Quantum information geometry by the ground-state energy and the criticality of the scalar curvature

Takemi Nakamura

Physica A: Statistical Mechanics and its Applications, 2025, vol. 658, issue C

Abstract: We introduce the Hessian of the negative ground-state energy as a Riemannian metric on the parametric family of the ground states of a parameterized Hamiltonian of a quantum system and study the critical behavior of the scalar curvature of this new metric. Taking the anisotropic XY chain in a transverse field as an example, we study the critical behaviors of the scalar curvature associated with the quantum phase transitions both numerically and analytically. The behaviors are found to be different from those of the Fubini–Study metric but in agreement with the scalar curvature for the Bogoliubov–Kubo–Mori metric in thermodynamic geometry from the perspective of the universality class. We also briefly discuss the Legendre structure concerning this Hessian metric.

Keywords: Quantum information geometry; Canonical correlation; Scalar curvature; Quantum phase transitions; Quantum XY chain (search for similar items in EconPapers)
Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:658:y:2025:i:c:s0378437124007969

DOI: 10.1016/j.physa.2024.130286

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