# Spinon Confinement and a Sharp Longitudinal Mode in Yb$_2$Pt$_2$Pb in Magnetic Fields

## TL;DR

This study uses neutron scattering to explore how magnetic fields induce a transition from a gapped, ordered state to a disordered Luttinger-liquid state in Yb2Pt2Pb, revealing spinon confinement and a novel longitudinal mode.

## Contribution

It demonstrates the magnetic field-driven transition in Yb2Pt2Pb and provides experimental evidence of spinon confinement and a sharp longitudinal mode, supported by theoretical calculations.

## Key findings

- Magnetic field closes the spin gap and induces a Luttinger-liquid state.
- Inter-chain coupling causes spinon confinement similar to quark confinement.
- A gapless, dispersive longitudinal mode emerges from confinement.

## Abstract

The fundamental excitations in an antiferromagnetic chain of spins-1/2 are spinons, de-confined fractional quasiparticles that when combined in pairs, form a triplet excitation continuum. In an Ising-like spin chain the continuum is gapped and the ground state is N{\'e}el ordered. Here, we report high resolution neutron scattering experiments, which reveal how a magnetic field closes this gap and drives the spin chains in \YPP\ to a critical, disordered Luttinger-liquid state. In \YPP\ the effective spins-1/2 describe the dynamics of large, Ising-like Yb magnetic moments, ensuring that the measured excitations are exclusively longitudinal, which we find to be well described by time-dependent density matrix renormalization group calculations. The inter-chain coupling leads to the confinement of spinons, a condensed matter analog of quark confinement in quantum chromodynamics. Insensitive to transverse fluctuations, our measurements show how a gapless, dispersive longitudinal mode arises from confinement and evolves with magnetic order.