Quantum phases of a frustrated spin-1 system: The 5/7 skewed ladder

Abstract

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 various 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.