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 $J_2=\alpha J_1>0$between second neighbors, and axial anisotropy $0\le \Delta \le 1$. In zero field, the gs is in the $S_z=0$ sector for the relevant parameters and is doubly degenerate at multiple points ${\gamma }_m=({\alpha }_m,{\Delta }_m)$ in the $\alpha$, $\Delta$ 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 ${\gamma }_1=(-1/4,1)$ to a singlet in the isotropic ($\Delta =1$) chain. The transition from high to low spin $S(\alpha ,\Delta )$ is continuous for $\Delta <{\Delta }_B=0.95\pm 0.01$ on the degeneracy line ${\alpha }_1(\Delta )$. The gs has staggered magnetization between ${\Delta }_A=0.72$ and ${\Delta }_B$, and a BOW for $\Delta <{\Delta }_A$. When both inversion and spin parity are reversed at ${\gamma }_m$, the correlation functions $C(p)$ for spins separated by $p$ sites are identical. $C(p)$ minima are shifted by $\pi /2$ 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 $\alpha$, $\Delta$ chains, with good agreement for order parameters along the line ${\alpha }_1(\Delta )$.

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

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