Detecting topological transitions in two dimensions by Hamiltonian evolution

TL;DR

This paper demonstrates that the evolution of particles in a 2D spin-orbit lattice can identify topological phase transitions through observable changes in particle distribution and density profiles, aiding experimental detection.

Contribution

It introduces a method to detect topological transitions via Hamiltonian evolution, linking band gap closing to measurable distribution features in 2D systems.

Findings

Kink in mean particle width indicates band gap closing.

Characteristic rings in density profiles signal topologically non-trivial phases.

Method applicable to ultracold atoms and photonic lattice experiments.

Abstract

We show that the evolution of two-component particles governed by a two-dimensional spin-orbit lattice Hamiltonian can reveal transitions between topological phases. A kink in the mean width of the particle distribution signals the closing of the band gap, a prerequisite for a quantum phase transition between topological phases. Furthermore, for realistic and experimentally motivated Hamiltonians the density profile in topologically non-trivial phases displays characteristic rings in the vicinity of the origin that are absent in trivial phases. The results are expected to have immediate application to systems of ultracold atoms and photonic lattices.