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.
Citation Formats
Casini, H, and Huerta, M.
Reduced density matrix and internal dynamics for multicomponent regions.
United Kingdom: N. p.,
2009.
Web.
doi:10.1088/0264-9381/26/18/185005.
Casini, H, & Huerta, M.
Reduced density matrix and internal dynamics for multicomponent regions.
United Kingdom.
https://doi.org/10.1088/0264-9381/26/18/185005
Casini, H, and Huerta, M.
2009.
"Reduced density matrix and internal dynamics for multicomponent regions."
United Kingdom.
https://doi.org/10.1088/0264-9381/26/18/185005.
@misc{etde_21376193,
title = {Reduced density matrix and internal dynamics for multicomponent regions}
author = {Casini, H, and Huerta, M}
abstractNote = {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.}
doi = {10.1088/0264-9381/26/18/185005}
journal = []
issue = {18}
volume = {26}
place = {United Kingdom}
year = {2009}
month = {Sep}
}
title = {Reduced density matrix and internal dynamics for multicomponent regions}
author = {Casini, H, and Huerta, M}
abstractNote = {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.}
doi = {10.1088/0264-9381/26/18/185005}
journal = []
issue = {18}
volume = {26}
place = {United Kingdom}
year = {2009}
month = {Sep}
}