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MP: Fachverband Theoretische und Mathematische Grundlagen der Physik

MP 10: AdS/CFT

MP 10.7: Talk

Thursday, March 21, 2024, 12:00–12:20, HL 001

Entanglement in interacting Majorana chains and transitions of von Neumann algebras — •Pablo Basteiro, Giuseppe Di Giulio, Johanna Erdmenger, and Zhuo-Yu Xian — Institute for Theoretical Physics and Astrophysics and Würzburg-Dresden Excellence Cluster ct.qmat, Julius Maximilians University Würzburg, Am Hubland, 97074 Würzburg, Germany

We consider Majorana lattices with two-site interactions in the form of a general function of the fermion bilinear. The model is exactly solvable in the limit of large number N of on-site fermions. For four-site chains, we detect a first order quantum phase transition by tuning the relative hopping strength between sites, which manifests itself in a discontinuous entanglement entropy. Inspired by recent analyses of the AdS/CFT correspondence, we identify type I_∞, type II₁, and type III operator algebras in various limits of the phase diagram. In the strongly interacting limit, we find that an abrupt change between type II₁ and I_∞ algebras occurs at the phase transition point.

Keywords: Interacting models; Entanglement; von Neumann algebras; phase transition; AdS/CFT