Decoupled phase of frustrated spin-1/2 antiferromagnetic chains with and without long range order in the ground state

Abstract

The quantum phases of one-dimensional spin $s=1/2$ chains are discussed for models with two parameters, frustrating exchange $g=J_2>0$ between second neighbors and normalized nonfrustrating power-law exchange with exponent $\hat{I}\pm$ and distance dependence $r^{-\hat{I}\pm }$. The ground state (GS) at $g=0$ has long-range order (LRO) for $\hat{I}\pm <2$, long-range spin fluctuations for $\hat{I}\pm >2$. The models conserve total spin $S=S_A+S_B$, have singlet GS for any $g$, $\hat{I}\pm \ge 0$ and decouple at $1/g=0$ to linear Heisenberg antiferromagnets on sublattices $A$ and $B$ of odd and even-numbered sites. Exact diagonalization of finite chains gives the sublattice spin $<S_A^2>$, the magnetic gap $E_m$ to the lowest triplet state and the excitation $E_{\ddot{I}}ƒ$ to the lowest singlet with opposite inversion symmetry to the GS. An analytical model that conserves sublattice spin has a first order quantum transition at $g_c=1/4ln2$ from a GS with perfect LRO to a decoupled phase with $S_A=S_B=0$ for $g\ge 4/\ddot{I}{€}^2$ and no correlation between spins in different sublattices. The model with $\hat{I}\pm =1$ has a first order transition to a decoupled phase that closely resembles the analytical model. The bond order wave (BOW) phase and continuous quantum phase transitions of finite models with $\hat{I}\pm \ge 2$ are discussed in terms of GS degeneracy where $E_{\ddot{I}}ƒ(g)=0$, excited state degeneracy where $E_{\ddot{I}}ƒ(g)=E_m(g)$, and $<S_A^2>$. The decoupled phase at large frustration has nondegenerate GS for any exponent $\hat{I}\pm$ and excited states related to sublattice excitations.

10 pages 8 figures