Adiabatic quantum dynamics of the Lipkin-Meshkov-Glick model

Details Adiabatic quantum dynamics of the Lipkin-Meshkov-Glick model Adiabatic quantum dynamics of the Lipkin-Meshkov-Glick model

2008-06-27

arxiv.org/abs/0806.4455v2

Phys. Rev. B 78, 104426 (2008)

Physics

Condensed Matter

Statistical Mechanics

8 pages, 7 figures. (v2) minor revisions, published version

Scientific paper

10.1103/PhysRevB.78.104426

The adiabatic quantum evolution of the Lipkin-Meshkov-Glick (LMG) model across its quantum critical point is studied. The dynamics is realized by linearly switching the transverse field from an initial large value towards zero and considering different transition rates. We concentrate our attention on the residual energy after the quench in order to estimate the level of diabaticity of the evolution. We discuss a Landau-Zener approximation of the finite size LMG model, that is successful in reproducing the behavior of the residual energy as function of the transition rate in the most part of the regimes considered. We also support our description through the analysis of the entanglement entropy of the evolved state. The system proposed is a paradigm of infinite-range interaction or high-dimensional models.

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