Two-fermion negativity and confinement in the Schwinger model

Journal Article · 08 April 2024 · Physical Review. D.

DOI: https://doi.org/10.1103/physrevd.109.l071501 · OSTI ID:2335522

Florio, Adrien  ^[1]

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1. Brookhaven National Laboratory (BNL), Upton, NY (United States)

We consider the fermionic (logarithmic) negativity between two fermionic modes in the Schwinger model. Recent results pointed out that fermionic systems can exhibit stronger entanglement than bosonic systems, exhibiting a negativity that decays only algebraically. The Schwinger model is described by fermionic excitations at short distances, while its asymptotic spectrum is the one of a bosonic theory. We show that the two-mode negativity detects this confining, fermion-to-boson transition, shifting from an algebraic decay to an exponential decay at distances of the order of the de Broglie wavelength of the first excited state. We derive analytical expressions in the massless Schwinger model and confront them with tensor network simulations. We also perform tensor network simulations in the massive model, which is not solvable analytically, and close to the Ising quantum critical point of the Schwinger model, where we show that the negativity behaves as its bosonic counterpart.

• Research Organization: Brookhaven National Laboratory (BNL), Upton, NY (United States); National Quantum Information Science (QIS) Research Centers (United States). Co-design Center for Quantum Advantage (C2QA)
• Sponsoring Organization: USDOE Office of Science (SC), Nuclear Physics (NP); USDOE
• Grant/Contract Number: SC0012704
• OSTI ID: 2335522
• Alternate ID(s): OSTI ID: 2406881
• Report Number(s): BNL-225847-2024-JAAM; TRN: US2501369
• Journal Information: Physical Review. D., Vol. 109, Issue 7; ISSN 2470-0010
• Publisher: American Physical Society (APS)Copyright Statement
• Country of Publication: United States
• Language: English