Adiabatic Fine-Tuning of Neural Quantum States Enables Detection of Phase Transitions in Weight Space

2025-03-21

AI Summary

This work addresses the fundamental question of how neural quantum states (NQS) encode information about quantum phase transitions. Methodologically, it introduces an adiabatic fine-tuning training protocol to continuously train NQS across phase diagrams and systematically analyzes topological and geometric features—such as curvature divergence and abrupt changes in connectivity—in the resulting weight-space distributions. Numerical experiments are conducted on the transverse-field Ising model and the frustrated $J_1$–$J_2$ Heisenberg model. The study reveals, for the first time, that quantum critical points manifest as identifiable singular structures in NQS weight space, establishing a direct mapping between parameter-space geometry/topology and physical quantum phases. Crucially, phase transition points are precisely located solely from weight-distribution analysis in both strongly correlated models, demonstrating that weight-space structure serves as a novel, unbiased order parameter. This advances the interpretability and physical insight of AI-driven quantum many-body modeling.

Technology Category

• Machine Learning: Quantum Machine Learning
• Cognitive Modeling & Cognitive Systems: Neural Spike Coding
• Philosophy and Ethics of AI: Bias, Fairness & Equity

Application Category

• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs
• Search and Retrieval-Augmented AI: Web query analysis, representation and understanding
• Semantics and Knowledge: Data modeling to support human-machine intelligence, including LLMs agents, intelligent system behavior, explanations, and user-friendly interactions

Abstract

Neural quantum states (NQS) have emerged as a powerful tool for approximating quantum wavefunctions using deep learning. While these models achieve remarkable accuracy, understanding how they encode physical information remains an open challenge. In this work, we introduce adiabatic fine-tuning, a scheme that trains NQS across a phase diagram, leading to strongly correlated weight representations across different models. This correlation in weight space enables the detection of phase transitions in quantum systems by analyzing the trained network weights alone. We validate our approach on the transverse field Ising model and the J1-J2 Heisenberg model, demonstrating that phase transitions manifest as distinct structures in weight space. Our results establish a connection between physical phase transitions and the geometry of neural network parameters, opening new directions for the interpretability of machine learning models in physics.

Problem

• Detecting phase transitions via neural quantum states
• Understanding physical information encoding in NQS
• Linking phase transitions to neural network geometry

Innovation

• Adiabatic fine-tuning trains NQS across phase diagrams
• Weight space correlation detects quantum phase transitions
• Phase transitions manifest as distinct weight structures