Charge Order Stabilized Quantum Spin Liquid in Hollandite K$_2$V$_8$O$_{16}$

TL;DR

This study demonstrates that charge order in Hollandite K$_2$V$_8$O$_{16}$ stabilizes a quantum spin liquid state, confirmed by muon spin relaxation measurements showing persistent spin dynamics down to very low temperatures.

Contribution

It provides the first experimental evidence of a charge order stabilized quantum spin liquid in a Hollandite compound, revealing a gapless Tomonaga-Luttinger liquid behavior in a stoichiometric material.

Findings

No long-range magnetic order observed down to 100 mK.

Relaxation rate remains temperature independent below 2 K.

QSL behavior confirmed by dynamic ground state measurements.

Abstract

Quantum spin liquid is an elusive state that display strong many-body entanglement with potential applications in future quantum computing. This study reports muon spin relaxation ($\mu^+$SR) measurements on a novel high-pressure synthesized material, the Hollandite K$_{2}$V$_8$O$_{16}$. In this quasi-one-dimensional compound, charge ordering (CO) at $T_{\rm MIT}\approx160$~K effectively isolates half of the vanadium chains and model-like Heisenberg spin-1/2 chains are realized. Our zero field $\mu^+$SR measurements show exponential like relaxation down to the lowest temperature $T=100$~mK and the absence of long range ordering is confirmed. The relaxation rate is found to be temperature independent below $T_{\rm QSL}\approx2$~K and measurements in longitudinal field confirms a highly dynamic ground state. These results represents the first confirmation of quantum spin liquid (QSL) behavior within the Hollandite family, stabilized by the CO. Finally, the presence of strong local electron correlation and one dimensional Fermi surface suggest this QSL to be a gapless Tomonaga-Luttinger liquid (TLL), which here uniquely presents itself in a stoichiometric compound under zero applied magnetic field and at ambient pressure.