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

TL;DR

This study uses exact diagonalization to analyze finite spin-1/2 chains with frustrated exchange interactions, revealing quantum phase transitions, order parameters, and symmetry-breaking phenomena in the ground state.

Contribution

It provides detailed numerical results on order parameters and phase transitions in frustrated spin chains, extending understanding of quantum critical behavior and symmetry breaking.

Findings

Discontinuous transition from high to low spin ground state.

Existence of staggered magnetization and bond order wave phases.

Correlation functions indicate chiral order and helicity.

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 $\alpha_1(\Delta)$.