Speak so a physicist can understand you! TetrisCNN for detecting phase transitions and order parameters

TL;DR

This paper introduces TetrisCNN, a convolutional neural network that not only detects phases in spin systems but also expresses their key properties, called order parameters, in a symbolic, interpretable form, enhancing understanding of quantum phases.

Contribution

The novel TetrisCNN architecture combines multiple kernels to detect phases and explicitly express order parameters, bridging neural network detection with traditional physics descriptors.

Findings

TetrisCNN accurately detects phases in 1D transverse-field Ising model.

It can identify complex order parameters in 2D Ising gauge theory.

The model provides interpretable, symbolic expressions for order parameters.

Abstract

Recently, neural networks (NNs) have become a powerful tool for detecting quantum phases of matter. Unfortunately, NNs are black boxes and only identify phases without elucidating their properties. Novel physics benefits most from insights about phases, traditionally extracted in spin systems using spin correlators. Here, we combine two approaches and design TetrisCNN, a convolutional NN with parallel branches using different kernels that detects the phases of spin systems and expresses their essential descriptors, called order parameters, in a symbolic form based on spin correlators. We demonstrate this on the example of snapshots of the one-dimensional transverse-field Ising model taken in various bases. We show also that TetrisCNN can detect more complex order parameters using the example of two-dimensional Ising gauge theory. This work can lead to the integration of NNs with quantum simulators to study new exotic phases of matter.