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TT: Fachverband Tiefe Temperaturen

TT 80: Low-Dimensional Systems - Poster Session

TT 80.21: Poster

Mittwoch, 2. April 2014, 15:00–19:00, P2

Leaf-to-leaf distances and their moments in finite and infinite m-ary acyclic graphs — •Andrew M. Goldsborough, S. Alex Rautu, and Rudolf A. Römer — University of Warwick, Coventry, UK

It has recently been shown [1] that two-point correlation functions in tensor network wavefunctions are related to the length of the path through the network that connects the two lattice sites. In reference to a binary tree tensor network (TTN) [2], we analyse the geometry of a complete regular binary tree where the leaves represent the points on a 1-D lattice. We find an analytic expression for the average path length for a given separation in a tree with n levels. This expression is then generalised to give any raw statistical moment for m-ary trees with open and periodic boundary conditions. We also present first results for random binary trees.
G. Evenbly and G. Vidal, J. Stat. Phys. 145, 891 (2011)
Y. Shi, L. Duan, and G. Vidal, Phys. Rev. A 74, 022320 (2006)