We have proposed an exactly solvable quantum spin-$3/2$ model on a square lattice. Its ground state is a quantum spin liquid with a half-integer spin per unit cell. The fermionic excitations, dubbed as “spinons”, are gapless with a linear dispersion, while the topological “vison” excitations are gapped. Moreover, these massless fermionic spinon excitations are topologically stable. Thus, this model is, to the best of our knowledge, the first exactly solvable model of half-integer spins whose ground state is an “algebraic spin liquid.”

• Received 29 October 2008

DOI:https://doi.org/10.1103/PhysRevLett.102.217202