Zusammenfassung
We elaborate on a previous proposal by Hartman and Maldacena on a tensor
network which accounts for the scaling of the entanglement entropy in a system
at a finite temperature. In this construction, the ordinary entanglement
renormalization flow given by the class of tensor networks known as the Multi
Scale Entanglement Renormalization Ansatz (MERA), is supplemented by an
additional entanglement structure at the length scale fixed by the temperature.
The network comprises two copies of a MERA circuit with a fixed number of
layers and a pure matrix product state which joins both copies by entangling
the infrared degrees of freedom of both MERA networks. The entanglement
distribution within this bridge state defines reduced density operators on both
sides which cause analogous effects to the presence of a black hole horizon
when computing the entanglement entropy at finite temperature in the AdS/CFT
correspondence. The entanglement and correlations during the thermalization
process of a system after a quantum quench are also analyzed. To this end, a
full tensor network representation of the action of local unitary operations on
the bridge state is proposed. This amounts to a tensor network which grows in
size by adding succesive layers of bridge states. Finally, we discuss on the
holographic interpretation of the tensor network through a notion of distance
within the network which emerges from its entanglement distribution.
Nutzer