Learning quantum phase transitions through Topological Data Analysis

TL;DR

This paper demonstrates how Topological Data Analysis can be used to identify quantum phase transitions in complex systems, validated through simulations of the 2D Anderson and Hubbard models, showing promising results for future quantum research.

Contribution

The paper introduces a novel application of Topological Data Analysis to study quantum phase transitions, validated with unbiased quantum Monte Carlo simulations.

Findings

Quantum critical points match literature values

TDA effectively captures topological features of quantum phases

Method shows potential for analyzing challenging quantum systems

Abstract

We implement a computational pipeline based on a recent machine learning technique, namely the Topological Data Analysis (TDA), that has the capability of extracting powerful information-carrying topological features. We apply such a method to the study quantum phase transitions and, to showcase its validity and potential, we exploit such a method for the investigation of two paramount important quantum systems: the 2D periodic Anderson model and the Hubbard model on the honeycomb lattice, both cases on the half-filling. To this end, we have performed unbiased auxiliary field quantum Monte Carlo simulations, feeding the TDA with snapshots of the Hubbard-Stratonovich fields through the course of the simulations The quantum critical points obtained from TDA agree quantitatively well with the existing literature, therefore suggesting that this technique could be used to investigate quantum systems where the analysis of the phase transitions is still a challenge.