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.'
author:
- Yi Zhou
- Kazushi Kanoda
- 'Tai-Kai Ng'
bibliography:
- 'refall.bib'
title: Quantum Spin Liquid States
---

Introduction
============

Quantum spin liquid (QSL) states in dimensions of $d>1$ have been a long-sought dream in condensed matter physics. The general idea is that when acting on spin systems, quantum mechanics may lead to exotic ground states and low-energy behaviors that cannot be captured by traditional semi-classical approaches. The difficulty in implementing this idea is that we have no natural place to start once we have left the comfort zone of semi-classical approaches, at least in dimensions larger than one. Except for a few exactly solvable models, we must rely heavily on numerical or variational approaches to “guess" the correct ground state wavefunctions and on a combination of sophisticated numerical and analytical techniques to understand the corresponding low-energy excitations.

Several excellent reviews are available on QSLs [@Lee08; @Balents10] and frustrated magnetism [@BookDiep; @BookLacroix]. 