Quantum MERA Channels

TL;DR

This paper introduces a transfer matrix formalism for quantum channels related to MERA tensor networks, enabling analysis of critical systems and their exponents in the thermodynamic limit.

Contribution

It develops a novel transfer matrix approach to connect MERA channels with critical system properties and their convergence behaviors.

Findings

Established a method to compute MERA channels in the thermodynamic limit

Linked critical exponents to convergence rates of associated channels

Provided a framework for analyzing critical quantum many-body systems

Abstract

Tensor networks representations of many-body quantum systems can be described in terms of quantum channels. We focus on channels associated with the Multi-scale Entanglement Renormalization Ansatz (MERA) tensor network that has been recently introduced to efficiently describe critical systems. Our approach allows us to compute the MERA correspondent to the thermodynamic limit of a critical system introducing a transfer matrix formalism, and to relate the system critical exponents to the convergence rates of the associated channels.