Statistical mechanics of the Cluster-Ising model

@article{Smacchia2011StatisticalMO,
  title={Statistical mechanics of the Cluster-Ising model},
  author={Pietro Smacchia and Luigi Amico and Paolo Facchi and Rosario Fazio and Giuseppe Florio and Saverio Pascazio and Vlatko Vedral},
  journal={Physical Review A},
  year={2011},
  volume={84},
  pages={022304}
}
We study a Hamiltonian system describing a three-spin-1/2 clusterlike interaction competing with an Ising-like antiferromagnetic interaction. We compute free energy, spin-correlation functions, and entanglement both in the ground and in thermal states. The model undergoes a quantum phase transition between an Ising phase with a nonvanishing magnetization and a cluster phase characterized by a string order. Any two-spin entanglement is found to vanish in both quantum phases because of a… 
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77 References

On the critical behavior of the Ising model with mixed two- and three-spin interactions

A study is made of a two-dimensional Ising model with staggered three-spin interactions in one direction and two-spin interactions in the other. The phase diagram of the model and its critical…

Phase transitions and localizable entanglement in cluster-state spin chains with Ising couplings and local fields

We consider a one-dimensional spin chain for which the ground state is the cluster state, capable of functioning as a quantum computational wire when subjected to local adaptive measurements of…

Three-spin interactions in optical lattices and criticality in cluster Hamiltonians.

We demonstrate that in a triangular configuration of an optical lattice of two atomic species a variety of novel spin-1/2 Hamiltonians can be generated. They include effective three-spin interactions…

Thermal quantum and classical correlations and entanglement in the XY spin model with three-spin interaction

Pairwise quantum discord (QD) and classical correlation (CC) are studied in the XY spin chain with three-spin interaction. We analyze their capability in detecting quantum phase transitions (QPTs) at…

Localizable Entanglement

We consider systems of interacting spins and study the entanglement that can be localized , on average, between two separated spins by performing local measurements on the remaining spins. This…

Entanglement in quantum critical phenomena.

The results establish a precise connection between concepts of quantum information, condensed matter physics, and quantum field theory, by showing that the behavior of critical entanglement in spin systems is analogous to that of entropy in conformal field theories.

Quantum computation on the edge of a symmetry-protected topological order.

This work shows that the logical information of a universal quantum computer can be written and processed perfectly on the edge state of the system, supported by the persistent entanglement from the bulk even when the ground state and its evolution cannot be exactly analyzed.

Two Soluble Models of an Antiferromagnetic Chain

Analytic relations between localizable entanglement and string correlations in spin systems.

It is proved that a general class of spin-1 systems, which includes the Heisenberg model, can be used as a perfect quantum channel.

The Spin-Spin Correlation Function in the Two-Dimensional Ising Model in a Magnetic Field at $T=T_c$

...