Bond-order wave phase, spin solitons and thermodynamics of a frustrated linear spin-1/2 Heisenberg antiferromagnet

The linear spin-1/2 Heisenberg antiferromagnet with exchanges $J_1$, $J_2$ between first and second neighbors has a bond-order wave (BOW) phase that starts at the fluid-dimer transition at $J_2/J_1 = 0.2411$ and is particularly simple at $J_2/J_1 = 1/2$. The BOW phase has a doubly degenerate singlet ground state, broken inversion symmetry and a finite energy gap $E_m$ to the lowest triplet state. The interval $0.4<J_2/J_1<1.0$ has large $E_m$ and small finite size corrections. Exact solutions are presented up to $N=28$ spins with either periodic or open boundary conditions and for thermodynamics up to $N=18$. The elementary excitations of the BOW phase with large $E_m$ are topological spin-1/2 solitons that separate BOWs with opposite phase in a regular array of spins. The molar spin susceptibility $\chi_M(T)$ is exponentially small for $T \ll E_m$ and increases nearly linearly with $T$ to a broad maximum. $J_1$, $J_2$ spin chains approximate the magnetic properties of the BOW phase of Hubbard-type models and provide a starting point for modeling alkali-TCNQ salts.