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arXiv:2603.10255

Topological structure of the entanglement radius of Yang-Mills flux tubes

Rocco Amorosso, Sergey N. Syritsyn, Raju Venugopalan B

Published Mar 10, 2026• 0 citations
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Abstract

We expand on recent work arXiv:2601.17199 demonstrating the existence of a novel entanglement radius $ξ_0$ characterizing flux tube entanglement entropy (FTE$^2$) in (2+1)D Yang-Mills theory. This physical scale corresponds to the intrinsic thickness of the flux tube that must be fully severed by an entangling region for color degrees of freedom in the flux tube to contribute non-zero FTE$^2$. We consider here geometries of the entanglement region $V$ on the lattice where the length of the region cross-cutting the flux tube is of the same magnitude as $ξ_0$. Our results further the conclusions of arXiv:2601.17199 by adding detailed new information on the topological structure of the entanglement radius of color flux tubes.

DOI
10.48550/arxiv.2603.10255

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We expand on recent work arXiv:2601.17199 demonstrating the existence of a novel entanglement radius ξ0ξ_0ξ0​ characterizing flux tube entanglement entropy (FTE2^22) in (2+1)D Yang-Mills theory. This physical scale corresponds to the intrinsic thickness of the flux tube that must be fully severed by an entangling region for color degrees of freedom in the flux tube to contribute non-zero FTE2^22. We consider here geometries of the entanglement region VVV on the lattice where the length of the region cross-cutting the flux tube is of the same magnitude as ξ0ξ_0ξ0​. Our results further the conclusions of arXiv:2601.17199 by adding detailed new information on the topological structure of the entanglement radius of color flux tubes.
We expand on recent work [1] demonstrating the existence of a novel entanglement radius ξ0\xi_0ξ0​ characterizing flux tube entanglement entropy (FTE2^22) in (2+1)D Yang-Mills theory. This physical scale corresponds to the intrinsic thickness of the flux tube that must be fully severed by an entangling region for color degrees of freedom in the flux tube to contribute non-zero FTE2^22. We consider here geometries of the entanglement region VVV on the lattice where the length of the region cross-cutting the flux tube is of the same magnitude as ξ0\xi_0ξ0​. Our results further the conclusions of [1] by adding detailed new information on the topological structure of the entanglement radius of color flux tubes.
In recent work Amorosso et al. (2024), we computed a novel flux tube entanglement entropy (FTE) of the color flux tube stretched between a heavy quark-antiquark pair on a Euclidean lattice in (2+1)D Yang–Mills theory. Our numerical results suggested that FTE can be partitioned into an internal color entanglement entropy and a vibrational entropy corresponding to the transverse excitations of a QCD string, with the latter described by a thin string model. Since the color flux tube does not have transverse excitations in (1+1)D Yang–Mills theory, we use this simpler framework to perform an exact analytical computation of the contribution of the internal color degrees of freedom to FTE. For the multipartite partitioning of the color flux tube, we find the remarkable result that FTE depends only on the dimension of the color group representation and the number of times the flux tube crosses the boundary between the traced and untraced spatial regions but not on the string length. Our proof is independent of whether the replica and region boundaries on the lattice are placed on vertices or in plaquette centers.
Recent lattice QCD studies have revealed an excess entanglement entropy (flux tube entanglement entropy, FTE 2 ) in the color flux tube between static quark–antiquark pairs, which grows linearly with the quark separation. In this paper, we illustrate a possible analogy in a simplified string-net model based on the Fibonacci fusion category, where the non-trivial object [Formula: see text] (analogous to color charge) cannot exist in isolation due to the fusion rule [Formula: see text], naturally exhibiting “confinement”. We compute the entanglement entropy of the flux tube connecting two [Formula: see text] objects and find an entropy density of [Formula: see text] ([Formula: see text] is the golden ratio), which quantitatively agrees with the lattice QCD measured FTE 2 density (approximately 0.3–0.5). Minimizing the free energy [Formula: see text] at fixed temperature and volume, the competition between the energy term [Formula: see text] and the entropy term [Formula: see text] yields a confinement-deconfinement phase transition at critical temperature [Formula: see text]. This model provides a heuristic demonstration platform as a minimal model for understanding the entropic properties of the QCD flux tube.
We calculate the entanglement entropy using a SU(3) quenched lattice gauge simulation. We find that the entanglement entropy scales as 1/l21/l^21/l2 at small lll as in the conformal field theory. Here lll is the size of the system, whose degrees of freedom is left after the other part are traced out. The derivative of the entanglement entropy with respect to lll hits zero at about l∗=0.6∼0.7l^{\ast} = 0.6 \sim 0.7l∗=0.6∼0.7 [fm] and vanishes above the length. It may imply that the Yang-Mills theory has the mass gap of the order of 1/l∗1/l^{\ast}1/l∗. Within our statistical errors, no discontinuous change can be seen in the entanglement entropy. We discuss also a subtle point appearing in gauge systems when we divide a system with cuts.
Recent lattice studies have revealed that the color flux tube between static quark-antiquark pairs exhibits an excess entanglement entropy (flux tube entanglement entropy, FTE2) that scales linearly with the quark separation L. In this paper, we demonstrate similar behavior in a string-net model based on SU(2)k fusion categories, where the nontrivial object j=1/2 (analogous to color charge) cannot exist in isolation due to the fusion rules, naturally exhibiting “confinement”. We compute the entanglement entropy of the flux tube connecting two j=1/2objects using the topological definition S(R)=ln⁡(dim⁡(Hom(R))) and find an entropy density σk=ln⁡ d1/2=ln⁡(2cos⁡(π/(k+2))). For k=3, the category reduces to the Fibonacci case, yielding an entropy density σ3 = ln φ ≈ 0.481 (φ is the golden ratio), which is qualitatively comparable in magnitude to the scale inferred from lattice studies and the entropy-surface mechanism. Minimizing the free energy F=E-TS yields a confinement–deconfinement transition at Tc=J/σk.The parameter k offers a tunable knob, making the SU(2)k family a computable laboratory for entropic confinement. The predicted entropy-density jump and critical scaling can be directly tested in quantum simulator platforms (e.g., Rydberg arrays or superconducting circuits) that realize Fibonacci anyonic models.
Recent lattice studies have revealed that the color flux tube between static quark–antiquark pairs exhibits an excess entanglement entropy (flux-tube entanglement entropy, FTE2) that scales linearly with the quark separation L. In this paper, we demonstrate similar behavior in a string-net model based on SU(2)k fusion categories, where the nontrivial object j=1/2 (analogous to color charge) cannot exist in isolation due to the fusion rules, naturally exhibiting “confinement”. We compute the entanglement entropy of the flux tube connecting two j=1/2 objects using the microcanonical (equal-weight) prescription S(R)=ln(dim(Hom(R))) and find an entropy density σk=lnd1/2=ln(2cosπk+2). For k=3, the category reduces to the Fibonacci case, yielding an entropy density σ3 = ln φ ≈ 0.4812 (φ is the golden ratio), which is qualitatively comparable in magnitude to the scale inferred from lattice studies and the entropy surface mechanism. Under a thermalization assumption for the fusion-channel degrees of freedom, minimizing the free energy F=(J−Tσk)L yields a confinement–deconfinement transition at (Tc=J/σk), which is first-order-like (tension sign reversal) rather than a continuous critical transition. The parameter k offers a tunable knob, making the SU(2)k family a computable laboratory for entropic confinement. The predicted entropy-density jump can be directly tested in quantum simulator platforms (e.g., Rydberg arrays or superconducting circuits) that realize Fibonacci anyonic models.