Identifying Topological Invariants of Non-Hermitian Systems via Domain-Adaptive Multimodal Model for Mathematics

TL;DR

This paper introduces a domain-adaptive multimodal large language model framework that effectively identifies topological invariants in non-Hermitian systems by processing eigenvalues and eigenvectors, advancing computational methods in high-dimensional topological physics.

Contribution

It presents a novel multimodal LLM approach tailored for mathematical physics, specifically for extracting topological invariants from complex quantum systems, with a decoupled reasoning architecture.

Findings

Successfully identified topological invariants in non-Hermitian systems.

Demonstrated improved effectiveness over traditional methods.

Provided a new paradigm for using LLMs in topological physics.

Abstract

The emergence of the non-Hermitian skin effect, distinguished by the exponential localization of bulk states onto boundaries in open systems, has redefined the conventional band theory. It can be established through the generalized Brillouin zone framework, the amoeba formulation or generalized Fermi surface in the different dimensions. However, its algorithmic implementation is still challenging in the high-dimensional cases. The large language models (LLM), functioning as the new paradigm in machine learning, can help tack scientific problems. Here, we propose a framework composed by domain-adaptive Multimodal model for mathematics to identify topological invariants. We feed the eigenvalues and eigenvectors of the Hamiltonian in momentum space into our model as two input modalities. Since our research requires the MLLM to process complex numerical calculations and mathematical reasoning simultaneously, we replace the general reasoning backbone with a specific mathematic LLM. This design decouples front-end physical representation alignment from back-end mathematical inference, allowing our model to extract topological information more effectively. Our results provide a paradigm for future studies on topological invariants identification via LLMs.