Controlling frustrated liquids and solids with an applied field in a kagome Heisenberg antiferromagnet

Abstract

Quantum spin-1/2 kagome Heisenberg antiferromagnet is the representative frustrated system possibly hosting a spin liquid. Clarifying the nature of this elusive topological phase is a key challenge in condensed matter; however, even identifying it still remains unsettled. Here we apply a magnetic field and discover a series of spin-gapped phases appearing at five different fractions of magnetization by means of a grand canonical density matrix renormalization group, an unbiased state-of-the-art numerical technique. The magnetic field dopes magnons and first gives rise to a possible Z3 spin liquid plateau at 1/9 magnetization. Higher field induces a self-organized super-lattice unit, a six-membered ring of quantum spins, resembling an atomic orbital structure. Putting magnons into this unit one by one yields three quantum solid plateaus. We thus find that the magnetic field could control the transition between various emergent phases by continuously releasing the frustration. Quantum spin liquids—quantum states in which spins show no order even at very low temperatures—are possibly hosted in a kagome Heisenberg antiferromagnet. Using a powerful numerical method, the authors show that applying a magnetic field leads to various exotic plateau states, including two spin liquids.