# Reduced density matrix and internal dynamics for multicomponent regions

H. Casini, M. Huerta

Arxiv ID: 0903.5284•Last updated: 7/16/2020

We find the density matrix corresponding to the vacuum state of a massless
Dirac field in two dimensions reduced to a region of the space formed by
several disjoint intervals. We calculate explicitly its spectral decomposition.
The imaginary powers of the density matrix is a unitary operator implementing
an internal time flow (the modular flow). We show that in the case of more than
one interval this evolution is non-local, producing both, advance in the causal
structure and "teleportation" between the disjoint intervals. However, it only
mixes the fields on a finite number of trajectories, one for each interval. As
an application of these results we compute the entanglement entropy for the
massive multi-interval case in the small mass limit.

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