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-$\frac{1}{2}$ zigzag chains. In this Rapid Communication, 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-$\frac{1}{2}$ 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.

Figure 1

(Color online) Temperature and field dependence of the NMR relaxation rate $1/T_1$ in (a) multipolar phases in spin-$\frac{1}{2}$-frustrated zigzag chains and in (b) standard TL liquids (e.g., the AF Heisenberg chain in magnetic field). The parameter $K$ controls correlations in TL liquids (see the text).

Figure 2

(Color online) Low-energy relevant parts of $S^{zz}\left(k,\omega \right)$ and $S^{+-}\left(k,\omega \right)$ in the multipolar and ${\text{SDW}}_p$ phases of the spin-$\frac{1}{2}$-frustrated zigzag chain in magnetic field [(a)–(c) and (e)] and in the TL liquid of spin-$\frac{1}{2}$ AF chains in magnetic field [(d) and (f)].