Quantum entanglement in the neighborhood of pseudo-transition for a spin-1/2 Ising-XYZ diamond chain

Abstract

Recently has been observed for some one-dimensional models that exhibit unexpected pseudotransitions and quasi-phases. This pseudo-transition resembles a first-and second-order phase transition simultaneously. One of those models is the spin-1/2 Ising-XYZ diamond chain, composed of Ising spin particles at the nodal sites and the Heisenberg spin particles at the interstitial sites. Where we assume Ising-type interaction between the nodal and interstitial sites, the Heisenberg-type interaction between interstitial sites, and with an external magnetic field applied along the z-axis. This model presents an exact analytical solution applying the transfer matrix technique, which shows 3 phases at zero temperature in the vicinity of pseudo-transition. The pseudo-transition separates quasi-phases, these quasi-phases still hold at a finite temperature most of the pattern configurations of a true phase at zero temperature. Here we study the quantum entanglement of pair spin particles in the quasi-phase regions, which can be measured through the concurrence. Then we observe an unexpected behavior in the concurrence, that is below pseudocritical temperature the concurrence remains almost constant up to pseudo-critical temperature, but above the pseudo-critical temperature, the concurrence behaves as for the standard one-dimensional spin models.Further, we consider the entropy behavior of the system, below pseudo-critical temperature the entropy becomes almost null, while above pseudo-critical temperature the system exhibits standard behavior as for ordinary one-dimensional spin models.

A Conjecture on the Relationship Between Critical Residual Entropy and Finite Temperature Pseudo-transitions of One-dimensional Models

“…In contrast, the phase boundary between F I and F R 2 is described by J z = −15 (red dashed line). The CRE satisfying the relation (11) becomes S c = ln(2), since the adjacent phases degeneracies are given by g c 1,0 = 2 and g c −1,0 = 1, which is in accordance with Fig. 1b.…”

“…Because, at zero temperature, the ground state energy for both phases MF 0 and MF 2 are non-degenerate, which implies that the residual entropy is S = 0. Besides, CRE also becomes null according to relation (11), which is easily verified on the density plot of entropy.…”

“…Below we present an accurate mathematical formulation [20] of the residual entropy around the critical point found in (11).…”

“…On the other hand, the term "pseudo-transition" was introduced by Timonin [9] in 2011 while studying the spin ice in a field, and refers to a sudden change in the first derivative of free energy, whereas a strong vigorous peak appears in the second derivative of free energy, although there are no discontinuity or divergence, respectively. Later this definition was adopted for our group [10][11][12] because we found the same kind of property. The pseudo-transition does not violate the Perron-Frobenius theorem [8], since the free energy is always analytic.…”

A conjecture on the relationship between critical residual entropy and finite temperature pseudo-transitions of one-dimensional models

“…On the other hand, the term "pseudo-transition" was introduced by Timonin [7] in 2011 when studied the spin ice in a field, to refer to a sudden change in first derivative of the free energy, while a strong vigorous peak appears in the second derivative of free energy, although there are no discontinuity or divergence, respectively. Later this definition was adopted for our group [8,9,10] because we found the same kind of property. The pseudo-transition does not violate the Perron-Frobenius theorem, because the free energy is always analytic.…”