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New fingerprint of the entanglement on the thermodynamic properties

Somaye Nemati, S. Mahdavifar

Published Dec 1, 2017• 0 citations
Publisher

Abstract

The realization that entanglement can affect macroscopic properties of bulk solid-state systems is a challenge in physics and Chemistry. Theoretical physicists often are considered the entanglement between nearest-neighbor (NN) spins and tried to find its characterizations in terms of macroscopic thermodynamics observables as magnetization and specific heat. Here, we focus on the entanglement between next nearest neighbor (NNN) and the next to next nearest neighbor (NNNN) spins in an exactly solvable model. We show that there is a much clearer fingerprint of the longer-distance entanglement on the thermodynamic properties like the specific heat, the magnetocaloric effect and the magnetic susceptibility.

DOI
10.22051/jitf.2017.16439.1009

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The pairwise entanglement of the Heisenberg XX chain with next-nearest-neighbor (NNN) interactions was investigated by using the concurrence measure. The results show that for the nearest-neighbor sites, the entanglement may be improved or suppressed depending on the magnitudes of the NNN coupling constant J, while for the next-nearest-neighbor sites, it always increases with the increase of |J|. The critical temperature Tc decreases with the increase of J for the nearest-neighbor entanglement and increases with the increase of |J| for the next-nearest-neighbor entanglement, respectively. We also show that the general Heisenberg XX model still can be used to create the entangled W states of three and four qubits, and that the presence of NNN coupling has no effect on the creation of four-qubit W states, while it shifts the instant of time at which the three-qubit W states are created.
We report results from a Wang–Landau study of the random bond square Ising model with nearest-neighbor ( J nn ) and next-nearest-neighbor ( J nnn ) antiferromagnetic interactions. We consider the case R = J nn / J nnn = 1 for which the competitive nature of interactions produces a sublattice ordering known as superantiferromagnetism and the pure system undergoes a second-order transition with a positive specific heat exponent α. For a particular disorder strength we study the effects of bond randomness and we find that, while the critical exponents of the correlation length ν, magnetization β, and magnetic susceptibility γ increase as compared to the pure model, the ratios β/ν and γ/ν remain unchanged. Thus, the disordered system obeys weak universality and hyperscaling similarly to other two-dimensional disordered systems. However, the specific heat exhibits an unusually strong saturating behavior which distinguishes the present case of competing interactions from other two-dimensional random bond systems studied previously.
The features of the concurrences between the nearest-neighbors and that of the next-nearest-neighbors for the one-dimensional Heisenberg model with next-nearest-neighbor coupling JJJ are studied as functions of temperature and JJJ. The two concurrences exhibit a different dependence on JJJ at the ground state, which could be interpreted from the point of view of the correlation functions. The threshold temperature at which the concurrence is zero and the temperature effect on the two concurrences for systems up to 12 sites are studied numerically.