Tensor Network and Black Hole

TL;DR

This paper introduces a tensor network formalism for thermofield dynamics, linking Hilbert spaces with an event horizon analogy, and demonstrates MERA's effectiveness in representing AdS black holes at finite temperature.

Contribution

It presents a novel tensor network approach to thermofield dynamics, connecting tensor ranks with black hole entropy and illustrating MERA's role in AdS/CFT correspondence.

Findings

Tensor network formalism relates Hilbert space and tilde space via an event horizon analogy.

Logarithm of tensor rank corresponds to black hole entropy.

MERA reproduces finite-temperature AdS black hole geometry.

Abstract

A tensor network formalism of thermofield dynamics is introduced. The formalism relates the original Hilbert space with its tilde space by a product of two copies of a tensor network. Then, their interface becomes an event horizon, and the logarithm of the tensor rank corresponds to the black hole entropy. Eventually, multiscale entanglement renormalization anzats (MERA) reproduces an AdS black hole at finite temperature. Our finding shows rich functionalities of MERA as efficient graphical representation of AdS/CFT correspondence.