Topology Obstructs Pure Foundation Neural Quantum States

2026-09-07

AI Summary

研究解决了纯态基础模型在非平凡基态丛的有隙哈密顿量族中表征拓扑障碍的问题，提出使用算子值模型来避免这些障碍。

Abstract

Foundation models for ground states in spin-1/2 systems are a promising method for problems ranging from quantum chemistry to identifying new phase diagrams. Nearly all such models are currently pure-states that condition on the Hamiltonian's parameters, whose Monte Carlo samples give energy estimates according to the variational principle. In this contribution, we show that this representation is topologically obstructed. For any gapped Hamiltonian family whose ground-state bundle is non-trivial, every continuous normalized state-vector model has zero fidelity with the ground state at some parameter value in the Hamiltonian family. For that value, the energy is at least one spectral gap, $\Delta$, with an $O(\Delta)$ gap in an open-neighbourhood of that point. We show that this is a sufficient no-go also in the case of degenerate ground-state manifolds, time dynamics, and periodic systems with mixed space-time topology, demonstrating these obstructions on one- and two-qubit systems. We discuss how this causes a spike in the fidelity susceptibility, giving a numerical signature of a phase-transition where there is none. We then show that operator-valued models canonically avoid these obstructions and preserve topological information, implying a structural necessity in representation for foundation neural quantum states.

Problem

• Topology
• Foundation Models
• Quantum States
• Spin-1/2 Systems
• Hamiltonian

Innovation

• topological obstruction
• operator-valued models
• ground-state bundle