Quantum correlation and phase transitions in a two-dimensional doubly decorated Ising-Heisenberg model

Abstract

We investigate the pairwise quantum correlation, characterized by quantum entanglement (QE) and quantum discord (QD), of a two-dimensional Ising-Heisenberg model on a planar doubly decorated lattice. At zero temperature, the concurrence (a measurement of pairwise entanglement) and the QD are related to the correlation function qxx and the staggered magnetization δSz, respectively, and both of them indicate the quantum phase transition (QPT) of the system. However, in a finite-temperature phase transition, all the pairwise entanglement vanishes thus it fails to detect the critical temperature TC , while the derivative of QD diverges at TC . This shows clearly that QD can capture the signal of phase transition in a separable state, thus it has a broader scope of application than QE in detecting phase transitions.

Global Quantum Discord in Transverse‐Field Ising Models on N × N Square Lattices

“…For instance, quantum discord is found to exhibit long‐range decay as a function of distance in spin chains, where two‐site entanglement is short‐ranged . Furthermore, for some quantum states where the quantum entanglement vanishes thus fails in detecting the quantum phase transitions in the systems, it has been found that the quantum discord survives and plays the role very well . These findings show that quantum discord is a valuable measure of quantum correlations for condensed matter physics.…”

“…For a larger N (which means more sites in the environment block), the sub‐square would share a larger amount of “external” correlations with its environment. Consequently, a smaller amount of “internal” correlations could be reserved in the sub‐square, since the “total” correlations which the 2 × 2 sub‐square can carry is finite . That's why the peak value of the curves decreases gradually as the increase of N .…”

“…Among various measures of quantum correlations, quantum discord has attracted much attention recently, which turns out to be a valuable complement to quantum entanglement. Two‐site quantum discord has been studied in various low‐dimensional quantum spin models, such as the matrix‐product‐state (MPS) models, the XY chain, the XXZ chain, the two‐leg spin ladder with ring exchange, and the Ising‐Heisenberg decorated lattice . In these models, quantum discord has shown some interesting properties.…”

Thermal Entanglement and Quantum Non-Locality along the Stepwise Magnetization Curve of the Spin-1/2 Ising-Heisenberg Trimerized Chain

“…It is worthwhile to remark, however, that the quantum entanglement and non-locality are distinct albeit closely related features of quantum-mechanical systems [3]. Moreover, it has been evidenced that the quantum entanglement and non-locality are also capable of detecting phase transitions of quantum spin systems [4][5][6].…”

“…It is worthwhile to remark, however, that the quantum entanglement and non-locality are distinct albeit closely related features of quantum-mechanical systems [3]. Moreover, it has been evidenced that the quantum entanglement and non-locality are also capable of detecting phase transitions of quantum spin systems [4][5][6].Quantum effects may have striking macroscopic consequences like for instance presence of quantized plateaux in low-temperature magnetization curves. The magnetization plateaux of quantum spin chains should satisfy Oshikawa-Yamanaka-Affleck rule [7]: p(S u − m u ) = Z, where p is the ground-state period, S u and m u is the total spin and total magnetization of elementary unit and Z is an integer number.…”