Correlation functions and excitation spectrum of the frustrated ferromagnetic spin-$\frac{1}{2}$ chain in an external magnetic field

Magnetic field effects on the one-dimensional frustrated ferromagnetic chain are studied by means of effective field-theory approaches in combination with numerical calculations utilizing Lanczos diagonalization and the density matrix renormalization group method. The nature of the ground state is shown to change from a spin-density-wave region to a nematiclike one upon approaching the saturation magnetization. The excitation spectrum is analyzed, and the behavior of the single-spin-flip excitation gap is studied in detail, including the emergent finite-size corrections.

Figure 1

(Color online) Correlation functions at $J_1=-J_2<0$ and magnetization $M=3∕8$: (a) longitudinal component $S_x^z$, (b) transverse component $S_x^{\pm }$, and (c) spin nematic $S_x^{\pm }{S}_{x+1}^{\pm }$. $x$ is the distance in a single-chain notation. ED results for periodic boundary conditions are shown by symbols, and fits by lines. Note the logarithmic scale of the vertical axis in panel (b).

Figure 2

(Color online) Density matrix renormalization group results for the gaps at $J_1=-0.3$ $J_2<0$ as a function of magnetization $M$. Panel (a) shows the single-spin excitation gap [Eq. (16)], and panel (b) the finite-size gap [Eq. (19)] for two flipped spins multiplied by the chain length $L$.

Figure 3

(Color online) Numerical dispersion spectrum in the subspaces of odd $S^z$ computed for $L=24$ and $J_1=-J_2<0$. The wave vector is given relative to the ground-state wave vector (0 for $S^z=0$, 4, 8 and $\pi$ for $S^z=2,6$).