Monotonicity of the scalar curvature of the quantum exponential family for transverse-field Ising chains

DOI10.1007/978-3-031-38299-4_37arXiv2303.12008OpenAlexW4385417187MaRDI QIDQ6179024

Takemi Nakamura

Publication date: 16 January 2024

Published in: Lecture Notes in Computer Science (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2303.12008

zbMATH Keywords

scalar curvatureIsing modelquantum exponential family

Mathematics Subject Classification ID

Applications of differential geometry to physics (53Z05) Quantum equilibrium statistical mechanics (general) (82B10) Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics (82B20)

Cites Work

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• Information geometry of finite Ising models
• On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric
• Quantum Ising phases and transitions in transverse Ising models
• The Bogoliubov inner product in quantum statistics
• Relationship between d-Dimensional Quantal Spin Systems and (d+1)-Dimensional Ising Systems: Equivalence, Critical Exponents and Systematic Approximants of the Partition Function and Spin Correlations
• On the monotonicity of scalar curvature in classical and quantum information geometry
• Information-Theoretic Differential Geometry of Quantum Phase Transitions
• Geometry of canonical correlation on the state space of a quantum system

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