Criticality, factorization, and long-range correlations in the anisotropic XY model

Campbell, Steve; Richens, Jonathan; Lo Gullo, Nicola; Busch, Thomas

Criticality, factorization, and long-range correlations in the anisotropic XY model

Files

3535.pdf(3.02 MB)

Published Version

Date

2013

Authors

Campbell, Steve

Richens, Jonathan

Lo Gullo, Nicola

Busch, Thomas

Publisher

American Physical Society

Published Version

10.1103/PhysRevA.88.062305

Abstract

We study the long-range quantum correlations in the anisotropic XY model. By first examining the thermodynamic limit, we show that employing the quantum discord as a figure of merit allows one to capture the main features of the model at zero temperature. Furthermore, by considering suitably large site separations we find that these correlations obey a simple scaling behavior for finite temperatures, allowing for efficient estimation of the critical point. We also address ground-state factorization of this model by explicitly considering finite-size systems, showing its relation to the energy spectrum and explaining the persistence of the phenomenon at finite temperatures. Finally, we compute the fidelity between finite and infinite systems in order to show that remarkably small system sizes can closely approximate the thermodynamic limit.

Keywords

Statistical-mechanics , Broken symmetry , Critical-point , Quantum , Entanglement , State

Citation

Campbell, S., Richens, J., Gullo, N. L. and Busch, T. (2013) 'Criticality, factorization, and long-range correlations in the anisotropic XY model', Physical Review A, 88(6), 062305. (8pp). doi: 10.1103/PhysRevA.88.062305