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

TL;DR

This paper investigates a superfluid-insulator transition of magnons in a frustrated quasi-one-dimensional ferrimagnet, revealing a Tonks-Girardeau limit and multiple phase transitions including a singlet magnetic spiral phase.

Contribution

It introduces a hard-core boson mapping and demonstrates the occurrence of a superfluid-insulator transition driven by frustration in a quantum ferrimagnet, highlighting novel quantum phases.

Findings

Magnon superfluid-insulator transition due to frustration.

Magnons approach the Tonks-Girardeau limit near the transition.

Observation of a first-order transition to a singlet magnetic spiral phase.

Abstract

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