# Entanglement in the XY spin chain

@article{Its2004EntanglementIT, title={Entanglement in the XY spin chain}, author={Alexander Its and Bufan Jin and Vladimir E. Korepin}, journal={Journal of Physics A}, year={2004}, volume={38}, pages={2975-2990} }

We consider the entanglement in the ground state of the XY model of an infinite chain. Following Bennett, Bernstein, Popescu and Schumacher, we use the entropy of a sub-system as a measure of entanglement. Vidal, Latorre, Rico and Kitaev have conjectured that the von Neumann entropy of a large block of neighbouring spins approaches a constant as the size of the block increases. We evaluate this limiting entropy as a function of anisotropy and transverse magnetic field. We use the methods based…

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## References

SHOWING 1-10 OF 55 REFERENCES

### Quantum Spin Chain, Toeplitz Determinants and the Fisher—Hartwig Conjecture

- Physics
- 2004

We consider the one-dimensional quantum spin chain, which is called the XX model (XX0 model or isotropic XY model) in a transverse magnetic field. We are mainly interested in the entropy of a block…

### Natural thermal and magnetic entanglement in the 1D Heisenberg model.

- PhysicsPhysical review letters
- 2001

It is found that the entanglement in an antiferromagnetic chain can be increased by increasing the temperature or the external field, and increasing the field can also createEntanglement between otherwise disentangled spins.

### Diverging entanglement length in gapped quantum spin systems.

- PhysicsPhysical review letters
- 2004

It is proved the existence of gapped quantum Hamiltonians whose ground states exhibit an infinite entanglement length, as opposed to their finite correlation length, and it is reported on evidence that the ground state of an antiferromagnetic chain can be used as a perfect quantum channel if local measurements on the individual spins can be implemented.

### Temperature correlations of quantum spins.

- PhysicsPhysical review letters
- 1993

The problem of the evaluation of asymptotics of temperature correlations is solved and the physical meaning of the result is explained.

### Universality of entropy scaling in one dimensional gapless models.

- PhysicsPhysical review letters
- 2004

An explicit formula for the entropy of the subsystem at any temperature is obtained by means of conformal field theory and the second law of thermodynamics and is universal.

### Entanglement in quantum critical phenomena.

- PhysicsPhysical review letters
- 2003

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.

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

- PhysicsPhysical review letters
- 2004

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…

### Entanglement in a simple quantum phase transition

- Physics
- 2002

What entanglement is present in naturally occurring physical systems at thermal equilibrium? Most such systems are intractable and it is desirable to study simple but realistic systems that can be…

### Universality of entanglement and quantum-computation complexity

- Physics
- 2004

We study the universality of scaling of entanglement in Shor's factoring algorithm and in adiabatic quantum algorithms across a quantum phase transition for both the NP-complete exact cover problem…