NMR relaxation rate and dynamical structure factors in nematic and multipolar liquids of frustrated spin chains under magnetic fields

Recently, it has been shown that spin nematic (quadrupolar) or higher multipolar correlation functions exhibit a quasi long-range order in the wide region of the field-induced Tomonaga-Luttinger-liquid (TLL) phase in spin-1/2 zigzag chains. In this paper, we point out that the temperature dependence of the NMR relaxation rate 1/T_1 in these multipolar TLLs is qualitatively different from that in more conventional TLLs of one-dimensional quantum magnets (e.g., the spin-1/2 Heisenberg chain); 1/T_1 decreases with lowering temperature in multipolar TLL. We also discuss low-energy features in spin dynamical structure factors which are characteristic of the multipolar TLL phases.