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Resonating valence bond states in the PEPS formalism

Schuch, Norbert and Poilblanc, Didier and Cirac, Juan I. and Pérez García, David (2012) Resonating valence bond states in the PEPS formalism. Physical review B, 86 (11). ISSN 1098-0121

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Abstract

We study resonating valence bond (RVB) states in the projected entangled pair states (PEPS) formalism. Based on symmetries in the PEPS description, we establish relations between the toric code state, the orthogonal dimer state, and the SU(2) singlet RVB state on the kagome lattice: We prove the equivalence of toric code and dimer state, and devise an interpolation between the dimer state and the RVB state. This interpolation corresponds to a continuous path in Hamiltonian space, proving that the RVB state is the fourfold degenerate ground state of a local Hamiltonian on the (finite) kagome lattice. We investigate this interpolation using numerical PEPS methods, studying the decay of correlation functions, the change of overlap, and the entanglement spectrum, none of which exhibits signs of a phase transition.

Item Type:Article
Uncontrolled Keywords:Heisenberg-antiferromagnet; ground-states; quantum; phase
Subjects:Sciences > Mathematics > Mathematical analysis
ID Code:16764
References:

P. W. Anderson, Mater. Res. Bull. 8, 153 (1973).

G. Misguich and C. Lhuillier, in Frustrated Spin Systems, edited by H. T. Diep (World-Scientific, 2003).

P. Mendels, F. Bert, M. A. de Vries, A. Olariu, A. Harrison, F. Duc, J. C. Trombe, J. Lord, A. Amato, and C. Baines, Phys. Rev. Lett. 98,(2007).

Z. Y. Meng, T. C. Lang, S.Wessel, F. F. Assaad, and A. Muramatsu, Nature (London) 464, 847 (2010).

F. Mezzacapo and M. Boninsegni, Phys. Rev. B 85,(2012).

S. Yan, D. A. Huse, and S. R. White, Science 332, (2011).

S. Depenbrock, I. P. McCulloch, and U. Schollw¨ock, Phys. Rev. Lett. 109,(2012).

A. Seidel, Phys. Rev. B 80, (2009).

D. S. Rokhsar and S. A. Kivelson, Phys. Rev. Lett. 61, (1988).

R. Moessner and S. L. Sondhi, Phys. Rev. Lett. 86, (2001).

G. Misguich, D. Serban, and V. Pasquier, Phys. Rev. Lett. 89, (2002).

J. Cano and P. Fendley, Phys. Rev. Lett. 105, (2010).

F. Verstraete and J. I. Cirac, Phys. Rev. A 70, (2004).

F. Verstraete and J. I. Cirac, arXiv:cond-mat/0407066.

D. Perez-Garcia, F.Verstraete, J. I. Cirac, andM.M.Wolf, Quantum Inf. Comput. 8, (2008).

N. Schuch, I. Cirac, and D. P´erez-Garc´ıa, Ann. Phys. 325, (2010).

F. Verstraete, M. M. Wolf, D. Perez-Garcia, and J. I. Cirac, Phys. Rev. Lett. 96, (2006).

A. Kitaev, Ann. Phys. 303, 2 (2003).

P. Zanardi and N. Paunkovi´c, Phys. Rev. E 74, (2006).

C. Nayak and K. Shtengel, Phys. Rev. B 64, (2001).

V. Elser and C. Zeng, Phys. Rev. B 48, (1993).

K. S. Raman, R. Moessner, and S. L. Sondhi, Phys. Rev. B 72, (2005).

T. Barthel, M. Kliesch, and J. Eisert, Phys. Rev. Lett. 105, (2010).

D. Poilblanc, N. Schuch, D. P´erez-Garc´ıa, and J. I. Cirac, Phys. Rev. B 86, (2012).

J. I. Cirac, D. Poilblanc, N. Schuch, and F. Verstraete, Phys. Rev. B 83, (2011).

S. Bravyi, M. Hastings, and S. Michalakis, J. Math. Phys. 51, (2010).

J. T. Chayes, L. Chayes, and S. A. Kivelson, Commun. Math. Phys. 123, 53 (1989).

J. Wildeboer and A. Seidel, Phys. Rev. B 83, (2011).

L. Campos Venuti and P. Zanardi, Phys. Rev. Lett. 99, (2007).

Deposited On:18 Oct 2012 11:23
Last Modified:18 Oct 2012 11:23

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