Dresden 2014 – scientific programme

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TT: Fachverband Tiefe Temperaturen

TT 4: Low-Dimensional Systems: 1D - Theory

TT 4.8: Talk

Monday, March 31, 2014, 11:30–11:45, HSZ 201

Self-assembling tensor networks and holography in disordered spin chains — •Andrew M. Goldsborough and Rudolf A. Römer — University of Warwick, Coventry, UK

We show that the numerical strong disorder renormalization group algorithm (SDRG) of Hikihara et al. for the disordered Heisenberg model [1] naturally describes a tree tensor network (TTN) with an irregular structure defined by the strength of the couplings. Using developments from TTNs [2] and the multi-scale entanglement renormalization ansatz (MERA) [3] we can efficiently calculate expectation values and entanglement entropy directly from the tensor network wavefunction. We also analyse the effect of the disordered geometry of the TTN on the two-point correlation functions and entanglement entropy. We show that disorder averaged correlation scales with the average path length through the tensor network, as suggested by Evenbly and Vidal [4] in the context of regular tensor network geometries and that entanglement entropy increases with both disorder and length, resulting in an area-law violation consistent with the results of [5].
T. Hikihara, A. Furusaki, M. Sigrist, Phys. Rev. B 60, 12116 (1999)
L. Tagliacozzo, G. Evenbly, G. Vidal, Phys. Rev. B 80, 235127 (2009)
G. Evenbly and G. Vidal, Phys. Rev. B 79, 144108 (2009)
G. Evenbly and G. Vidal, J. Stat. Phys. 145, 891 (2011)
G. Refael and J. E. Moore, Phys. Rev. B 76, 024419 (2007)