Reduced density matrix and internal dynamics for multicomponent regions

By S. C. Bariloche, Ŕ. Negro. 2009

200 citations recorded by the source corpus.

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.

Subfields: Artificial Intelligence, Atomic and Molecular Physics, and Optics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/c40d5a2297c72896a08f3954377982216fe67186

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Citations in the corpus

Holographic entanglement entropy: an overview (2009, background): “In the case where the subsystem A consists of multiple intervals, recent discussions are available in [74, 110, 111].”
Relative entropy equals bulk relative entropy (2015, background): “For a generic region, the modular flow might be complicated, see [31] for some discussion about modular flows for fermions in 1+1 dimensions.”
Bulk locality from modular flow (2017, background): “The explicit expression for θ(x1, s) can be found in [41, 42] and x1(s), x2(s) are the corresponding local modular trajectories , which are given explicitly”
Entanglement entropy and conformal field theory (2009, methodology): “In [16, 75, 76], the entanglement entropy for two disjoint intervals has been calculated for a free Dirac fermion, that corresponds to a compactified boson with η = 1/2 [34].”