Nematic and supernematic phases in Kagome quantum antiferromagnets under a magnetic field

TL;DR

This study uses advanced tensor network methods to explore various magnetic phases in Kagome antiferromagnets under magnetic fields, revealing complex nematic and supernematic states with distinct symmetry-breaking and magnetization properties.

Contribution

The paper introduces a detailed tensor network analysis of Kagome quantum antiferromagnets, identifying new nematic and supernematic phases and their phase transitions under magnetic fields.

Findings

Identification of magnetization plateaux at specific fractions for spin-1 and spin-2.

Discovery of superfluid nematic phases breaking multiple symmetries.

Characterization of phase transition types between different magnetic states.

Abstract

Optimizing translationally invariant infinite-Projected Entangled Pair States (iPEPS), we investigate the spin-2 Affleck-Kennedy-Lieb-Tasaki (AKLT) and spin-1 Heisenberg models on the Kagome lattice as a function of magnetic field. We found that the magnetization curves offer a wide variety of compressible and incompressible phases. Incompressible nematic phases breaking the lattice $C_3$ rotation -- for which we propose simple qualitative pictures -- give rise to magnetization plateaux at reduced magnetization $m_z=5/6$ and $m_z=1/3$ for spin-2 and spin-1, respectively, in addition to the $m_z=0$ plateaux characteristic of zero-field gapped spin liquids. Moving away from the plateaux we observe a rich variety of compressible superfluid nematic -- named "supernematic" -- phases breaking spontaneously both point group and spin-U(1) symmetries, as well as a superfluid phase preserving lattice symmetries. We also identify the nature -- continuous or first-order -- of the various phase transitions. Possible connections to experimental spin-1 systems are discussed.