Numerical tests of CFT conjectures for 3D spin systems

Martin Weigel

Rong-Xin Miao

There appears a universal logarithmic term of entanglement entropy, i.e., −a(Ω)log(H/δ), for 3d CFTs when the entangling surface has a sharp corner. a(Ω) is a function of the corner opening angle and behaves as a(Ω → π) ≃ σ(π − Ω)2 and a(Ω → 0) ≃ κ/Ω, respectively. Recently, it is conjectured that σ/C T = π 2 /24, where C T is central charge in the stress tensor correlator, is universal for general CFTs in three dimensions. In this paper, by applying the general higher curvature gravity, we give a holographic proof of this conjecture. We also clarify some interesting problems. Firstly, we find that, in contrast to σ/C T , κ/C T is not universal. Secondly, the lower bound a E (Ω)/C T associated to Einstein gravity can be violated by higher curvature gravity. Last but not least, we find that there are similar universal laws for CFTs in higher dimensions. We give some holographic tests of these new conjectures.

Makoto Kaburagi, Takashi Tonegawa, T. Nishino

Y. Miyatake, Yuuzi Yamada, K. Nishino +2 more

Cristian Voinea, Ruihua Fan, Nicolas Regnault +1 more

The recently introduced “fuzzy-sphere” method has enabled accurate numerical regularizations of certain three-dimensional (3D) conformal field theories (CFTs). The regularization is provided by the noncommutative geometry of the lowest Landau level filled by electrons, such that the charge is trivially gapped due to the Pauli exclusion principle at filling factor ν = 1 , while the electron spins encode the desired CFT. Successful applications of the fuzzy sphere to paradigmatic CFTs, such as the 3D Ising model, raise an important question: How finely tuned does the underlying electron system need to be? Here, we show that the 3D Ising CFT can also be realized at electron fillings. In such cases, the CFT spectrum is intertwined with the charge-neutral spectrum of the underlying fractional quantum Hall state—a feature that is trivially absent in the previously studied ν = 1 case. Remarkably, we show that the mixing between the CFT spectrum and the fractional quantum Hall spectrum is strongly suppressed within the numerically accessible system sizes. Moreover, we demonstrate that the CFT critical point is unaffected by the exchange statistics of the particles and by the nature of topological order in the charge sector. Our results set the stage for the fuzzy-sphere exploration of conformal critical points between topologically ordered states.

Eric S. Swanson