R\'enyi and Shannon mutual information in critical and decohered critical system
Abstract
We investigate a critical many-body system by introducing a R\'enyi generalized mutual information, connecting between R\'enyi mutual information and R\'enyi Shannon mutual information. This R\'enyi 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\'enyi Shannon mutual information by replacing the measurement into decoherence by environment, the R\'enyi generalized Shannon mutual information maintains the CFT properties such as subsystem CFT scaling law and its central charge observed through both the conventional R\'enyi Shannon mutual information and R\'enyi mutual information. Furthermore, we apply a local decoherence to the critical ground state of the TFIM and numerically observe the R\'enyi generalized mutual information by changing the parameter controlling environment effect (corresponding to the strength of measurement) in the R\'enyi generalized mutual information and the strength of the decoherence to which the entire system subjects. We find that R\'enyi-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.
Turn this paper into a full lesson
ArcXiv compiles a staged curriculum from this paper: 8-12 lessons across beginner → advanced, synthesised section guides, visuals, flashcards, a quiz, exercises, and on-demand deep dives per section. Grounded in the abstract, never invented.