Estimation of field dependent Luttinger parameter in a single crystal of a Tomonaga-Luttinger liquid C14H18CuN4O10 via muon spin rotation

The ground state of a spin ½ Heisenberg antiferromagnetic chain is a Tomonaga-Luttinger liquid (TLL) where quantum mechanical fluctuations do not allow for long range order even at T = 0 K. The TLL is quantum critical with respect to an applied magnetic field upto a saturation field Hs above which it transforms to a fully polarized state. The excitation spectra of the TLL is gapless comprising spin ½ interacting fermions known as spinons. The statics and dynamics of the spinons can be understood in terms of two parameters, namely, the Luttinger parameter K, which quantifies the interaction strength between spinons, and the Fermi velocity u, which links energy and momentum of the low-energy dynamics. C14H18CuN4O10 has been shown to be an excellent realization of a TLL with an exchange coupling constant J/kB = 1.23 K and a moderate value of Hs = 1.72 T. By doing a field dependent muon spin rotation measurement on C14H18CuN4O10, we wish to estimate the field variation of K, and consequently, the kind of interaction (repulsive/attractive) that may be at play.