Tensor Networks are emerging as a new tool to analyze and possibly solve old standing problems in theoretical physics due to i) their ability to address both the strong and the weak coupling regime of many body systems, ii) their ability to deal with antiferromagnets, fermions and anyons.

At Strathclyde we are interested in both applying and developing new Tensor Networks methods,

Among the results we have obtained in this field there are

  • The discovery of finite entanglement scaling, where the approach to criticality is controlled by the amount of entanglement the tensor network is able to describe

  • The extension of exact diagonalization techniques for 2D systems based on exploiting the area law for the entanglement entropy.

  • The recipe to encode exactly local symmetries in Renormalization Group inspired tensor networks

  • New optimization methods for both Matrix Product States and Tree Tensor Networks.

  • Techniques for extracting the entropies from Tensor Networks states.

Online talks about our results

Trieste talk at the joint ICTP/SISSA Statistical Physics Seminar about Tensor Networks for 1D quantum phase transitions, Winter-2013.
Benasque talk about local quenches with Tensor Networks

Relevant Publications

Collaborators

Marie Carmen Banuls, Philippe Corboz, Glen Evenbly, Sofyan Iblisdir, Thomas Koffel, Maciej Lewenstein, Ian McCulloch, Bogdan Pirvu, German Sierra, Erik Tonni, Frank Verstraete, Guifre Vidal