# Tomonaga-Luttinger Liquid Behavior and Spinon Confinement in YbAlO$_3$

## TL;DR

This paper reports on YbAlO$_3$, a rare-earth perovskite that exhibits quantum spin chain behavior, including Tomonaga-Luttinger liquid properties and spinon confinement-deconfinement transitions, advancing experimental understanding of low-dimensional quantum magnets.

## Contribution

It demonstrates that YbAlO$_3$ is a rare-earth magnet realizing both Tomonaga-Luttinger liquid behavior and spinon confinement, providing experimental insights into low-dimensional quantum physics.

## Key findings

- YbAlO$_3$ exhibits Tomonaga-Luttinger liquid behavior.
- YbAlO$_3$ shows spinon confinement-deconfinement transitions.
- Experimental phase diagram reveals different magnetic regimes.

## Abstract

Low dimensional quantum magnets are interesting because of the emerging collective behavior arising from strong quantum fluctuations. The one-dimensional (1D) S = 1/2 Heisenberg antiferromagnet is a paradigmatic example, whose low-energy excitations, known as spinons, carry fractional spin S = 1/2. These fractional modes can be reconfined by the application of a staggered magnetic field. Even though considerable progress has been made in the theoretical understanding of such magnets, experimental realizations of this low-dimensional physics are relatively rare. This is particularly true for rare-earth based magnets because of the large effective spin anisotropy induced by the combination of strong spin-orbit coupling and crystal field splitting. Here, we demonstrate that the rare-earth perovskite YbAlO$_3$ provides a realization of a quantum spin S = 1/2 chain material exhibiting both quantum critical Tomonaga-Luttinger liquid behavior and spinon confinement-deconfinement transitions in different regions of magnetic field-temperature phase diagram.