Dresden 2009 – scientific programme

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TT: Fachverband Tiefe Temperaturen

TT 20: Correlated Electrons: (General) Theory 1

TT 20.4: Talk

Tuesday, March 24, 2009, 16:15–16:30, HSZ 301

Simulating strongly correlated fermions with unitary networks — •Carlos Pineda and Jens Eisert — University of Potsdam, 14476 Potsdam, Germany

One of the central challenges in the numerical study of quantum many-body systems is to efficiently identify ground state properties of strongly correlated two- and higher-dimensional quantum systems. Recently, it has become clear that efficiently contractable tensor networks offer new perspectives for such simulations: In one dimension, the density-matrix renormalization group method and entanglement renormalization can both be grasped as such networks, with natural higher-dimensional analogues [1,2,3,4]. In this work, we introduce a framework of unitary tensor networks for fermions, which is not overburdened by encountering non-local string operators in the spin representation. In fact, there is only a constant overhead in the effort to compute local expectation values. We present a formalism of dynamical relabeling of fermions and dicuss first results on this framework.

[1] G. Vidal, Phys. Rev. Lett. 99, 220405 (2007).

[2] C.M. Dawson, J. Eisert, T.J. Osborne, Phys. Rev. Lett. 100, 130501 (2008).

[3] M.-C. Banuls, D.P.-García, M.M. Wolf, F. Verstraete, J.I. Cirac, Phys. Rev. A 77, 052306 (2008).

[4] U. Schollwoeck, Rev. Mod. Phys. 77, 259 (2005).