  The quantum phases in a spin-1 skewed ladder system formed by alternately
fusing five- and seven-membered rings are studied numerically using the exact
diagonalization technique up to 16 spins and using the density matrix
renormalization group method for larger system sizes. The ladder has a fixed
isotropic antiferromagnetic (AF) exchange interaction ($J_2 = 1$) between the
nearest-neighbor spins along the legs and a varying isotropic AF exchange
interaction ($J_1$) along the rungs. As a function of $J_1$, the system shows
many interesting ground states (gs) which vary from different types of
nonmagnetic and ferrimagnetic gs. The study of diverse gs properties such as
spin gap, spin-spin correlations, spin density and bond order reveal that the
system has four distinct phases, namely, the AF phase at small $J_1$; the
ferrimagnetic phase with gs spin $S_G = n$ for $1.44 < J_1 < 4.74$ and with
$S_G = 2n$ for $J_1 > 5.63$, where $n$ is the number of unit cells; and a
reentrant nonmagnetic phase at $4.74 < J_1 < 5.44$. The system also shows the
presence of spin current at specific $J_1$ values due to simultaneous breaking
of both reflection and spin parity symmetries.
