The Lieb excitations and topological flat mode of spectral function of Tonks-Girardeau gas in Kronig-Penney potential

TL;DR

This paper investigates the spectral function of a Tonks-Girardeau gas in a finite Kronig-Penney potential, revealing gapped Lieb excitations and a robust topological flat mode near the Fermi energy, with implications for experimental quantum gases.

Contribution

It demonstrates the emergence of gapped Lieb excitations and a topological flat mode in a Tonks-Girardeau gas within a Kronig-Penney potential, highlighting their robustness and scaling behaviour.

Findings

Lieb-I and Lieb-II excitations can become gapped with increasing barrier height.

A topological flat mode exists near the Fermi energy and is robust to perturbations.

Spectral function exhibits divergent behaviour analyzed through scaling.

Abstract

Lieb excitations are fundamental to the understanding of the low energy behaviour of many-body quantum gases. Here we study the spectral function of a Tonks-Girardeau gas in a finite sized Kronig-Penney potential and show that the Lieb-I and Lieb-II excitations can become gapped as a function of the barrier height. Moreover, we reveal the existence of a topological flat mode near the Fermi energy and at zero momentum and show that this is robust to perturbations in the system. Through a scaling analysis, we determine the divergent behaviour of the spectral function. Our results provide a significant reference for the observation and understanding of the gapped Lieb excitations and the topological flat mode of quantum gases in experimentally realistic subwavelength optical lattice potentials.