  We study the quantum lattice gas model in one dimension introduced by
Lesanovsky, who showed that the exact ground state and a couple of excited
states can be obtained analytically. The Hamiltonian of the model depends
solely on the parameter $z$, the meaning of which is a fugacity in the
corresponding classical lattice gas model. For small $z$ ($0<z<1$), we prove
that there is an energy gap between the ground state and the excited states by
applying Knabe's method.
