Scaling behavior for a class of quantum phase transitions

Wen-ge Wang, Pinquan Qin, Qian Wang, Giuliano Benenti, Giulio Casati

Published 2012-04-25, updated 2012-08-28Version 2

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 $\lambda_1$ and $\lambda_2$ of the controlling parameter $\lambda$, only depend on the ratio $\eta=(\lambda_1-\lambda_c)/(\lambda_2-\lambda_c)$, where $\lambda=\lambda_c$ 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.