Entanglement of Purification in Many Body Systems and Symmetry Breaking

Abstract

We study the entanglement of purification (EoP), a measure of total correlation between two subsystems $A$ and $B$, for free scalar field theory on a lattice and the transverse-field Ising model by numerical methods. In both of these models, we find that the EoP becomes a non-monotonic function of the distance between $A$ and $B$ when the total number of lattice sites is small. When it is large, the EoP becomes monotonic and shows a plateau-like behavior. Moreover, we show that the original reflection symmetry which exchanges $A$ and $B$ can get broken in optimally purified systems. In the Ising model, we find this symmetry breaking in the ferromagnetic phase. We provide an interpretation of our results in terms of the interplay between classical and quantum correlations.

12 pages, 18 figures

References in corpus (4)

• Strong and weak thermalization of infinite non-integrable quantum systems
• Uncertainty, Monogamy, and Locking of Quantum Correlations
• Holographic Entanglement of Purification from Conformal Field Theories
• Non-Additivity of the Entanglement of Purification (Beyond Reasonable Doubt)

Cited by in corpus (3)

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• Evolution of Entanglement Wedge Cross Section Following a Global Quench
• Quantum Information Approaches to Quantum Gravity