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arXiv:cond-mat/0208011 · Physical Review A

Macroscopic entanglement jumps in model spin systems

Indrani Bose, Emily Chattopadhyay

Published Dec 31, 2002• 94 citations
arXivHTMLPDF

Abstract

In this paper, we consider some frustrated spin models for which the ground states are known exactly. The concurrence, a measure of the amount of entanglement can be calculated exactly for entangled spin pairs. Quantum phase transitions involving macroscopic magnetization changes at critical values of the magnetic field are accompanied by macroscopic jumps in the $T=0$ entanglement. A specific example is given in which magnetization plateaus give rise to a plateau structure in the amount of entanglement associated with nearest-neighbor bonds. We further show that macroscopic entanglement changes can occur in quantum phase transitions brought about by the tuning of exchange interaction strengths.

DOI
10.1103/physreva.66.062320

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In this paper, we consider some frustrated spin models for which the ground states are known exactly. The concurrence, a measure of the amount of entanglement can be calculated exactly for entangled spin pairs. Quantum phase transitions involving macroscopic magnetization changes at critical values of the magnetic field are accompanied by macroscopic jumps in the T=0T=0T=0 entanglement. A specific example is given in which magnetization plateaus give rise to a plateau structure in the amount of entanglement associated with nearest-neighbor bonds. We further show that macroscopic entanglement changes can occur in quantum phase transitions brought about by the tuning of exchange interaction strengths.
The entanglement and quantum correlation measures have been investigated for the ground state of a spin chain with a Kitaev-type exchange interactions on alternating bonds, along with a transverse magnetic field. There is a macroscopic degeneracy in the ground state for zero magnetic field, implying a quantum critical point. In this model, many entanglement and correlation measures, except the macroscopic multispecies entanglement measure, do not show true singular behavior in the vicinity of the critical point, as seen in the transverse-Ising model ground state and related models. We compute the pair concurrence measure of entanglement, the pair quantum discord to track the quantum correlations, and a global entanglement measure and a multispecies entanglement measure to investigate multiparty entanglement, both analytically and numerically. The nearest-neighbor concurrence shows a peak structure as a function of magnetic field, near the critical point, for various values of the ratio of interaction strengths, but its derivative does not show a singular behavior close to the critical point. A similar behavior is shown by the quantum discord and the global entanglement. The multispecies entanglement shows a clear signature of the critical point behavior, and the first-order derivative shows a divergence near zero magnetic field, for equal interaction strengths.
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We investigate the entanglement properties of a one-dimensional chain of qubits coupled via nearest-neighbor spin-spin interactions. The entanglement measure used is the -concurrence, which is distinct from other measures on spin chains such as bipartite entanglement in that it can quantify ``global'' entanglement across the spin chain. Specifically, it computes the overlap of a quantum state with its time-reversed state. As such, this measure is well suited to study ground states of spin-chain Hamiltonians that are intrinsically time-reversal-symmetric. We study the robustness of -concurrence of ground states when the interaction is subject to a time-reversal antisymmetric magnetic field perturbation. The -concurrence in the ground state of the isotropic model is computed and it is shown that there is a critical magnetic field strength at which the entanglement experiences a jump discontinuity from the maximum value to zero. The -concurrence for thermal mixed states is derived and a threshold temperature is computed below which the system has nonzero entanglement.
Abstract We compute concurrence, a measure of bipartite entanglement, of the first excited state of the 1-D Heisenberg frustrated J 1 - J 2 spin-chain and observe a sudden change in the entanglement of the eigen state near the coupling strength α = J 2 / J 1 ≈ 0.241, where a quantum phase transition from spin-fluid phase to dimer phase has been previously reported. We numerically observe this phenomena for spin-chain with 8 sites to 16 sites, and the value of α at which the change in entanglement is observed, asymptotically tends to a value α c ≈ 0.24116. We have calculated the finite-size scaling exponents for spin chains with even and odd spins. It may be noted that bipartite as well as multipartite entanglement measures applied on the ground state of the system, fail to detect any quantum phase transition from the gapless to the gapped phase in the 1-D Heisenberg frustrated J 1 - J 2 spin-chain. Furthermore, we measure bipartite entanglement of first excited states for other spin models like 2-D Heisenberg J 1 - J 2 model and Shastry-Sutherland model and find similar indications of quantum phase transitions.