Hamburg 2009 – scientific programme
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Q: Fachverband Quantenoptik und Photonik
Q 9: Quanteninformation: Konzepte II
Q 9.1: Talk
Monday, March 2, 2009, 14:00–14:15, VMP 6 HS-D
Sequentially generated states for the study of two dimensional systems — •Mari-Carmen Banuls1, David Perez-Garcia2, Michael M. Wolf3, Frank Verstraete4, and J. Ignacio Cirac1 — 1Max-Planck-Institut fuer Quantenoptik, 85748 Garching, Germany — 2Depto. Analisis Matematico, Universidad Complutense de Madrid, 28040 Madrid, Spain — 3Niels Bohr Institut, 2100 Copenhagen , Denmark — 4Fakultaet fuer Physik, Universitaet Wien, A-1090 Wien, Austria
The family of Matrix Product States represents a powerful tool for the study of physical one-dimensional quantum many-body systems, such as spin chains. Besides, Matrix Product States can be defined as the family of quantum states that can be sequentially generated in a one-dimensional system. We have introduced a new family of states which extends this sequential definition to two dimensions. Like in Matrix Product States, expectation values of few body observables can be efficiently evaluated and, for the case of translationally invariant systems, the correlation functions decay exponentially with the distance. We show that such states are a subclass of Projected Entangled Pair States and investigate their suitability for approximating the ground states of local Hamiltonians.