Dynamical probing of a topological phase of bosons in one dimension

TL;DR

This paper investigates the dynamical response of a one-dimensional topological bosonic phase, the Haldane insulator, using linear response theory and mean-field methods to understand its excitations and phase transitions.

Contribution

It provides a detailed analysis of the absorption spectrum and critical excitations at the topological phase transition in the Haldane insulator, linking theory with microscopic models.

Findings

Absorption spectrum reveals trivial quantum number excitations at the transition.

Critical excitations are particles and holes at zero momentum.

The non-local mean-field approach confirms the spectral predictions.

Abstract

We study the linear response to time-dependent probes of a symmetry-protected topological phase of bosons in one-dimension, the Haldane insulator (HI). This phase is separated from the ordinary Mott insulator (MI) and density-wave (DW) phases by continuous transitions, whose field theoretical description is here reviewed. Using this technique, we compute the absorption spectrum to two types of periodic perturbations and relate the findings to the nature of the critical excitations at the transition between the different phases. The HI-MI phase transition is topological and the critical excitations possess trivial quantum numbers: they correspond to particles and holes at zero momentum. Our findings are corroborated by a non-local mean-field approach, which allows us to directly relate the predicted spectrum to the known microscopic theory.