Exact analytical partition function and spin gap for a 2×3 quantum spin ladder

Abstract The energy levels E(k 1 , k 2 ) , spin gap, and partition function of a 3×2 quantum spin ladder are derived analytically by using an exact diagonalization method from our earlier work. The behavior of the ladder is strongly dependent on the value of the interchain coupling J2. For positive intrachain coupling J1 along the chains, the spin gap is non-zero, zero, and nearly zero for J2 larger than, equal to, and less than zero, correspondingly. For positive J2, the ground state consists of the same eigenstate, irrespectively of the value of J1. This state is spatially symmetric along the chains and antisymmetric along the rungs, corresponding to the spin wave numbers k1=0 and k2=π.