# Tomonaga-Luttinger liquid spin dynamics in the quasi-one dimensional Ising-like antiferromagnet BaCo$_2$V$_2$O$_8$

## TL;DR

This study combines neutron scattering and simulations to explore the spin dynamics of BaCo$_2$V$_2$O$_8$, revealing a quantum phase transition and Luttinger liquid behavior in a quasi-one-dimensional Ising antiferromagnet.

## Contribution

It provides experimental evidence of Tomonaga-Luttinger liquid behavior in a real material undergoing a quantum phase transition under magnetic field.

## Key findings

- Observation of a quantum phase transition at 3.8 T
- Reconfiguration of spin dynamics near the critical field
- Emergence of longitudinal excitations characteristic of Luttinger liquids

## Abstract

Combining inelastic neutron scattering and numerical simulations, we study the quasi-one dimensional Ising anisotropic quantum antiferromagnet \bacovo\ in a longitudinal magnetic field. This material shows a quantum phase transition from a N\'eel ordered phase at zero field to a longitudinal incommensurate spin density wave at a critical magnetic field of 3.8 T. Concomitantly the excitation gap almost closes and a fundamental reconfiguration of the spin dynamics occurs. These experimental results are well described by the universal Tomonaga-Luttinger liquid theory developed for interacting spinless fermions in one dimension. We especially observe the rise of mainly longitudinal excitations, a hallmark of the unconventional low-field regime in Ising-like quantum antiferromagnet chains.