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

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