Metric response of relative entropy: a universal indicator of quantum criticality

• URL: http://arxiv.org/abs/2509.22515v1
• Date: Fri, 26 Sep 2025 15:58:00 GMT
• Title: Metric response of relative entropy: a universal indicator of quantum criticality
• Authors: Pritam Sarkar, Diptiman Sen, Arnab Sen,
• Abstract summary: We show that fidelity susceptibility diverges at quantum critical points (QCPs) in the thermodynamic limit.<n>We demonstrate distinct scaling behaviors for the peak of the QRE susceptibility as a function of $N$.<n>This susceptibility encodes uncertainty of entanglement Hamiltonian gradients and is also directly connected to other information measures such as Petz-R'enyi entropies.
• Score: 8.746991125888744
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: The information-geometric origin of fidelity susceptibility and its utility as a universal probe of quantum criticality in many-body settings have been widely discussed. Here we explore the metric response of quantum relative entropy (QRE), by tracing out all but $n$ adjacent sites from the ground state of spin chains of finite length $N$, as a parameter of the corresponding Hamiltonian is varied. The diagonal component of this metric defines a susceptibility of the QRE that diverges at quantum critical points (QCPs) in the thermodynamic limit. We study two spin-$1/2$ models as examples, namely the integrable transverse field Ising model (TFIM) and a non-integrable Ising chain with three-spin interactions. We demonstrate distinct scaling behaviors for the peak of the QRE susceptibility as a function of $N$: namely a square logarithmic divergence in TFIM and a power-law divergence in the non-integrable chain. This susceptibility encodes uncertainty of entanglement Hamiltonian gradients and is also directly connected to other information measures such as Petz-R\'enyi entropies. We further show that this susceptibility diverges even at finite $N$ if the subsystem size, $n$, exceeds a certain value when the Hamiltonian is tuned to its classical limits due to the rank of the RDMs being finite; unlike the divergence associated with the QCPs which require $N \rightarrow \infty$.

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