Sequentially generated states for the study of two-dimensional systems

M. C. Bañuls, D. Pérez-García, M. M. Wolf, F. Verstraete, and J. I. Cirac
Phys. Rev. A 77, 052306 – Published 7 May 2008

Abstract

Matrix product states can be defined as the family of quantum states that can be sequentially generated in a one-dimensional system [Schön et al., Phys. Rev. Lett. 95, 110503 (2005)]. We introduce a family of states that extends this 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.

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  • Received 18 February 2008

DOI:https://doi.org/10.1103/PhysRevA.77.052306

©2008 American Physical Society

Authors & Affiliations

M. C. Bañuls1,*, D. Pérez-García2, M. M. Wolf1, F. Verstraete3, and J. I. Cirac1

  • 1Max-Planck-Institut für Quantenoptik, Hans-Kopfermann-Strasse 1, 85748 Garching, Germany
  • 2Departamento Análisis Matemático, Universidad Complutense de Madrid, 28040 Madrid, Spain
  • 3Fakultät für Physik, Universität Wien, Boltzmanngasse 5, A-1090 Wien, Austria

  • *banulsm@mpq.mpg.de

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Vol. 77, Iss. 5 — May 2008

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