Quantum spin liquid states

TLDR

Quantum spin liquid (QSL) states arise in frustrated spin systems where quantum fluctuations suppress magnetic order, yielding exotic ground states beyond semi‑classical approaches. The article introduces recent developments in the physics of quantum spin liquid states. It reviews theoretical frameworks for QSLs, including fermionic spin‑½ representations, SU(2)/U(1)/Z₂ classifications, extensions with spin‑orbit coupling and higher spin, as well as tensor‑network and Kitaev‑model approaches. Experimental evidence from anisotropic triangular, kagome, and hyperkagome materials is reviewed and contrasted with theoretical predictions.

Abstract

This article is an introductory review of the physics of quantum spin liquid (QSL) states. Quantum magnetism is a rapidly evolving field, and recent developments reveal that the ground states and low-energy physics of frustrated spin systems may develop many exotic behaviors once we leave the regime of semi-classical approaches. The purpose of this article is to introduce these developments. The article begins by explaining how semi-classical approaches fail once quantum mechanics become important and then describes the alternative approaches for addressing the problem. We discuss mainly spin $1/2$ systems, and we spend most of our time in this article on one particular set of plausible spin liquid states in which spins are represented by fermions. These states are spin-singlet states and may be viewed as an extension of Fermi liquid states to Mott insulators, and they are usually classified in the category of so-called $SU(2)$, $U(1)$ or $Z_2$ spin liquid states. We review the basic theory regarding these states and the extensions of these states to include the effect of spin-orbit coupling and to higher spin ($S>1/2$) systems. Two other important approaches with strong influences on the understanding of spin liquid states are also introduced: (i) matrix product states and projected entangled pair states and (ii) the Kitaev honeycomb model. Experimental progress concerning spin liquid states in realistic materials, including anisotropic triangular lattice systems ($\kappa$-(ET)$_{2}$Cu$_{2}$(CN)$_{3}$ and EtMe$_{3}$Sb[(Pd(dmit)$_{2}$]$_{2}$), kagome lattice systems (ZnCu$_{3}$(OH)$_{6}$Cl$_{2}$) and hyperkagome lattice systems (Na$_{4}$Ir$_{3}$O$_{8}$), is reviewed and compared against the corresponding theories.