Unsupervised Learning of Quantum Phase Transitions for Bose-Hubbard lattice systems

TL;DR

This paper introduces an unsupervised diffusion map method to identify quantum phase transitions in Bose-Hubbard systems, applicable to experimental data without prior knowledge of order parameters.

Contribution

It demonstrates a novel, data-driven approach for detecting complex quantum phases in lattice systems, including topological and nonequilibrium regimes, without handcrafted features.

Findings

Successfully identifies phase transitions in various Bose-Hubbard models.

Detects symmetry-protected topological phases and many-body localization.

Applicable to experimental measurement data from quantum simulators.

Abstract

Characterizing quantum many-body phase structure is a major goal for quantum simulation. Here, we employ an unsupervised learning approach based on diffusion maps to learn phase transitions in bosonic lattice systems described by Bose-Hubbard type models, which can be realized in ultracold atoms and related quantum simulation platforms. We demonstrate that this approach identifies phase structure across distinct settings without prior knowledge of order parameters or handcrafted observables, including ground-state transitions involving symmetry-protected topological phases and nonequilibrium regimes distinguishing ergodic and many-body localized behavior. Our results indicate that the approach has the potential for direct application to experimentally accessible measurement data for learning quantum phases in current quantum simulators.