Exploring phases of the Su-Schrieffer-Heeger model with tSNE

TL;DR

This paper demonstrates the use of tSNE to visualize and identify phases in the Su-Schrieffer-Heeger model and its variants, effectively revealing phase diagrams from high-dimensional data.

Contribution

It introduces tSNE as a novel tool for phase diagram visualization in topological models, including non-Hermitian extensions, using wavefunctions and Bloch vectors.

Findings

tSNE effectively visualizes phase regions in the SSH model.

The method works well for non-Hermitian extended models with multiple phases.

Wavefunction data can also be used as input for phase visualization.

Abstract

T-distributed stochastic neighborhood embedding (tSNE) is used as a tool to reveal the phase diagram of the Su-Schrieffer-Heeger model and some of its extended and non-Hermitian variants. Bloch vectors calculated at different points in the parameter space are mapped to a two-dimensional reduced space. The clusters in the reduced space are used to visualize different phase regions included in the input. The tSNE mapping is shown to be effective even in the challenging case of the non-Hermitian extended model where five different phases are present. An example of using wavefunction input, instead of Bloch vectors, is presented also.