Regensburg 2013 – scientific programme

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DF: Fachverband Dielektrische Festkörper

DF 12: Poster 1

DF 12.16: Poster

Tuesday, March 12, 2013, 10:30–13:30, Poster D

The Strong Disorder Renormalisation Group and Tensor Network Methods — •Andrew Goldsborough and Rudolf Römer — Department of Physics and Centre for Scientific Computing, The University of Warwick, Coventry, United Kingdom

We have developed a tensor network method of performing the numerical strong disorder renormalisation group (SDRG) approach [1] on the random 1D spin-1/2 Heisenberg model. We use matrix product operators (MPOs) as a means of describing the Hamiltonian. The coarse-graining is achieved by concentrating on the interaction with the largest energy gap and calculating the lowest eigenvectors of the two-site hamiltonian. This unitary operator can then be contracted with the two-site MPO to create a new one site MPO. The idea can be interpreted as a multi-level coarse-graining of the Hamiltonian or as a multi-level tensor network state with the form of a binary tree tensor network (TTN). This realisation enables us to use the methods of TTNs and MERAs (multi-scale entanglement renormalisation ansatz) to gain more control over the system. We will show first results and compare the performance all methods.

[1] T. Hikihara, A. Furusaki, and M. Sigrist, Phys. Rev. B 60,12116 (1999)