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Valence Bond States : Link models

Rico, E. and Hübener, R. and Montangero, S. and Moran, N. and Pirvu, P. and Vala, J. and Briegel, H.J. (2009) Valence Bond States : Link models. Annals of Physics, 324 (9). pp. 1875-1896. ISSN 0003-4916

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Abstract

An isotropic anti-ferromagnetic quantum state on a square lattice is characterized by symmetry arguments only. By construction, this quantum state is the result of an underlying valence bond structure without breaking any symmetry in the lattice or spin spaces. A detailed analysis of the correlations of the quantum state is given (using a mapping to a 2D classical statistical model and methods in field theory like mapping to the non-linear sigma model or bosonization techniques) as well as the results of numerical treatments (regarding exact diagonalization and variational methods). Finally, the physical relevance of the model is motivated. A comparison of the model to known anti-ferromagnetic Mott-Hubbard insulators is given by means of the twopoint equal-time correlation function obtained i) numerically from the suggested state and ii) experimentally from neutron scattering on cuprates in the anti-ferromagnetic insulator phase.

Item Type: Article
Additional Information: Preprint version of original article. This work was supported by networks DARPA, EMALI, EUROSQIP, FWF, MURI, NAMEQUAM, OLAQUI and SCALA and developed using the DMRG code released within the PwP project (http://www.dmrg.it). J.V. and N.M. acknowledge the support of SFI through the PIYRA and the computing resources of ICHEC. E.R. would like to thank The Hebrew University of Jerusalem for their hospitality during the winter school 2008 on Condensed Matter and Quantum Information. N.M and E.R. also would like to thank the Ecole de Physique Les Houches for their hospitality during the summer school 2008 on "Exact methods in low-dimensional Statistical Physics and Quantum Computing", where part of this work was done. The authors thank I. Affleck, M.A. Martin-Delgado, G. Sierra and F. Verstraete for useful and constructive comments and G. Aeppli’s group for providing their experimental data on neutron scattering.
Keywords: Quantum anti-ferromagnet; Mott–Hubbard insulator; Valence bond state;
Subjects: Science & Engineering > Mathematical Physics
Item ID: 2788
Identification Number: 10.1016/j.aop.2009.06.001
Depositing User: Dr. Jiri Vala
Date Deposited: 24 Oct 2011 15:31
Journal or Publication Title: Annals of Physics
Publisher: Elsevier
Refereed: No
URI:

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