Particle-hole character of the Higgs and Goldstone modes in strongly-interacting lattice bosons

TL;DR

This paper investigates the particle-hole nature of Higgs and Goldstone modes in strongly-interacting lattice bosons, revealing mode-dependent symmetries and clarifying the behavior of amplitude and phase oscillations across the phase diagram.

Contribution

It introduces a Gutzwiller-based analysis of excitations in the Bose-Hubbard model, uncovering mode-specific particle-hole symmetry and elucidating the nature of Higgs and Goldstone modes away from criticality.

Findings

Mode-dependent particle-hole symmetry on specific phase diagram lines

Identification of pure amplitude Higgs mode behavior away from critical point

Suppression of condensate density oscillations in Goldstone mode

Abstract

We study the low-energy excitations of the Bose-Hubbard model in the strongly-interacting superfluid phase using a Gutzwiller approach and extract the single-particle and single-hole excitation amplitudes for each mode. We report emergent mode-dependent particle-hole symmetry on specific arc-shaped lines in the phase diagram connecting the well-known Lorentz-invariant limits of the Bose-Hubbard model. By tracking the in-phase particle-hole symmetric oscillations of the order parameter, we provide an answer to the long-standing question about the fate of the pure amplitude Higgs mode away from the integer-density critical point. Furthermore, we point out that out-of-phase oscillations are responsible for a full suppression of the condensate density oscillations of the gapless Goldstone mode. Possible detection protocols are also discussed.