Information geometry of non-equilibrium quantum states: Mixed metric structures on an extended information manifold

Abstract:We discuss an information-geometric framework for characterizing quantum states in non-equilibrium dynamics. Using the transverse-field Ising chain model as a laboratory, we investigate the quantum Fisher information metric with particular emphasis on the mixed metric component $g_{ht}$ and related geometric observables, where $h$ is a controllable post-quench Hamiltonian parameter and $t$ is real time. The framework treats $h$ and $t$ as coordinates of an extended information manifold $(h,t)$. The geometric observables characterize the speed of evolution on the manifold and the alignment between the temporal and parameter-deformation directions. Correlations between these geometric quantities and two widely used measures of non-equilibrium dynamics, the entanglement entropy and the Loschmidt echo, are analyzed.

Quantum Physics (quant-ph); Statistical Mechanics (cond-mat.stat-mech); High Energy Physics - Phenomenology (hep-ph)

arXiv:2609.00977 [quant-ph]

(or arXiv:2609.00977v1 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2609.00977 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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