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
- 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
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
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
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