not applied [@Baxter]. We conjectured that TPVF was more suitable for models on the pentagonal hyperbolic lattice due to off-critical and weakly correlated characteristics [@DaniskaGendiar].

In this work we expand the set of hyperbolic lattices investigated by the TPVF to a series of lattices constructed from congruent $p$-sided polygons, where $p \in \{5,6, \dots, 11\}$. In analogy to our previous studies of classical spin models on these hyperbolic lattices [@hctmrg-Ising-5-4; @hctmrg-Ising-p-4; @hctmrg-Ising-3-q; @hctmrg-Ising-3-qn], we expect fast convergence of the phase transition magnetic field of the quantum TFIM as well as the ground-state energies of the quantum XY and Heisenberg models toward the asymptotic case $p \rightarrow \infty$, which represents the Bethe lattice [@hctmrg-Ising-p-4]. Numerical results presented in the following sections are in complete agreement with the expectations. The key feature of this work is the consequent indirect analysis of the quantum TFIM, XY, and Heisenberg models on the Bethe lattice with coordination number four, which has not been considered yet.

The article is organized as follows. In Sec. II we define the three Hamiltonians on the respective hyperbolic lattices and give a brief description of the principles of the TPVF algorithm, which have been discussed in [@DaniskaGendiar]. An accurate analysis 