# Unveiling phase transitions with machine learning

## TL;DR

This paper introduces machine learning methods to identify quantum phase transitions, offering a computationally efficient alternative to traditional techniques, demonstrated on the ANNNI model with promising transfer learning capabilities.

## Contribution

It presents a novel machine learning framework for detecting phase transitions using minimal data, including both unsupervised and supervised approaches with transfer learning.

## Key findings

- Unsupervised learning detects three phases in the ANNNI model.
- Supervised learning enables transfer learning for new phases.
- Effective with low-dimensional, small-size data sets.

## Abstract

The classification of phase transitions is a central and challenging task in condensed matter physics. Typically, it relies on the identification of order parameters and the analysis of singularities in the free energy and its derivatives. Here, we propose an alternative framework to identify quantum phase transitions, employing both unsupervised and supervised machine learning techniques. Using the axial next-nearest neighbor Ising (ANNNI) model as a benchmark, we show how unsupervised learning can detect three phases (ferromagnetic, paramagnetic, and a cluster of the antiphase with the floating phase) as well as two distinct regions within the paramagnetic phase. Employing supervised learning we show that transfer learning becomes possible: a machine trained only with nearest-neighbour interactions can learn to identify a new type of phase occurring when next-nearest-neighbour interactions are introduced. All our results rely on few and low dimensional input data (up to twelve lattice sites), thus providing a computational friendly and general framework for the study of phase transitions in many-body systems.