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Thermal nature of confining strings

Sebastian Grieninger1,2,3,4,*, Dmitri E. Kharzeev3,4,5,†, and Eliana Marroquin3,4,‡

  • *Contact author: segrie@uw.edu
  • †Contact author: dmitri.kharzeev@stonybrook.edu
  • ‡Contact author: eliana.marroquin@stonybrook.edu
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Phys. Rev. D 113, 036013 – Published 13 February, 2026

DOI: https://doi.org/10.1103/v8mv-185x

Abstract

We investigate the quantum statistical properties of the confining string connecting a static fermion-antifermion pair in the massive Schwinger model. By analyzing the reduced density matrix of the subsystem located in between the fermion and antifermion, we demonstrate that as the interfermion separation approaches the string-breaking distance, the overlap between the microscopic density matrix and an effective thermal density matrix exhibits a pronounced, narrow peak, approaching unity at the onset of string breaking. This behavior reveals that the confining flux tube evolves toward a genuinely thermal state as the separation between the charges grows, even in the absence of an external heat bath. In other words, one cannot tell whether a reduced state of the subsystem arises from a surrounding heat bath or from entanglement with the rest of the system. The entanglement spectrum near the critical string-breaking distance exhibits a rapid transition from the dominance of a single state describing the confining electric string towards a strongly entangled state containing virtual fermion-antifermion pairs. Our findings establish a quantitative link between confinement, entanglement, and emergent thermality, and suggest that string breaking corresponds to a microscopic thermalization transition within the flux tube.

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Phys. Rev. D 113, 036013– Published 13 February, 2026
  • Received 3 November 2025
  • Accepted 12 January 2026
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP3.

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