Geometric Phase Transitions via Spectral Density Analysis

Jincheng Zhang

Published Sep 5, 2026• 0 citations

Abstract

This paper investigates the application of spectral density analysis to quantify geometric phase transitions within complex systems. Traditional approaches often rely on complex numerical simulations, limiting accessibility and hindering thorough investigation. We propose a novel algorithm that extracts the spectral density of a system's geometry, correlating it with the onset of phase transitions, offering a direct and quantitative mapping of transition behavior. The algorithm's design incorporates a refined approach to identifying and characterizing the geometry-transition relationship, addressing limitations of existing methods. The primary goal is to establish a robust and mathematically rigorous framework for understanding geometric phase transitions, facilitating new insights into fundamental physical phenomena.

DOI: 10.5281/zenodo.22315132

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