  The quantum phases in a spin-1 skewed ladder system formed by alternately
fusing five- and seven-membered rings is studied numerically using exact
diagonalization technique up to 16 spins and using density matrix
renormalization group method for larger system sizes. The ladder has isotropic
antiferromagnetic (AF) exchange interaction ($J_2 = 1$) between the nearest
neighbor spins along the legs, 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
gs to different types of ferrimagnetic gs. Study of different gs properties
such as spin gap, spin-spin correlations, spin density and bond order reveal
that the system has four distinct phases namely, AF phase at small $J_1$,
ferrimagnetic phase with gs spin $S_G = 1$ per unit cell for $1.5 < J_1 < 4.7$
and with $S_G = 2$ for $J_1 > 5.9$, a reentrant AF phase at $4.8 < J_1 < 5.9$.
The system also shows the presence of spin current at specific $J_1$ values due
to simultaneously breaking of both reflection symmetry and spin parity
symmetry.
