Investigation of Quantum Correlations for A S = 1/2 Ising–Heisenberg Model on a Symmetrical Diamond Chain

Abstract

We consider the quantum correlations for a S=1/2 Ising-Heisenberg model of a symmetrical diamond chain. Firstly, we compare concurrence, quantum discord and 1-norm geometric quantum discord of an ideal diamond chain (J m = 0) in the absence of magnetic field. The results show no simple ordering relations between these quantum correlations, so that quantum discord may be smaller or larger than the 1-norm geometric quantum discord, which this observation contradict the previous result that provided by F. M. Paula [1]. Symmetrical behavior of quantum correlation versus ferromagnetic and anti-ferromagnetic coupling constant J is considerable. The effect of external magnetic field H and temperature-dependence is also considered. Furthermore, we study quantum discord and geometric measure of quantum discord with the effect of next nearest neighbor interaction between nodal Ising sites for a generalized diamond chain (J m = 0), and we observe coexistence of phases with different values of magnetic field for quantum correlations. Moreover, entanglement sudden death occurs while quantum discord, 1-norm geometric quantum discord and geometric quantum discord are immune from sudden death.

Absence of actual plateaus in zero-temperature magnetization curves of quantum spin clusters and chains

“…The magnetization curves, thus, for the Ising-Heisenberg spin systems share almost all features with the magnetization curves of the small spin clusters, but can contain much more intermediate magnetization plateaus. Various variants of the Ising-Heisenberg chains have been examined: diamond-chain, [14][15][16][17][18][19][20][21][22][23][24][25][26][27][28] saw-tooth chain, 29,30 orthogonal-dimer chain, [31][32][33] tetrahedral chain, [34][35][36][37][38] and some special examples relevant to real magnetic materials. [39][40][41][42] In the present work, we will rigorously examine a magnetization process of a few quantum Heisenberg spin clusters and Ising-Heisenberg diamond chain, which will not display strict magnetization plateaus on assumption that some constituent spins have different Landé g-factors and may be a XY-anisotropy of the exchange interaction.…”

Exactly solvable spin-1 Ising–Heisenberg diamond chain with the second-neighbor interaction between nodal spins

“…In spite of a certain over-simplification, the generalized version of the spin-1/2 Ising-Heisenberg diamond chain qualitatively reproduces magnetization, specific heat and susceptibility data reported on the azurite Cu 3 (CO 3 ) 2 (OH) 2 , which represents the most prominent experimental realization of the spin-1/2 diamond chain [3,4,5,6]. A lot of attention has been therefore paid to a comprehensive analysis of quantum and thermal entanglement [7,8,9,10,11], correlation functions [12], Lyapunov exponent [13], zeros of partition function [14], magnetocaloric effect [15], the influence of asymmetric [16,17], further-neighbor [18] and four-spin interactions [19,20].…”

Exactly solved mixed spin-(1,1/2) Ising–Heisenberg distorted diamond chain

“…23 whereas they differ from the analogous ground states MD and QAF just by the symmetric (instead of antisymmetric) 24 quantum superposition of the antiferromagnetic states | ↑, ↓⟩ k and | ↓, ↑⟩ k of the Heisenberg spin pairs. The eigenenergies per primitive cell, which correspond to the respective ground states (19), follow from…”

“…(4)), we can directly apply the transfer-matrix method [47,48]. For convenience we define the elements V ij of the 24 transfer matrix V as follows:…”