Universal role of correlation entropy in critical phenomena

Abstract

In statistical physics, if we successively divide an equilibrium system into two parts, we will face a situation that, within a certain length $\xi$, the physics of a subsystem is no longer the same as the original system. Then the extensive properties of the thermal entropy $S($AB$)=S($A$)+S($B$)$ is violated. This observation motivates us to introduce the concept of correlation entropy between two points, as measured by mutual information in the information theory, to study the critical phenomena. A rigorous relation is established to display some drastic features of the non-vanishing correlation entropy of the subsystem formed by any two distant particles with long-range correlation. This relation actually indicates the universal role of the correlation entropy in understanding critical phenomena. We also verify these analytical studies in terms of two well-studied models for both the thermal and quantum phase transitions: two-dimensional Ising model and one-dimensional transverse field Ising model. Therefore, the correlation entropy provides us with a new physical intuition in critical phenomena from the point of view of the information theory.

10 pages, 9 figures

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• Density Matrix Spectra and Order Parameters in the 1D Extended Hubbard Model
• Thermal entanglement of Hubbard dimers in the nonextensive statistics
• Universal quantum correlation close to quantum critical phenomena
• Duality between predictability and reconstructability in complex systems
• Rényi Information flow in the Ising model with single-spin dynamics
• Magnetic phases of XY model with three-spin terms: interplay of topology and entanglement
• Order parameter conditions from mutual information and symmetry conditions
• Multiscale complexity of two-dimensional Ising systems with short-range, ferromagnetic interactions
• Probing phase transitions in non-Hermitian systems with quantum entanglement
• Non-local spin entanglement in a fermionic chain