Hannover 2013 – wissenschaftliches Programm

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Q: Fachverband Quantenoptik und Photonik

Q 67: Quantum information: Concepts and methods V

Q 67.7: Vortrag

Freitag, 22. März 2013, 15:30–15:45, E 214

Improved contraction schemes for Projected Entangled Pair States — •Michael Lubasch, Juan Ignacio Cirac, and Mari-Carmen Bañuls — Max Planck Institute of Quantum Optics, Hans-Kopfermann-Strasse 1, 85748 Garching, Germany

Projected Entangled Pair States (PEPS) represent the natural generalization of Matrix Product States (MPS) in higher dimensions. The strength of MPS in the numerical simulation of 1D quantum many-body systems is well established, as they are the variational class of states underlying the Density Matrix Renormalization Group and the latter is nowadays considered numerically exact for systems comprising hundreds of quantum particles. In algorithms based on MPS or PEPS, the bond dimension D of the state determines the number of variational parameters and the computational cost. While bond dimensions on the order of hundreds and thousands are feasible with MPS, standard 2D PEPS algorithms are limited to values in the range 2 to 6 due to the much worse scaling of the computational cost with D. Recently, a new algorithm based on an alternative contraction has been proposed [1] that reduces this cost significantly. It resorts to the single-layer picture where the contraction is done in ket and bra separately. We investigate the advantages and disadvantages of this algorithm which can be understood in terms of the PEPS’s boundary approximation [2].

[1] I. Pižorn, L. Wang, and F. Verstraete, Phys. Rev. A 83, 052321 (2011).

[2] J. I. Cirac, D. Poilblanc, N. Schuch, and F. Verstraete, Phys. Rev. B 83, 245134 (2011).