Abstract
The frustrated quantum spin system on the distorted diamond chain lattice suitable for the alumoklyuchevskite is investigated using the numerical diagonalization of finite-size clusters and the level spectroscopy analysis. It is found that this model exhibits three quantum phases; the ferrimagnetic phase, the spin gap one, and the gapless Tomonaga-Luttinger liquid depending on the exchange coupling parameters. The ground state phase diagram is presented.
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