Ground-state fidelity in one-dimensional gapless model

Abstract

A general relation between quantum phase transitions and the second derivative of the fidelity (or the "fidelity susceptibility") is proposed. The validity and the limitation of the fidelity susceptibility in characterizing quantum phase transitions is thus established. Moreover, based on the bosonization method, general formulas of the fidelity and the fidelity susceptibility are obtained for a class of one-dimensional gapless systems known as the Tomonaga-Luttinger liquid. Applying these formulas to the one-dimensional spin-1/2 $XXZ$ model, we find that quantum phase transitions, even of the Beresinskii-Kosterlitz-Thouless type, can be signaled by the fidelity susceptibility.

4+ pages, no figure, published version

References in corpus (2)

• Quantum critical scaling of the geometric tensors
• Quantum Phase Transitions and Bipartite Entanglement

Cited by in corpus (7)

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• Intrinsic relation between ground-state fidelity and the characterization of a quantum phase transition
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• Scaling Properties of Fidelity in Spin-one Anisotropic Model
• Fidelity approach to Gaussian transitions
• Ground-state fidelity of Luttinger liquids: A wave functional approach