Thermal nature of confining strings

TL;DR

This paper shows that the confining flux tube in the massive Schwinger model behaves like a thermal state as the fermion-antifermion separation approaches the string-breaking distance, linking confinement, entanglement, and emergent thermality.

Contribution

It demonstrates that the flux tube evolves into a genuinely thermal state during string breaking, revealing a microscopic thermalization process in a confining gauge theory without an external heat bath.

Findings

Overlap with thermal density matrix peaks near string breaking

Entanglement spectrum shifts from single state to highly entangled state

Flux tube exhibits thermal characteristics as separation increases

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.