Quantum critical scaling of fidelity susceptibility

A. Fabricio Albuquerque, Fabien Alet, Clément Sire, and Sylvain Capponi
Phys. Rev. B 81, 064418 – Published 18 February 2010

Abstract

The behavior of the ground-state fidelity susceptibility in the vicinity of a quantum critical point is investigated. We derive scaling relations describing its singular behavior in the quantum critical regime. Unlike in previous studies, these relations are solely expressed in terms of conventional critical exponents. We also describe in detail a quantum Monte Carlo scheme that allows for the evaluation of the fidelity susceptibility for a large class of many-body systems and apply it in the study of the quantum phase transition for the transverse-field Ising model on the square lattice. Finite-size analysis applied to the so-obtained numerical results confirms the validity of our scaling relations. Furthermore, we analyze the properties of a closely related quantity, the ground-state energy’s second derivative, which can be numerically evaluated in a particularly efficient way. The usefulness of both quantities as alternative indicators of quantum criticality is examined.

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  • Received 18 December 2009

DOI:https://doi.org/10.1103/PhysRevB.81.064418

©2010 American Physical Society

Authors & Affiliations

A. Fabricio Albuquerque, Fabien Alet, Clément Sire, and Sylvain Capponi

  • Laboratoire de Physique Théorique, (IRSAMC), Université de Toulouse (UPS), F-31062 Toulouse, France and LPT (IRSAMC), CNRS, F-31062 Toulouse, France

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Issue

Vol. 81, Iss. 6 — 1 February 2010

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