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arXiv · 1204.5769

Scaling behavior for a class of quantum phase transitions

Wen-ge Wang·Pinquan Qin·Qian Wang·Giuliano Benenti·Giulio Casati
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Abstract

We show that for quantum phase transitions with a single bosonic zero mode at the critical point, like the Dicke model and the Lipkin-Meshkov-Glick model, metric quantities such as fidelity, that is, the overlap between two ground states corresponding to two values $λ_1$ and $λ_2$ of the controlling parameter $λ$, only depend on the ratio $η=(λ_1-λ_c)/(λ_2-λ_c)$, where $λ=λ_c$ at the critical point. Such scaling property is valid also for time-dependent quantities such as the Loschmidt echo, provided time is measured in units of the inverse frequency of the critical mode.

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Wen-ge Wang, Pinquan Qin, Qian Wang, Giuliano Benenti, Giulio Casati. 2012-08-28. Scaling behavior for a class of quantum phase transitions. https://doi.org/10.1103/physreve.86.021124

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