Entanglement in interacting Majorana chains and transitions of von Neumann algebras

• URL: http://arxiv.org/abs/2401.04764v1
• Date: Tue, 9 Jan 2024 19:00:01 GMT
• Title: Entanglement in interacting Majorana chains and transitions of von Neumann algebras
• Authors: Pablo Basteiro, Giuseppe Di Giulio, Johanna Erdmenger, Zhuo-Yu Xian
• Abstract summary: We consider Majorana lattices with two-site interactions consisting of a general function of the fermion bilinear. The models are exactly solvable in the limit of a large number of on-site fermions.
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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We consider Majorana lattices with two-site interactions consisting of a general function of the fermion bilinear. The models are exactly solvable in the limit of a large number of on-site fermions. The four-site chain exhibits a quantum phase transition controlled by the hopping parameters and manifests itself in a discontinuous entanglement entropy, obtained by constraining the one-sided modular Hamiltonian. Inspired by recent work within the AdS/CFT correspondence, we identify transitions between types of von Neumann operator algebras throughout the phase diagram. We find transitions of the form II$_1\leftrightarrow\,$III$\,\,\leftrightarrow\,\,$I$_\infty$ that reduce to II$_1\leftrightarrow\,\,$I$_\infty$ in the strongly interacting limit, where they connect non-factorized and factorized ground states. Our results provide novel realizations of such transitions in a controlled many-body model.

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