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.

arXiv comment21 pages, 7 figures

References in corpus (19)

• Gauge Theory Correlators from Non-Critical String Theory
• The Large N Limit of Superconformal Field Theories and Supergravity
• Unpaired Majorana fermions in quantum wires
• Gapless Spin-Fluid Ground State in a Random Quantum Heisenberg Magnet
• Comments on the Sachdev-Ye-Kitaev model
• Calculation of reduced density matrices from correlation functions
• Notes on Some Entanglement Properties of Quantum Field Theory
• Bekenstein-Hawking Entropy and Strange Metals
• Local criticality, diffusion and chaos in generalized Sachdev-Ye-Kitaev models
• An Algebra of Observables for de Sitter Space
• Gravity and the Crossed Product
• Large N algebras and generalized entropy
• Notes on the type classification of von Neumann algebras
• Towards Explicit Discrete Holography: Aperiodic Spin Chains from Hyperbolic Tilings
• Aperiodic quantum XXZ chains: Renormalization-group results
• Central charges of aperiodic holographic tensor network models
• Entanglement entropy in aperiodic singlet phases
• Aperiodic spin chains at the boundary of hyperbolic tilings
• Boundary theories of critical matchgate tensor networks

Cited by in corpus (2)

• Wormhole-induced effective coupling in SYK chains
• Hawking-Page transition on a spin chain