Entanglement in interacting Majorana chains and transitions of von Neumann algebras

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.

21 pages, 7 figures

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Cited by in corpus (2)

• Wormhole-induced effective coupling in SYK chains
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