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We provide evidence of a superfluid-insulator transition (SIT) of magnons ina quasi-one-dimensional quantum ferrimagnet with {\it isotropic} competingantiferromagnetic spin interactions. This SIT occurs between two distinctferrimagnetic phases due to the frustration-induced closing of the gap to amagnon excitation. It thus causes a coherent superposition of singlet andtriplet states at lattice unit cells and a power-law decay on the staggeredspin correlation function along the transverse direction to the spontaneousmagnetization. A hard-core boson map suggests that asymptotically close to theSIT the magnons attain the Tonks-Girardeau limit. The quantized nature of thecondensed singlets is observed before a first-order transition to a singletmagnetic spiral phase accompanied by critical antiferromagnetic ordering. Inthe limit of strong frustration, the system undergoes a decoupling transitionto an isolated gapped two-leg ladder and a critical single linear chain.

Frustration-induced quantum phase transitions in a quasi-one-dimensional ferrimagnet: Hard-core boson map and the Ton ks-Girardeau limit