Mereological Quantum Phase Transitions

• URL: http://arxiv.org/abs/2510.06389v1
• Date: Tue, 07 Oct 2025 19:12:31 GMT
• Title: Mereological Quantum Phase Transitions
• Authors: Paolo Zanardi, Emanuel Dallas, Faidon Andreadakis,
• Abstract summary: We introduce the concept of mereological quantum phase transition (m-QPTs)<n>We illustrate this framework through analytical examples involving quantum coherence and operator entanglement.
• Score: 0.0
• License: http://creativecommons.org/licenses/by-sa/4.0/
• Abstract: We introduce the novel concept of mereological quantum phase transition (m-QPTs). Our framework is based on a variational family of operator algebras defining generalized tensor product structures (g-TPS), a parameter-dependent Hamiltonian, and a quantum scrambling functional. By minimizing the scrambling functional, one selects a g-TPS, enabling a pullback of the natural information-geometric metric on the g-TPS manifold to the parameter space. The singularities of this induced metric -- so-called algebra susceptibility -- in the thermodynamic limit characterize the m-QPTs. We illustrate this framework through analytical examples involving quantum coherence and operator entanglement. Moreover, spin-chains numerical simulations show susceptibility sharp responses at an integrability point and strong growth across disorder-induced localization, suggesting critical reorganizations of emergent subsystem structure aligned with those transitions.

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