Scaling of temporal correlations in an attractive Tomonaga-Luttinger spin liquid

TL;DR

This study demonstrates that the local dynamic structure factor in a quantum spin ladder exhibits temperature-dependent scaling consistent with an attractive Tomonaga-Luttinger liquid, confirmed by neutron scattering and numerical calculations.

Contribution

First experimental verification of attractive Tomonaga-Luttinger liquid scaling in a quantum spin ladder using neutron scattering and DMRG simulations.

Findings

Measured Luttinger parameter K ≈ 1.25

Observed scaling form matches theoretical predictions

Excellent agreement between experiment and numerical models

Abstract

We report temperature-dependent neutron scattering measurements of the local dynamic structure factor in the quantum spin ladder (C$_{7}$H$_{10}$N)$_{2}$CuBr$_{4}$ in a magnetic field $H=9$~T, in its gapless quantum-critical phase. We show that the measured quantity has a scaling form consistent with expectations for a Tomonaga-Luttinger liquid with attraction. The measured Luttinger parameter $K\approx1.25$ and scaling function are in excellent agreement with density matrix renormalization group numerical calculations for the underlying spin Hamiltonian.