Entanglement entropy in integrable quantum systems

In this thesis I present the results I have been developing during my PhD studies at City University London. The original results are based on D Bianchini et al, D Bianchini, O Castro-Alvaredo and B Doyon, D Bianchini and F Ravanini, D Bianchini et al and D Bianchini and O Castro-Alvaredo. In all but one publications, we compute the entanglement of various systems. Using the celebrated “replica trick” we compute the entanglement entropy of non unitary systems using integrable tools in continuum and discrete models. In particular, in the first article we generalise the method described in the seventh article in order to take into account non unitary conformal systems. In the second article we use a form factor expansion to probe a non unitary system outside the critical point. In the fourth article we derive the explicit expressions of one dimensional quantum Hamiltonians which provide a lattice realisation of off critical non unitary minimal models. Using a Corner Transfer Matrix approach we compute the scaling of the entanglement of such spin chains. In the fifth article we study the scaling of various twist field correlation functions in order to compute the entanglement entropy and the logarithmic negativity in free boson massive theories.

Name dc:type.qualificationname

phd

Level dc:type.qualificationlevel

doctoral

Grantor dc:publisher.institution

City, University of London

Year dc:date.issued

2016

Author dc:creator

• Bianchini, D.

• QA Mathematics