Amplitude Mode in Quantum Magnets via Dimensional Crossover

TL;DR

This paper explores the Higgs amplitude mode in quantum magnets by using a quasi-one-dimensional approach, combining simulations and theoretical models to observe and distinguish it from other excitations.

Contribution

It demonstrates the emergence of the amplitude mode in quasi-1D quantum magnets and identifies it with sine-Gordon breathers, providing new insights into its detection.

Findings

Amplitude mode observed in longitudinal spin susceptibility.

Amplitude and bond fluctuations carry significant spectral weight in quasi-1D.

Amplitude mode corresponds to the second breather in sine-Gordon theory.

Abstract

We investigate the amplitude (Higgs) mode associated with longitudinal fluctuations of the order parameter at the continuous spontaneous symmetry breaking phase transition. In quantum magnets, due to the fast decay of the amplitude mode into low-energy Goldstone excitations, direct observation of this mode represents a challenging task. By focusing on a quasi-one-dimensional geometry, we circumvent the difficulty and investigate the amplitude mode in a system of weakly coupled spin chains with the help of quantum Monte Carlo simulations, stochastic analytic continuation, and a chain-mean field approach combined with a mapping to the field-theoretic sine-Gordon model. The amplitude mode is observed to emerge in the longitudinal spin susceptibility in the presence of a weak symmetry-breaking staggered field. A conventional measure of the amplitude mode in higher dimensions, the singlet bond mode, is found to appear at a lower than the amplitude mode frequency. We identify these two excitations with the second (first) breather of the sine-Gordon theory, correspondingly. In contrast to higher-dimensional systems, the amplitude and bond order fluctuations are found to carry significant spectral weight in the quasi-1D limit.