignacio (2010) PEPS as ground states: degeneracy and topology. Annals of Physics, 325 (10). pp. 2153-2192. ISSN 0003-4916

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Official URL: http://www.sciencedirect.com/science/article/pii/S0003491610000990

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Abstract

We introduce a framework for characterizing Matrix Product States (MPS) and Projected Entangled Pair States (PEPS) in terms of symmetries. This allows us to understand how PEPS appear as ground states of local Hamiltonians with finitely degenerate ground states and to characterize the ground state subspace. Subsequently, we apply our framework to show how the topological properties of these ground states can be explained solely from the symmetry: We prove that ground states are locally indistinguishable and can be transformed into each other by acting on a restricted region, we explain the origin of the topological entropy, and we discuss how to renormalize these states based on their symmetries. Finally, we show how the anyonic character of excitations can be understood as a consequence of the underlying symmetries.


Item Type:Article
Uncontrolled Keywords:Matrix Product States; Projected Entangled Pair States (PEPS); Tensor network states; Topological states; Quantum double models; Toric code state; Anyons; Exactly solvable models
Palabras clave (otros idiomas):Física matemática, Teoría cuántica, Quantum Physics, Mathematical Physics
Subjects:Sciences > Physics > Mathematical physics
Sciences > Physics > Quantum theory
ID Code:12159
Deposited On:03 Feb 2011 08:54
Last Modified:03 Dec 2014 15:55

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