arXiv:2411.03967 · Physical Review A

Quantum geometry in many-body systems with precursors of criticality

Jan Střeleček, Pavel Cejnar

Published Jan 15, 2025• 5 citations

Abstract

We analyze the geometry of the ground-state manifold in parameter-dependent many-body systems with quantum phase transitions (QPTs) and describe finite-size precursors of the singular geometry emerging at the QPT boundary in the infinite-size limit. In particular, we elucidate the role of diabolic points in the formation of first-order QPTs, showing that these isolated geometric singularities represent seeds generating irregular behavior of geodesics in finite systems. We also demonstrate that established approximations, namely the mean-field approximation in many-body systems composed of mutually interacting bosons and the two-level approximation near a diabolic point, are insufficient to provide a reliable description of geometry. The outcomes of the general analysis are tested and illustrated by a specific bosonic model from the Lipkin-Meshkov-Glick family.

DOI: 10.1103/physreva.111.012211

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