Mutual information on the fuzzy sphere

Holographic theories with classical gravity duals are maximally chaotic: they saturate a set of bounds on the spread of quantum information. In this paper we question whether non-locality can affect such bounds. Specifically, we consider the gravity dual of a prototypical theory with non-local interactions, namely, N " 4 non-commutative super Yang Mills. We construct shock waves geometries that correspond to perturbations of the thermofield double state with definite momentum and study several chaos related properties of the theory, including the butterfly velocity, the entanglement velocity, the scrambling time and the maximal Lyapunov exponent. The latter two are unaffected by the non-commutative parameter θ, however, both the butterfly and entanglement velocities increase with the strength of the noncommutativity. This implies that non-local interactions can enhance the effective light-cone for the transfer of quantum information, eluding previously conjectured bounds encountered in the context of local quantum field theory. We comment on a possible limitation on the retrieval of quantum information imposed by non-locality. arXiv:1808.10050v3 [hep-th] 15 Nov 2018 6 Conclusions and outlook 34 A Momentum space correlator and the butterfly velocity 36 B Shock wave parameter α as a function of r 0 38 C Divergence of K 3 pr 0 q 39 -1 -

Section: )supporting

confidence: 72%

Chaos and entanglement spreading in a non-commutative gauge theory

Fischler

Jahnke

Pedraza

2018

“…Leading order entanglement entropy of a spherical cap region on a commutative sphere is proportional to n sin θ, where n is a discretization parameter such that the total number of degrees of freedom is proportional to n 2 [10]. We can think of the discretized commu- tative sphere as a noncommutative sphere with N taken to infinity while n is held fixed.…”

Section: Entanglement Entropymentioning

confidence: 99%

“…Another quantity that behaves in an interesting way in strongly coupled theories [7] is mutual information. Mutual information is a useful quantity to study because it is UV finite andperhaps because of that-is the same on the fuzzy sphere as it is on the ordinary sphere [10]. Given this, we compute mutual information to validate our choice of method for the assignment of degrees of freedom.…”

Section: Mutual Informationmentioning

confidence: 99%

“…Following our notation for entanglement entropy, we denote mutual information on a commutative sphere with I(∞, n; θ). In [10] it was shown that I(n, n; θ) is independent of n and that I(n, n; θ) = I(∞, n; θ). Given this, we would expect that I(N, n; θ) would be independent of n over the entire range of N ∈ [n, ∞).…”

Section: Mutual Informationmentioning

confidence: 99%

“…Vacuum entanglement entropy in noncommutative field theories has been studied both holographically [4,5,6,7] and directly [8,9,10,11,12,13,14]. Holographically, for regions whose size is below a certain critical length scale L trans , the entanglement entropy grows with the volume of the region, while the area law is restored for regions whose dimensions are larger than the critical length scale L trans .…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Entanglement entropy on a fuzzy sphere with a UV cutoff

Chen

Karczmarek

2018

We introduce a UV cutoff into free scalar field theory on the noncommutative (fuzzy) two-sphere. Due to the IR-UV connection, varying the UV cutoff allows us to control the effective nonlocality scale of the theory. In the resulting fuzzy geometry, we establish which degrees of freedom lie within a specific geometric subregion and compute the associated vacuum entanglement entropy. Entanglement entropy for regions smaller than the effective nonlocality scale is extensive, while entanglement entropy for regions larger than the effective nonlocality scale follows the area law. This reproduces features previously obtained in the strong coupling regime through holography. We also show that mutual information is unaffected by the UV cutoff.

Renormalized entanglement entropy on cylinder

Banerjee

Nakaguchi

Nishioka

2016

Abstract:We develop a framework of calculating entanglement entropy for non-conformal field theories with the use of the dilaton effective action. To illustrate it, we locate a theory on a cylinder R × S 2 and compute entanglement entropy of a cap-like region perturbatively with respect to the mass for a free massive scalar field. A renormalized entanglement entropy (REE) is proposed to regularize the ultraviolet divergence on the cylinder. We find that the REE decreases monotonically both in the small and large mass regions as the mass increases. We confirm all of these behaviors by the numerical calculations, which further shows the monotonic decrease of the REE in the entire renormalization group flow.