Spin parity and broken symmetry in finite spin-1/2 chains with frustrated exchange: quantum transition from high to low spin

Abstract

Exact diagonalization of finite spin-1/2 chains with periodic boundary conditions is applied to the ground state (gs) of chains with ferromagnetic (F) exchange $J_1<0$between first neighbors, antiferromagnetic (AF) exchange $J_2=\hat{I}\pm J_1>0$between second neighbors, and axial anisotropy $0\le \hat{I}”\le 1$. In zero field, the gs is in the $S_z=0$ sector for the relevant parameters and is doubly degenerate at multiple points ${\hat{I}}_m^3=(\hat{I}{\pm }_m,\hat{I}{”}_m)$ in the $\hat{I}\pm$, $\hat{I}”$ plane. Degeneracy under inversion at sites or spin parity or both leads, respectively, to a bond order wave (BOW), to staggered magnetization or to vector chiral (VC) order. Exact results up to $N=28$ spins directly yield order parameters and spin correlation functions whose weak N dependencies allow inferences about infinite chains. The high-spin gs at $J_2=0$ changes discontinuously at ${\hat{I}}_1^3=(-1/4,1)$ to a singlet in the isotropic ($\hat{I}”=1$) chain. The transition from high to low spin $S(\hat{I}\pm ,\hat{I}”)$ is continuous for $\hat{I}”<\hat{I}{”}_B=0.95\pm 0.01$ on the degeneracy line $\hat{I}{\pm }_1(\hat{I}”)$. The gs has staggered magnetization between $\hat{I}{”}_A=0.72$ and $\hat{I}{”}_B$, and a BOW for $\hat{I}”<\hat{I}{”}_A$. When both inversion and spin parity are reversed at ${\hat{I}}_m^3$, the correlation functions $C(p)$ for spins separated by $p$ sites are identical. $C(p)$ minima are shifted by $\ddot{I}€/2$ from the minima of VC order parameters at separation $p$, consistent with right and left-handed helices along the z axis and spins in the xy plane. Degenerate gs of finite chains are related to quantum phase diagrams of extended $\hat{I}\pm$, $\hat{I}”$ chains, with good agreement for order parameters along the line $\hat{I}{\pm }_1(\hat{I}”)$.

9 pages, 10 figures, Phys. Rev. B (In Press)