Stuttgart 2012 – wissenschaftliches Programm

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Q: Fachverband Quantenoptik und Photonik

Q 2: Quanteninformation: Konzepte und Methoden 1

Q 2.6: Vortrag

Montag, 12. März 2012, 11:45–12:00, V7.03

Entanglement spectrum and boundary theories with projected entangled-pair states — Ignacio Cirac¹, Didier Poilblanc², •Norbert Schuch³, and Frank Verstraete⁴ — ¹Max-Planck-Institut für Quantenoptik, Garching, Germany — ²Laboratoire de Physique Theorique, C.N.R.S. and Universite de Toulouse, Toulouse, France — ³California Institute of Technology, Pasadena, USA — ⁴Universität Wien, Vienna, Austria

In many physical scenarios, close relations between the bulk properties of quantum systems and theories associated to their boundaries have been observed. In this work, we provide an exact duality mapping between the bulk of a quantum spin system and its boundary using Projected Entangled Pair States (PEPS). This duality associates to every region a Hamiltonian on its boundary, in such a way that the entanglement spectrum of the bulk corresponds to the excitation spectrum of the boundary Hamiltonian. We study various models and find that a gapped bulk phase with local order corresponds to a boundary Hamiltonian with local interactions, whereas critical behavior in the bulk is reflected on a diverging interaction length of the boundary Hamiltonian. Furthermore, topologically ordered states yield non-local Hamiltonians. As our duality also associates a boundary operator to any operator in the bulk, it in fact provides a full holographic framework for the study of quantum many-body systems via their boundary.