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Frustrated magnets host the promises of material realizations of new paradigmof quantum matter, while direct comparison of unbiased model calculations withexperimental measurements is still very challenging. Here, we design andimplement a protocol of employing many-body computation methodologies foraccurate model calculation -- both equilibrium and dynamical properties -- of afrustrated rare-earth magnet TmMgGaO$_4$ (TMGO), which perfectly explains thecorresponding experimental findings. Our results confirm TMGO is an idealrealization of triangular-lattice Ising model with an intrinsic transversefield. The magnetic order of TMGO is predicted to melt through two successiveKosterlitz-Thouless (KT) phase transitions, with a floating KT phase inbetween. The dynamical spectra calculated suggest remnant images of a vanishingmagnetic stripe order that represent vortex-antivortex pairs, resembling rotonsin a superfluid helium film. TMGO therefore constitutes a rare quantum magnetfor realizing KT physics and we further propose experimental detections of itsintriguing properties.

Kosterlitz-Thouless Melting of Magnetic Order in the Triangular Quantum Ising Material TmMgGaO$_4$