Curtis T. Asplund

Holographic entanglement entropy from 2d CFT: heavy states and local quenches

A bstractWe consider the entanglement entropy in 2d conformal field theory in a class of excited states produced by the insertion of a heavy local operator. These include both high-energy eigenstates of the Hamiltonian and time-dependent local quenches. We compute the universal contribution from the stress tensor to the single interval Renyi entropies and entanglement entropy, and conjecture that this dominates the answer in theories with a large central charge and a sparse spectrum of low-dimension operators. The resulting entanglement entropies agree precisely with holographic calculations in three-dimensional gravity. High-energy eigenstates are dual to microstates of the BTZ black hole, so the corresponding holographic calculation is a geodesic length in the black hole geometry; agreement between these two answers demonstrates that these individual microstates of holographic CFTs effectively thermalize at the level of the single-interval entanglement entropy. For local quenches, the dual geometry is a highly boosted black hole or conical defect. On the CFT side, the rise in entanglement entropy after a quench is directly related to the monodromy of a Virasoro conformal block.

Evidence for fast thermalization in the plane-wave matrix model.

We report on a numerical simulation of the classical evolution of the plane-wave matrix model with semiclassical initial conditions. Some of these initial conditions thermalize and are dual to a black hole forming from the collision of D-branes in the plane-wave geometry. In particular, we consider a large fuzzy sphere (a D2-brane) plus a single eigenvalue (a D0 particle) going exactly through the center of the fuzzy sphere and aimed to intersect it. Including quantum fluctuations of the off-diagonal modes in the initial conditions, with sufficient kinetic energy the configuration collapses to a small size. We also find evidence for fast thermalization: rapidly decaying autocorrelation functions at late times with respect to the natural time scale of the system.

Entanglement scrambling in 2d conformal field theory

A bstractWe investigate how entanglement spreads in time-dependent states of a 1+1 dimensional conformal field theory (CFT). The results depend qualitatively on the value of the central charge. In rational CFTs, which have central charge below a critical value, entanglement entropy behaves as if correlations were carried by free quasiparticles. This leads to long-term memory effects, such as spikes in the mutual information of widely separated regions at late times. When the central charge is above the critical value, the quasiparticle picture fails. Assuming no extended symmetry algebra, any theory with c > 1 has diminished memory effects compared to the rational models. In holographic CFTs, with c ≫ 1, these memory effects are eliminated altogether at strong coupling, but reappear after the scrambling time t ≳ β log c at weak coupling.

Large N classical dynamics of holographic matrix models

Using a numerical simulation of the classical dynamics of the plane wave and flat space matrix models of M theory, we study the thermalization, equilibrium thermodynamics, and fluctuations of these models as we vary the temperature and the size of the matrices, N. We present our numerical implementation in detail and several checks of its precision and consistency. We show evidence for thermalization by matching the time-averaged distributions of the matrix eigenvalues to the distributions of the appropriate traceless Gaussian unitary ensemble of random matrices. We study the autocorrelations and power spectra for various fluctuating observables and observe evidence of the expected chaotic dynamics as well as a hydrodynamic type limit at large N, including near-equilibrium dissipation processes. These configurations are holographically dual to black holes in the dual string theory or M theory, and we discuss how our results could be related to the corresponding supergravity black hole solutions.

Mutual information after a local quench in conformal field theory

We compute the entanglement entropy and mutual information for two disjoint intervals in two-dimensional conformal field theories as a function of time after a local quench, using the replica trick and boundary conformal field theory. We obtain explicit formulae for the universal contributions, which are leading in the regimes of, for example, close or well-separated intervals of fixed length. The results are largely consistent with the quasiparticle picture, in which entanglement above that present in the ground state is carried by pairs of entangled, freely propagating excitations. We also calculate the mutual information for two disjoint intervals in a proposed holographic local quench, whose holographic energy-momentum tensor matches the conformal field theory one. We find that the holographic mutual information shows qualitative differences from the conformal field theory results and we discuss possible interpretations of this.

Evolution of Entanglement Entropy in the D1-D5 Brane System

We calculate the evolution of the geometric entanglement entropy following a local quench in the D1D5 conformal field theory, a two-dimensional theory that describes a particular bound state of D1 and D5 branes. The quench corresponds to a localized insertion of the exactly marginal operator that deforms the field theory off of the orbifold (free) point in its moduli space. This deformation ultimately leads to thermalization of the system. We find an exact analytic expression for the entanglement entropy of any spatial interval as a function of time after the quench and analyze its properties. This process is holographically dual to one stage in the formation of a stringy black hole.

Massive quiver matrix models for massive charged particles in AdS

A bstractWe present a new class of N=4

Entanglement entropy converges to classical entropy around periodic orbits

\mathcal{N}=4