aqora

Topology and Phase Transitions II. Entropy and Topology

Roberto Franzosi, Marco Pettini

May 20, 20051 citation

Quantum geometry and geometric entanglement entropy of one-dimensional Floquet topological matter

Longwen Zhou

The geometry of quantum states could offer indispensable insights for characterizing the topological properties, phase transitions, and entanglement nature of many-body systems. In this work, we reveal the quantum geometry and the associated entanglement entropy (EE) of Floquet topological states in one-dimensional periodically driven systems. The quantum metric tensors of Floquet states are found to show nonanalytic signatures at topological phase transition points. Away from the transition points, the bipartite geometric EE of Floquet states exhibits an area-law scaling vs the system size, which holds for a Floquet band at any filling fractions. For a uniformly filled Floquet band, the EE further becomes purely quantum geometric. At phase transition points, the geometric EE scales logarithmically with the system size and displays cusps in the nearby parameter ranges. These discoveries are demonstrated by investigating typical Floquet models including periodically driven spin chains, Floquet topological insulators, and superconductors. Our findings uncover the rich quantum geometries of Floquet states, unveiling the geometric origin of EE for gapped Floquet topological phases, and introducing information-theoretic means of depicting topological transitions in Floquet systems.The geometry of quantum states could offer indispensable insights for characterizing the topological properties, phase transitions, and entanglement nature of many-body systems. In this work, we reveal the quantum geometry and the associated entanglement entropy (EE) of Floquet topological states in one-dimensional periodically driven systems. The quantum metric tensors of Floquet states are found to show nonanalytic signatures at topological phase transition points. Away from the transition points, the bipartite geometric EE of Floquet states exhibits an area-law scaling vs the system size, which holds for a Floquet band at any filling fractions. For a uniformly filled Floquet band, the EE further becomes purely quantum geometric. At phase transition points, the geometric EE scales logarithmically with the system size and displays cusps in the nearby parameter ranges. These discoveries are demonstrated by investigating typical Floquet models including periodically driven spin chains, Floquet topological insulators, and superconductors. Our findings uncover the rich quantum geometries of Floquet states, unveiling the geometric origin of EE for gapped Floquet topological phases, and introducing information-theoretic means of depicting topological transitions in Floquet systems.

arXiv:2408.05525Physical review. B./Physical review. BAug 14, 20244 citations

ENTROPY SIGNATURES OF TOPOLOGICAL PHASE TRANSITIONS

Y. M. Galperin

Журнал Экспериментальной и Теоретической ФизикиJan 1, 20182 citations

No Evidence of Golden Ratio Scaling in Disordered Topological Phase Transitions — E8 Intelligence Research

Andrew Stewart Caldin

FINDING: No direct evidence of golden ratio φ² scaling in disordered topological phase transitions found in provided sources. Sources are tangential: finite-size scaling in spin chains, unsupervised ML for topological phases, and a general video on golden ratio. The arXiv paper on XY ferromagnets with random anisotropy does not mention φ or topological transitions. MATH: No equations, constants, or ratios extracted. The arXiv paper (2208.10109v8) studies magnetization M and susceptibility χ vs temperature in 3D XY model with random anisotropy, but provides no specific scaling exponents or φ-related numbers. CONNECTION: No geometric harmony links (0.382, 0.618, 0.786, 1.618, 2.618, base-60, crystallographic symmetry) found in any source. The "Beyond the Golden Ratio" video is a general educational piece, not connected to topological phase transitions. DEPTH: 1 — The search query yielded no relevant mathematical findings. The sources are either unrelated (golden ratio video), too gene Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.comFINDING: No direct evidence of golden ratio φ² scaling in disordered topological phase transitions found in provided sources. Sources are tangential: finite-size scaling in spin chains, unsupervised ML for topological phases, and a general video on golden ratio. The arXiv paper on XY ferromagnets with random anisotropy does not mention φ or topological transitions. MATH: No equations, constants, or ratios extracted. The arXiv paper (2208.10109v8) studies magnetization M and susceptibility χ vs temperature in 3D XY model with random anisotropy, but provides no specific scaling exponents or φ-related numbers. CONNECTION: No geometric harmony links (0.382, 0.618, 0.786, 1.618, 2.618, base-60, crystallographic symmetry) found in any source. The "Beyond the Golden Ratio" video is a general educational piece, not connected to topological phase transitions. DEPTH: 1 — The search query yielded no relevant mathematical findings. The sources are either unrelated (golden ratio video), too gene Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com

Aug 1, 20260 citations

Rényi–Fisher entropy product as a marker of topological phase transitions

Juan Carlos Bolívar, Ágnes Nagy, E. Romera

Physica A Statistical Mechanics and its ApplicationsJan 31, 201819 citations

Topological phase transitions

M. A. Contínentino

Physica B Condensed MatterNov 3, 201625 citations

Scaling and Topological Phase Transitions: Energy vs. Entropy

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