Singularities in fidelity surfaces for quantum phase transitions: a geometric perspective

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dc.creatorZhou, Huan-Qiang
dc.creatorZhao, Jian-Hui
dc.creatorWang, Hong-Lei
dc.creatorLi, Bo
dc.date2007-11-29
dc.date.accessioned2026-07-07T08:45:59Z
dc.date.available2026-07-07T08:45:59Z
dc.descriptionThe fidelity per site between two ground states of a quantum lattice system corresponding to different values of the control parameter defines a surface embedded in a Euclidean space. The Gaussian curvature naturally quantifies quantum fluctuations that destroy orders at transition points. It turns out that quantum fluctuations wildly distort the fidelity surface near the transition points, at which the Gaussian curvature is singular in the thermodynamic limit. As a concrete example, the one-dimensional quantum Ising model in a transverse field is analyzed. We also perform a finite size scaling analysis for the transverse Ising model of finite sizes. The scaling behavior for the Gaussian curvature is numerically checked and the correlation length critical exponent is extracted, which is consistent with the conformal invariance at the critical point.
dc.description4+ pages, 3 figures
dc.identifierhttps://arxiv.org/abs/0711.4651
dc.identifierhttp://arxiv.org/abs/0711.4651
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/143137
dc.subjectStatistical Mechanics
dc.subjectStrongly Correlated Electrons
dc.titleSingularities in fidelity surfaces for quantum phase transitions: a geometric perspective
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