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The uniform two-dimensional variational tensor product state is applied tothe transverse-field Ising, XY, and Heisenberg models on a regular hyperboliclattice surface. The lattice is constructed by tessellation of the congruentpentagons with the fixed coordination number being four. As a benchmark, thethree models are studied on the flat square lattice simultaneously. Themean-field-like universality of the Ising phase transition is observed in fullagreement with its classical counterpart on the hyperbolic lattice. The tensorproduct ground state in the thermodynamic limit has an exceptionalthree-parameter solution. The variational ground-state energies of the spinmodels are calculated.

Tensor product variational formulation applied to pentagonal lattice