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

• Entanglement negativity in the critical Ising chain , Calabrese,
  Pasquale, Tagliacozzo, Luca, and Tonni, Erik, arXiv , Vol. Pag.
  arXiv:1302.1113, (2/2013), 2013arXiv1302.1113C,

• Koffel, Thomas, Lewenstein, M., & Tagliacozzo, Luca 2012, ArXiv e-prints
  Entanglement entropy for the long range Ising chain

• Tagliacozzo, L., Celi, A., Zamora, A., & Lewenstein, M. 2012, ArXiv
  e-prints Optical Abelian Lattice Gauge Theories

• Pirvu, B., Vidal, G., Verstraete, F., & Tagliacozzo, L. 2012, ArXiv
  e-prints Matrix product states for critical spin chains: finite size
  scaling versus finite entanglement scaling

• Sowiński, Tomasz, Dutta, Omjyoti, Hauke, Philipp, Tagliacozzo, Luca, &
  Lewenstein, Maciej 2012, Physical Review Letters Dipolar Molecules in
  Optical Lattices

• Alba, Vincenzo, Tagliacozzo, Luca, & Calabrese, Pasquale 2011, Journal of
  Statistical Mechanics: Theory and Experiment Entanglement entropy of two
  disjoint intervals in c = 1 theories

• Tagliacozzo, L. & Vidal, G. 2011, Physical Review B Entanglement
  renormalization and gauge symmetry

• Evenbly, G., Pfeifer, R. N. C., Picó, V., Iblisdir, S., Tagliacozzo, L.,
  McCulloch, I. P., & Vidal, G. 2010, Physical Review B Boundary quantum
  critical phenomena with entanglement renormalization

• Alba, Vincenzo, Tagliacozzo, Luca, & Calabrese, Pasquale 2010, Physical
  Review B Entanglement entropy of two disjoint blocks in critical Ising
  models

• Gliozzi, Ferdinando & Tagliacozzo, Luca 2010, Journal of Statistical
  Mechanics: Theory and Experiment Entanglement entropy and the complex
  plane of replicas

• Tagliacozzo, L., Evenbly, G., & Vidal, G. 2009, Physical Review B
  Simulation of two-dimensional quantum systems using a tree tensor network
  that exploits the entropic area law

• Tagliacozzo, L., de Oliveira, Thiago. R., Iblisdir, S., & Latorre, J. I.
  2008, Physical Review B Scaling of entanglement support for matrix
  product states

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