approach [@AA], including numerical algorithms based on tensor product states and tensor networks [@Orus; @TPS1; @TPS2; @TPS3; @HOTRG], all of which have been successfully applied to the description of the energy spectrum and matrix elements of local operators in either integrable lattice models and quantum spin chains or non-integrable quantum spin systems. However, the task of finding an appropriate approach to analyze the quantum models on hyperbolic lattices, which belongs to challenging problems related to the correspondence between the anti-de Sitter space and the conformal field theory [@QG], still remains an open question of the quantum gravity. A remarkable demand for an appropriate numerical tool persists. Implementation of the Monte Carlo simulations fails due to exponential increase of the number of the lattice sites for models on hyperbolic lattices with respect to the expanding lattice size from the lattice center [@MC1; @MC2]. Our desire is to propose a novel and sufficiently accurate numerical algorithm, which originates from the solid state physics and inherits the typical features coming from widely accepted renormalization group approaches, especially based on the Density Matrix Renormalization Group [@White; @Uli1; @Uli2].

Recently, we modified the Tensor Product Variational Formulation (TPVF) [@DaniskaGendiar], which is an algorithm combining an 