Genuine multipartite correlations in finite-size XY chains are studied as a function of the applied external magnetic field. We find that, for low temperatures, multipartite correlations are sensitive to the parity change in the Hamiltonian ground state, given that they exhibit a minimum every time that the ground state becomes degenerate. This implies that they can be used to detect the factorizing point, that is, the value of the external field such that, in the thermodynamical limit, the ground state becomes the tensor product of single-spin states.
The ground state of interacting spin chains in external magnetic fields can undergo a quantum phase transition (QPT) characterized by dramatic changes at a critical value of the magnetic field. In this paper, we use Bell-type inequalities to study the multipartite correlations (including multipartite entanglement and multipartite nonlocality in an
n-spin subsystem) in the QPT of an infinite
XY chain. An efficient numerical optimization procedure is proposed to figure out the violation measure
Mn of the inequalities. For $n\ensuremath{\le}7$, the magnetic-field ($\ensuremath{\lambda}$) dependence of
Mn is studied. We find the derivative of
Mn is divergent exactly at the QPT point ${\ensuremath{\lambda}}_{c}=1$ for any
n. In addition, with the increase of
n,
Mn converges quickly for $\ensuremath{\lambda}<{\ensuremath{\lambda}}_{c}$ and converges very slowly for $\ensuremath{\lambda}>{\ensuremath{\lambda}}_{c}$, which can be regarded as another signal for the QPT. Furthermore, in the vicinity of ${\ensuremath{\lambda}}_{c}$, high-order Bell-type inequalities will be violated as long as
n is large enough. This indicates that high-level multipartite correlation will be present when the system is in the vicinity of the QPT point. Nevertheless, genuine
n-partite entanglement or genuine
n-partite nonlocality is not observed in the QPT.
We examine the quantum correlations of spin pairs in the ground state of finite XY chains in a transverse field, by evaluating the quantum discord as well as other related entropic measures of quantum correlations. A brief review of the latter, based on generalized entropic forms, is also included. It is shown that parity effects are of crucial importance for describing the behavior of these measures below the critical field. It is also shown that these measures reach full range in the immediate vicinity of the factorizing field, where they become independent of separation and coupling range. Analytical and numerical results for the quantum discord, the geometric discord and other measures in spin chains with nearest neighbor coupling and in fully connected spin arrays are also provided.
We study the properties of multipartite quantum correlation (MQC) in a one-dimensional spin-1/2
XY chain, where the three-spin reduced states are focused on and the four introduced MQC measures are based on entanglement negativity and entanglement of formation. It is found that, even in the Ising case, the three-spin subsystems have long-range MQCs and the tripartite quantum correlations beyond the nearest-neighbor three spins can detect the quantum phase transition and obey the finite-size scaling around the critical point. Furthermore, in the
XY model, we show that the two selected MQCs can indicate exactly the factorization point of the ground state for the anisotropic model in the thermodynamic and finite-size cases. Moreover, the spatial distribution of MQC based on entanglement negativity can attain a much larger range by tuning the anisotropic parameter, and the newly defined MQC based on entanglement of formation can detect the bound entanglement in the three-spin subsystems when the entanglement negativity loses its efficacy.
We analyze the
XY model characterized by an anisotropy $\ensuremath{\gamma}$ in an external magnetic field,
h, with respect to its genuine multipartite entanglement content (in the thermodynamic and finite-size case). Despite its simplicity we show that the quantity---detecting genuine multipartite entanglement through permutation operators and being a lower bound on measures---witnesses the presence of genuine multipartite entanglement for nearly all values of $\ensuremath{\gamma}$ and
h. We further show that the phase transition and scaling properties are fully characterized by this multipartite quantity. Consequently, we provide a useful toolbox for other condensed-matter systems, where bipartite entanglement measures are known to fail.
We study the occurrence of multipartite entanglement in spin chains. We show that certain genuine multipartite entangled states, namely
W states, can be obtained as ground states of simple XX type ferromagnetic spin chains in a transverse magnetic field, for any number of sites. Moreover, multipartite entanglement is proven to exist even at finite temperatures. A transition from a product state to a multipartite entangled state occurs when decreasing the magnetic field to a critical value. Adiabatic passage through this point can thus lead to the generation of multipartite entanglement.
Multipartite nonlocality is an important measure of multipartite quantum correlations. In this paper, we show that the nonlocal
n-site Mermin-Klyshko operator ${\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{M}}_{n}$ can be exactly expressed as a matrix product operator with a bond dimension
D=2, and then the calculation of nonlocality measure
S can be simplified into standard one-dimensional (1D) tensor networks. With the help of this technique, we analyze finite-temperature multipartite nonlocality in several typical 1D spin chains, including an
XX model, an
XXZ model, and a Kitaev model. For the
XX model and the
XXZ model, in a finite-temperature region, the logarithm measure of nonlocality (
log2S) is a linear function of the temperature
T, i.e., ${log}_{2}\mathcal{S}\ensuremath{\sim}\ensuremath{-}aT+b$. It provides us with an intuitive picture about how thermodynamic fluctuations destroy multipartite nonlocality in 1D quantum chains. Moreover, in the
XX model
S presents a magnetic-field-induced oscillation at low temperatures. This behavior has a nonlocal nature and cannot be captured by local properties such as the magnetization. Finally, for the Kitaev model, we find that in the limit $T\ensuremath{\rightarrow}0$ and $N\ensuremath{\rightarrow}\ensuremath{\infty}$ the nonlocality measure may be used as an alternative order parameter for the topological-type quantum phase transition in the model.