# The Higgs Mode of Planar Coupled Spin-Ladders and its Observation in C$_9$H$_{18}$N$_2$CuBr$_4$

## TL;DR

This paper combines neutron scattering experiments and large-scale quantum Monte Carlo simulations to analyze the Higgs mode in a two-dimensional quantum spin ladder compound, revealing its evolution from classical to quantum limits.

## Contribution

It provides a detailed theoretical analysis of the Higgs mode in planar coupled spin-ladders, matching experimental data and tracing its evolution across different quantum regimes.

## Key findings

- Quantitative agreement with neutron scattering data
- Evolution of the Higgs mode from bound state to overdamped continuum
- Identification of the continuous transition from classical to quantum behavior

## Abstract

Polarized inelastic neutron scattering experiments recently identified the amplitude (Higgs) mode in C$_9$H$_{18}$N$_2$CuBr$_4$, a two-dimensional near-quantum-critical spin-1/2 two-leg ladder compound, which exhibits a weak easy-axis exchange anisotropy. Here, we theoretically examine the dynamic spin structure factor of such planar coupled spin-ladder systems using large-scale quantum Monte Carlo simulations. This allows us to provide a quantitative account of the experimental neutron scattering data within a consistent quantum spin model. Moreover, we trance the details of the continuous evolution of the amplitude mode from a two-particle bound state of coupled ladders in the classical Ising limit all the way to the quantum spin-1/2 Heisenberg limit with fully restored SU(2) symmetry, where it gets overdamped by the two-magnon continuum in neutron scattering.