Fermi liquid of spinons in quasi-one-dimensional antiferromagnets

We report the experimental observation of a shift of the boundaries of the spinon continuum caused by a Fermi-liquid interaction of spinons in the spin-liquid $S=1/2$ chain-type antiferromagnet K$_2$CuSO$_4$Br$_2$. The parameter of spinon interaction, which determines the probability of backscattering, is found. In the pseudospin $S=1/2$ chain-type strongly anisotropic antiferromagnet Cs$_2$CoCl$_4$, a shift in the magnetic resonance frequency is detected during the crossover from the disordered spin regime to the state of correlated XXZ-type spin chains at a temperature above the emergence of long-range antiferromagnetic order. This resonance shift is explained on the basis of the spectrum of spin excitations in correlated XXZ chains and corresponds to theoretical simulation of the spectra of spinon-type magnetic fluctuations in XXZ chains [P. Laurell et al. Phys. Rev. Lett. 127 037201 (2021)].