Visualizing Quantum Phases And Identifying Quantum Phase Transitions By Nonlinear Dimensionality Reduction

TL;DR

This paper introduces a visualization approach using nonlinear dimensionality reduction and machine learning to identify quantum phases and phase transitions directly from ground state distributions without prior knowledge.

Contribution

It proposes a novel visualization method that maps quantum states in Hilbert space to identify phases and transitions, bypassing the need for predefined order parameters.

Findings

Successfully distinguishes different quantum phases

Effectively detects quantum phase transitions

Applicable to complex strongly correlated systems

Abstract

Identifying quantum phases and phase transitions is key to understand complex phenomena in statistical physics. In this work, we propose an unconventional strategy to access quantum phases and phase transitions by visualization based on the distribution of ground states in Hilbert space. By mapping the quantum states in Hilbert space onto a two-dimensional feature space using an unsupervised machine learning method, distinct phases can be directly specified and quantum phase transitions can be well identified. Our proposal is benchmarked on gapped, critical, and topological phases in several strongly correlated spin systems. As this proposal directly learns quantum phases and phase transitions from the distributions of the quantum states, it does not require priori knowledge of order parameters of physical systems, which thus indicates a perceptual route to identify quantum phases and phase transitions particularly in complex systems by visualization through learning.