Abstract
We consider the time evolution of mixed state correlation measures in two-dimensional conformal field theories, such as logarithmic negativity, odd entropy, and reflected entropy, after quantum quenches of various kinds. These correlation measures, in the holographic context, are all associated to the entanglement wedge cross section. We contrast various classes of conformal field theories, both rational and irrational (pure) conformal field theories. First, for rational conformal field theories, whose dynamics can be well described by the quasi-particle picture, we find all four quantities for disjoint intervals to be proportional, regardless of the specific quench protocol. Second, using the light cone boot- strap, we generalize our results to irrational conformal field theories where we find sharp distinctions from the quasi-particle results and striking differences between mutual information and the other measures. The large surplus of logarithmic negativity relative to mutual information forces us to reconsider what mutual information and logarithmic negativity really measure. We interpret these results as a signature of information scrambling and chaos in irrational theories. These CFT results perfectly agree with our gravitational (holographic) calculations. Furthermore, using holography, we are able to generalize the results to outside of the light cone limit. Finally, due to the breakdown of the quasi-particle picture for irrational theories, we appeal to the “line-tension picture,” motivated by random unitary circuits, as a phenomenological description. We observe that random unitary circuits, with local Hilbert space dimension determined by the Cardy formula, have precisely the same entanglement dynamics as irrational (including holographic) conformal field theories.
Highlights
Of the reduced density matrix, and is expected to capture only quantum correlations [6,7,8,9,10,11]
The purpose of the paper is to study the time-evolution of the mixed state correlation measures after quantum quench, for rational and irrational conformal field theories
We study the theory independent part of correlation functions in boundary conformal field theory on the upper half plane
Summary
Of the reduced density matrix, and is expected to capture only quantum correlations [6,7,8,9,10,11]. Knowledge of the correlation properties of each quantity is quite limited, so our work serves to build intuition for what exactly they are measuring. What makes these new quantities intriguing is that, like negativity [14, 15], they are intimately related, in the holographic context, to a specific geometric object known as the entanglement wedge cross-section [16, 17]. In a global quantum quench, one first prepares the system in a short-ranged entangled state e.g. the ground state of a gapped Hamiltonian, H. We evolve in Lorentzian time with the gapless Hamiltonian to quench This has the effect of an instantaneous homogeneous injection of energy with effective temperature β. Global quenches are experimentally relevant [21,22,23] and have been intensely studied both numerically and analytically
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