Entropic Confinement in String-Net Models: An Analogue Study via SU(2)ₖ Fusion Categories

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 σ_k=ln⁡ d_1/2=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 T_c=J/σ_k.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.