  The uniform two-dimensional variational tensor product state is applied to
the transverse-field Ising, XY, and Heisenberg models on a regular hyperbolic
lattice surface. The lattice is constructed by tessellation of the congruent
pentagons with the fixed coordination number being four. As a benchmark, the
three models are studied on the flat square lattice simultaneously. The
mean-field-like universality of the Ising phase transition is observed in full
agreement with its classical counterpart on the hyperbolic lattice. The tensor
product ground state in the thermodynamic limit has an exceptional
three-parameter solution. The variational ground-state energies of the spin
models are calculated.
