R\'{e}nyi and Shannon mutual information in critical and decohered critical system

TL;DR

This paper introduces a Rényi generalized mutual information for critical many-body systems, demonstrating its robustness under decoherence and its ability to reflect conformal field theory properties like the central charge.

Contribution

It proposes a Rényi mutual information framework that remains consistent under decoherence and can be experimentally accessible for studying critical systems.

Findings

Rényi mutual information maintains CFT scaling laws under decoherence.

The Rényi-2 central charge remains robust against local environmental decoherence.

The approach provides a resilient measure for criticality in many-body quantum systems.

Abstract

We investigate a critical many-body system by introducing a R\'{e}nyi generalized mutual information, connecting between R\'{e}nyi mutual information and R\'{e}nyi Shannon mutual information. This R\'{e}nyi generalized mutual information can offer more experimentally accessible alternative than the conventional entanglement entropy. As a critical many-body state, we focus on the critical transverse-field Ising model (TFIM) described by the Ising conformal field theory (CFT). We show that even if we modify the non-selective projective measurement assumed in R\'{e}nyi Shannon mutual information by replacing the measurement into decoherence by environment, the R\'{e}nyi generalized Shannon mutual information maintains the CFT properties such as subsystem CFT scaling law and its central charge observed through both the conventional R\'{e}nyi Shannon mutual information and R\'{e}nyi mutual information. Furthermore, we apply a local decoherence to the critical ground state of the TFIM and numerically observe the R\'{e}nyi generalized mutual information by changing the parameter controlling environment effect (corresponding to the strength of measurement) in the R\'{e}nyi generalized mutual information and the strength of the decoherence to which the entire system subjects. We find that R\'{e}nyi-$2$ type central charge connected to the central charge is fairly robust, indicating the strong robustness of the Ising CFT properties against local decoherence by environment.