Year: 2015
Type: article
Abstract: We study the generalized mutual information ${\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{I}}_{n}$ of the ground state of different critical quantum chains. The generalized mutual information definition that we use is based on the well established concept of the R\'enyi divergence. We calculate this quantity numerically for several distinct quantum chains having either discrete $Z(Q)$ symmetries ($Q$-state Potts model with $Q=2,3,4$ and $Z(Q)$ parafermionic models with $Q=5,6,7,8$ and also Ashkin-Teller model with different anisotropies) or the $U(1)$ continuous symmetries (Klein-Gordon field theory, $XXZ$ and spin-1 Fateev-Zamolodchikov quantum chains with different anisotropies). For the spin chains these calculations were done by expressing the ground-state wave functions in two special bases. Our results indicate some general behavior for particular ranges of values of the parameter $n$ that defines ${\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{I}}_{n}$. For a system, with total size $L$ and subsystem sizes $\ensuremath{\ell}$ and $L\ensuremath{-}\ensuremath{\ell}$, the ${\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{I}}_{n}$ has a logarithmic leading behavior given by $\frac{{\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{c}}_{n}}{4}log[\frac{L}{\ensuremath{\pi}}sin(\frac{\ensuremath{\pi}\ensuremath{\ell}}{L})]$ where the coefficient ${\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{c}}_{n}$ is linearly dependent on the central charge $c$ of the underlying conformal field theory describing the system's critical properties.
Source: Physical Review B
Authors: F. C. Alcaraz, M. A. Rajabpour
Language: English
Topic: Quantum many-body systems
Subfield: Atomic and Molecular Physics, and Optics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2071716200