We show the positivity or negativity of truncated correlation functions in the quantum XY model with spin 1/2 (at any temperature) and spin 1 (in the ground state). These Griffiths-Ginibre inequalities of the second kind generalise an earlier result of Gallavotti.
We investigate the behaviour of quantum correlations (entanglement and
quantum discord) for homogeneous XY model at absolute zero and at finite temperature. Study of this correlation measures of quenched disordered
quantum spin models like the XY spin glass and random-field XY models is
also reviewed. We show that quenched averaged quantum correlations can
showcase the order-from-disorder phenomenon for finite-size systems and also
when the system is in the thermodynamic limit. Though we find some regions
with positive enhancement score. This order from disorder phenomena
is more prominent when the system is in the finite temparature with some
definite values of external parameter. We also look into correlation length.
Correlation functions of ground states typically decay exponentially with the
distance for quantum spin systems. In such systems, entanglement does not
survive when |i-j| ≳ 3. However, quantum discord survives long lattice
distances as it is not monogamous for this system. We investigate the effects
of quenched disorder on quantum correlation lengths of quenched averaged
entanglement and quantum discord, in the anisotropic XY spin glass chains.
We realize that there is practically neither diminution nor growth in entanglement
length while quantum discord length increases significantly with
the introduction of quenched disorder except near factorization point. Apart
from that, we also investigate the scaling behaviour of quantum entanglement
and quantum discord. We find that though entanglement follows finite size
scaling close to quantum phase transition, scaling can't be done for quantum
discord.
We examine the ability of quantum discord (QD) and entanglements (concurrence, EoF and negativity) to detect the critical points associated to quantum phase transitions (QPTs) for XY models, i.e., the isotropic XY model with three-spin interactions at zero temperature, and the anisotropic XY model in a transverse magnetic field h at finite temperatures. For the case of zero temperature, we found that both entanglements and QD can spotlight the critical points of QPTs for these two models. Moreover, QD versus distance M exhibits the long-range behavior of quantum correlation for the anisotropic XY model, while entanglement is short-ranged. For the case of finite temperatures, we found that negativity has the same behaviors with concurrence at or near transition points. Moreover, QD for the anisotropic XY model can increase with temperature even in the absence of a magnetic field.
We study the multi-spin entanglement for the 1D anisotropic XY model concentrating on the simplest case of three-spin entanglement. As compared to the pairwise entanglement, three-party quantum correlations have a longer range and they are more robust on increasing the temperature. We find regions of the phase diagram of the system where bound entanglement (BE) occurs, both at zero and finite temperature. BE in the ground state can be obtained by tuning the magnetic field. Thermal BE emerges naturally due to the effect of temperature on the free ground state entanglement.