Observer-Linked Entropy

Siddharth Dwivedi, Vivek Kumar Singh, Abhishek Roy

Abstract We study the multi-boundary entanglement structure of the state associated with the torus link complement S3\Tp,q in the set-up of three-dimensional SU(2)k Chern-Simons theory. The focal point of this work is the asymptotic behavior of the Rényi entropies, including the entanglement entropy, in the semiclassical limit of k → ∞. We present a detailed analysis of several torus links and observe that the entropies converge to a finite value in the semiclassical limit. We further propose that the large k limiting value of the Rényi entropy of torus links of type Tp,pn is the sum of two parts: (i) the universal part which is independent of n, and (ii) the non-universal or the linking part which explicitly depends on the linking number n. Using the analytic techniques, we show that the universal part comprises of Riemann zeta functions and can be written in terms of the partition functions of two-dimensional topological Yang-Mills theory. More precisely, it is equal to the Rényi entropy of certain states prepared in topological 2d Yang-Mills theory with SU(2) gauge group. Further, the universal parts appearing in the large k limits of the entanglement entropy and the minimum Rényi entropy for torus links Tp,pn can be interpreted in terms of the volume of the moduli space of flat connections on certain Riemann surfaces. We also analyze the Rényi entropies of Tp,pn link in the double scaling limit of k → ∞ and n → ∞ and propose that the entropies converge in the double limit as well.

Koichi Takahashi, Masatoshi Iwamoto

Stanley Gudder

Yifan 祎帆 Luo 罗, Zheng Tang, Li Chen +1 more

Abstract Quantum link models (QLMs) serve as experimentally accessible platforms for studying lattice gauge theories with finite-dimensional Hilbert spaces. In this work, we investigate information scrambling in the partially confined phase of a spin-1 quantum link model by calculating the dynamics of out-of-time-ordered correlators (OTOCs) and entanglement entropy. We observe that, in the partially confined phase, information scrambling exhibits significant asymmetry, manifested as the unidirectional propagation of both OTOCs and entanglement entropy. This phenomenon stands in stark contrast to the isotropic spreading observed in the deconfined phase and the localization characteristic of the confined phase. Furthermore, the simultaneous occurrence of the unidirectional propagation of both OTOCs and entanglement entropy, together with the θ -induced asymmetric excitation propagation, reveals a direct connection between information scrambling and charge confinement.

P. Castorina, Alfredo Iorio, Daniele Lanteri +1 more

Relying on previous results, that link entanglement entropy and parton distribution functions in deep inelastic scattering, and focusing on the small Bjorken scaling region we present here indications that gluon shadowing might indeed be explained as due to a depletion of the entanglement entropy, between observed and unobserved degrees of freedom, per nucleon within a nucleus, with respect to the free nucleon. We apply to gluon shadowing the general Page approach to the calculation of the entanglement entropy in bipartite systems, giving physical motivations of the results.

Dominik Janzing