International Journal of Modern Physics B

Multipartite quantum correlations in the extended J1–J2 Heisenberg model

Josep Amengual i Batle, Omar Husain Tarawneh, Koji Nagata, Tadao Nakamura, S. Abdalla, Ahmed Farouk

Published Jun 9, 2017• 0 citations

Abstract

Multipartite entanglement and the maximum violation of Bell inequalities are studied in finite clusters of spins in an extended J1–J2 Heisenberg model at zero temperature. The ensuing highly frustrated states will unveil a rich structure for different values of the corresponding spin–spin interaction strengths. The interplay between nearest-neighbors, next-nearest neighbors and further couplings will be explored using multipartite correlations. The model is relevant to certain quantum annealing computation architectures where an all-to-all connectivity is considered.

DOI: 10.1142/s021797921750206x

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International Journal of Modern Physics B

Multipartite quantum correlations in the extended J1–J2 Heisenberg model

Josep Amengual i Batle, Omar Husain Tarawneh, Koji Nagata, Tadao Nakamura, S. Abdalla, Ahmed Farouk

Published Jun 9, 2017• 0 citations

Publisher

Abstract

DOI: 10.1142/s021797921750206x

Related papers

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Multipartite quantum nonlocality and Bell-type inequalities are used to characterize quantum correlations in an infinite-size bond-alternating spin-

\frac{1}{2}

Heisenberg chain with next-nearest-neighbor interactions. With the help of powerful tensor-network algorithms, both zero and finite temperatures are considered. First, at zero temperature, both in the even-Haldane phase and in the odd-Haldane phase, a high hierarchy of multipartite nonlocality is observed. Nevertheless, in the two phases, the spread of the multipartite nonlocality among the lattice is different. Thereby, the nonlocality measures are relatively large in one phase and vanish in the other phase, and provide quite sharp signals for the topological quantum phase transitions (QPTs) between these two phases. The influence of the next-nearest-neighbor coupling $\ensuremath{\alpha}$ upon the multipartite nonlocality in the model is also discussed. Second, we find that the footprints of the QPTs survive at low temperatures. Third, based upon the scaling behavior of the finite-temperature nonlocality measure, we propose a quantity

\mathcal{K}

to characterize the finite-temperature nonlocality in the large-

n

limit. We find that in high-temperature regions,

\mathcal{K}

is reduced linearly as the temperature rises.

We study Heisenberg spin-1/2 and spin-1 chains with alternating ferromagnetic (

J_1^F

) and antiferromagnetic (

J_1^A

) nearest-neighbor interactions and ferromagnetic next-nearest-neighbor interaction (

J_2^F

). In this model frustration is induced by the non-zero

J_2^F

and the effect of dimerization is realized by changing the strength of

J_1^A

for a fixed value of

J_1^F

. The model with site spin

s

behaves like a Haldane spin chain with site spin 2

s

in the limit of vanishing

J_2^F

and large

J_1^F/J_1^A

. We show that the exact ground state of the model can be found along a line in the parameter space. The phase diagram in the space of

J_1^A-J_2^F

is determined using numerical techniques complemented by some analytical calculations. A number of quantities, including the ground state spin, energy gap, structure factor, entanglement entropy, and zero temperature magnetization, are studied to understand the complete phase diagram. An interesting and application-wise important feature of this model is that it exhibits a macroscopic magnetization jump in the presence of a magnetic field; we study this using an effective Hamiltonian.

Exchange interactions in spin systems can give rise to quantum entanglement in the ground and thermal states of the systems. We consider a spin tetramer, with spins of magnitude

\frac{1}{2}

, in which the spins interact via nearest-neighbor, diagonal, and four-spin interactions of strength

{J}_{1}

{J}_{2}

, and

K

, respectively. The ground- and thermal-state entanglement properties of the tetramer are calculated analytically in the various limiting cases. Both bipartite and multipartite entanglements are considered and a signature of the quantum phase transition (QPT), in terms of the entanglement ratio, is identified. The first-order QPT is accompanied by discontinuities in the nearest-neighbor and diagonal concurrences. The magnetic properties of a

S=\frac{1}{2}

antiferromagnetic polyoxovanadate compound V12 are well explained by tetramers, with

{J}_{2}=0

K=0

, in which the spins interact via the isotropic Heisenberg exchange interaction Hamiltonian. Treating the magnetic susceptibility $\ensuremath{\chi}$ as an entanglement witness (EW), an estimate of the lower bound of the critical entanglement temperature

{T}_{c}

below which entanglement is present in the experimental compound, is determined. Two other cases considered include the symmetric tetramer---i.e., tetrahedron

({J}_{1}={J}_{2},K=0)

---and the symmetric trimer. In both the cases, there is no entanglement between a pair of spins in the thermal state but multipartite entanglement is present. A second EW based on energy provides an estimate of the entanglement temperature

{T}_{E}

below which the thermal state is definitely entangled. This EW detects bipartite entanglement in the case of the tetramer describing a square of spins (the case of V12 ) and multipartite entanglement in the cases of the tetrahedron and symmetric trimer.

We present an exact diagonalization study on layered

J_{1}-J_{2}

antiferromagnetic Heisenberg spin model to examine the role of frustration induced by inplane next-nearest neighbor coupling

J_{2}

, in presence of interlayer antiferromagnetic coupling

J_{\perp}

. A finite lattice of 24 spins in layered geometry of

(4\times 3)\oplus (4\times 3)

is considered and the resulting Hamiltonian matrix diagonalized using Davidson iterative algorithm to obtain the ground and a few low-lying excited states. The lattice size (

24

spins with Hilbert space dimensionality of

2704156

S_{z}^{tot}=0

subspace) has been kept relatively small because of the large number of runs required to sample

J_{1}-J_{2}-J_{\perp}

parameter space. Quantities like spin-gap, Shannon entropy, spin-spin correlation, static spin structure-factor, magnetic specific-heat and magnetic susceptibility are calculated for various values of spin-spin coupling parameters. With increase in interlayer coupling, the system is driven to states with long range order and the interval of quantum paramagnetically disordered state, sandwiched between Néel and collinear ordered states, narrows on the scale of inplane frustration parameter.