Interpretable correlator Transformer for image-like quantum matter data

TL;DR

The paper introduces the correlator Transformer (CoTra), an interpretable neural network that classifies quantum phases of matter by learning and revealing physical correlation functions, effectively capturing both local and non-local structures.

Contribution

The novel CoTra architecture combines attention mechanisms with interpretability to identify and analyze complex correlation patterns in quantum matter data.

Findings

Successfully detects local order in the Heisenberg antiferromagnet

Identifies gauge constraints in lattice gauge theories

Distinguishes percolating from non-percolating images

Abstract

Due to their inherent capabilities of capturing non-local dependencies, Transformer neural networks have quickly been established as the paradigmatic architecture for large language models and image processing. Next to these traditional applications, machine learning methods have also been demonstrated to be versatile tools in the analysis of image-like data of quantum phases of matter, e.g. given snapshots of many-body wave functions obtained in ultracold atom experiments. While local correlation structures in image-like data of physical systems can reliably be detected, identifying phases of matter characterized by global, non-local structures with interpretable machine learning methods remains a challenge. Here, we introduce the correlator Transformer (CoTra), which classifies different phases of matter while at the same time yielding full interpretability in terms of physical correlation functions. The network's underlying structure is a tailored attention mechanism, which learns efficient ways to weigh local and non-local correlations for a successful classification. We demonstrate the versatility of the CoTra by detecting local order in the Heisenberg antiferromagnet, and show that local gauge constraints in one- and two-dimensional lattice gauge theories can be identified. Furthermore, we establish that the CoTra reliably detects non-local structures in images of correlated fermions in momentum space (Cooper pairs) and that it can distinguish percolating from non-percolating images.