Reduced density matrix and internal dynamics for multicomponent regions
- 7 September 2009
- journal article
- research article
- Published by IOP Publishing in Classical and Quantum Gravity
- Vol. 26 (18)
- https://doi.org/10.1088/0264-9381/26/18/185005
Abstract
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 power 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.Other Versions
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