  The quantum XY, Heisenberg, and transverse field Ising models on hyperbolic
lattices are studied by means of the Tensor Product Variational Formulation
algorithm. The lattices are constructed by tessellation of congruent polygons
with coordination number equal to four. The calculated ground-state energies of
the XY and Heisenberg models and the phase transition magnetic field of the
Ising model on the series of lattices are used to estimate the corresponding
quantities of the respective models on the Bethe lattice. The hyperbolic
lattice geometry induces the mean-field-like universality of the models. The
ambition to obtain results on the non-Euclidean lattice geometries has been
motivated by theoretical studies of the anti-de Sitter/conformal field theory
correspondence.
