Higgs and Nambu-Goldstone modes in a spin-1 \textit{XY} model with long-range interactions

TL;DR

This paper analyzes collective excitations, including Higgs and Nambu-Goldstone modes, in a long-range interacting spin-1 XY model, revealing suppressed Higgs damping and proposing experimental probing methods.

Contribution

It provides an analytical study of Higgs and NG modes in a long-range spin-1 XY model, highlighting the effects of algebraic decay on their dispersion and damping.

Findings

Higgs mode exhibits linear dispersion at two dimensions for dipole-like interactions.

Damping of the Higgs mode is significantly suppressed by long-range interactions.

Proposes experimental methods to excite and detect the Higgs mode in Rydberg-atom systems.

Abstract

We theoretically study the collective excitations in a spin-1 $XY$ model with a quadratic Zeeman term and a long-range interaction that decays algebraically with the distance. Using the quantum-field theory based on the finite-temperature Green's function formalism, we analyze properties of the Nambu-Goldstone (NG) and Higgs modes in order to analytically evaluate the damping rate of the Higgs mode in the $XY$ ferromagnetic ordered phase near the quantum phase transition to the disordered phase. When the power of the algebraic decay is 3 as in the case of dipole-dipole interactions in Rydberg-atom systems, we show that at two dimensions the excitation energy of the Higgs mode exhibits a linear dispersion whereas the dispersion of the NG mode becomes proportional to the square root of the momentum. We find that the damping of the Higgs mode is significantly suppressed by the long-range interaction. We also propose how to excite and probe the Higgs mode in Rydberg-atom experiments.