Interface entropy in four dimensions as Calabi's diastasis on the conformal manifold

We conjecture an equality between (1) the entropy associated with a Janus interface in a 4d N=2 superconformal field theory and (2) Calabi's diastasis, a particular combination of analytically continued Kahler potentials, on the conformal manifold (moduli space) of the 4d theory.Comment: 4 pages; v.2: reference and minor clarification added, version in JHE

CFT descriptions of bulk local states in the AdS black holes

We present a new method for reconstructing CFT duals of states excited by the bulk local operators in the three dimensional AdS black holes in the AdS/CFT context. As an important procedure for this, we introduce a map between the bulk points in AdS and those on the boundary where CFT lives. This gives a systematic and universal way to express bulk local states even inside black hole interiors. Our construction allows us to probe the interior structures of black holes purely from the CFT calculations. We analyze bulk local states in the single-sided black holes as well as the double-sided black holes.Comment: 38pages, Late

Causal Evolutions of Bulk Local Excitations from CFT

Bulk localized excited states in an AdS spacetime can be constructed from Ishibashi states with respect to the global conformal symmetry in the dual CFT. We study boundary two point functions of primary operators in the presence of bulk localized excitations in two dimensional CFTs. From two point functions in holographic CFTs, we observe causal propagations of radiations when the mass of dual bulk scalar field is close to the BF bound. This behavior for holographic CFTs is consistent with the locality and causality in classical gravity duals. We also show that this cannot be seen in free fermion CFTs. Moreover, we find that the short distance behavior of two point functions is universal and obeys the relation which generalizes the first law of entanglement entropy.Comment: 23pages, Late

Entanglement Dynamics of the Non-Unitary Holographic Channel

We study the dynamical properties of a strongly scrambling quantum circuit involving a projective measurement on a finite-sized region by studying the operator entanglement entropy and mutual information (OEE and BOMI) of the dual operator state that corresponds to this quantum circuit. The time-dependence of the OEE exhibits a new dynamical behavior of operator entanglement, namely an additional fractional coefficient that accompanies the linear time growth of the OEE. For a holographic system, this is equivalent to an additional fractional coefficient that modifies the linear growth rate of the wormhole volume. The time-dependence of the BOMI shows that the projective measurement may destroy the non-local correlations in this dual state. We also propose a gravity dual as well as a line-tension picture, which is an effective model, that describe this strongly scrambling quantum circuit.Comment: 30 pages + appendices, 12 figure

Scrambling and Recovery of Quantum Information in Inhomogeneous Quenches in Two-dimensional Conformal Field Theories

We study various quantum quench processes induced by the M\"obius/sine-square deformation of the Hamiltonian in two-dimensional conformal field theories starting from the thermofield double state in the two copies of the Hilbert space. These quantum quenches, some of which are directly related to the operator entanglement of the time-evolution operators, allow us to study scrambling and recovery of quantum information. In particular, under the SSD time-evolution, we show from the time-dependence of mutual information that the Bell pairs, initially shared by the subsystems of the two Hilbert spaces, may revive even after the mutual information for small subsystems is completely destroyed by quantum information scrambling dynamics. This mutual information is robust against the strong scrambling dynamics. As a consequence, the steady state has a non-local correlation shared not by any of two parties but by three parties. In the holographic dual description, a wormhole connecting the two Hilbert spaces may non-linearly grow with time during the quantum quenches. We also propose effective pictures that describe the dynamics of mutual information during the time-evolution by inhomogeneous Hamiltonians.Comment: 36+26 pages, 23 figure

Spatial deformation of many-body quantum chaotic systems and quantum information scrambling

We study the effect of spatial inhomogeneity on quantum information scrambling, a process of spreading and locally hiding quantum information in quantum many-body systems. As a paradigmatic example, we consider the quantum chaotic Ising spin chain and its inhomogeneous counterpart that is obtained by modulating the Hamiltonian density. Specifically, we consider the so-called M\"obius and sine-square deformations that were previously studied in the context of (1+1)-dimensional conformal field theories ($1+1$ d CFTs). In the spatial region where the modulated energy density is small, these deformations prevent the spreading of quantum information while in the region where the modulated energy density is large quantum information scrambling is accelerated. This suggests that we can control the scrambling and butterfly effect by spatially modulating the Hamiltonian density. We also found that the time dependence of energy density exhibits the signature of black-hole-like excitation found in the $1+1$ d CFTs even in the chaotic spin chain.Comment: 16 pages, 11 figure