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An emergent Fermi surface in a Mott insulator, an exotic quantum spin liquidstate, was suggested by Anderson in 1987. After a quick support for itsexistence in spin-half Heisenberg model in a square lattice in a RVB mean fieldtheory, pseudo Fermi surface was found only recently in an exactly solvablespin-3/2 model by Yao, Zhang and Kivelson. We show that a minimal spin-halfKitaev model on a decorated square lattice exhibits a Fermi surface. Volume andshape of the Fermi surface change with exchange couplings or on addition of a 3spin interaction terms.

Exact quantum spin liquids with Fermi surfaces in spin-half models