Magnetic properties of the transverse-field Ising model on curved
(hyperbolic) lattices are studied by a tensor product variational formulation
that we have generalized for this purpose. First, we identify the quantum phase
transition for each hyperbolic lattice by calculating the magnetization. We
study the entanglement entropy at the phase transition in order to analyze the
correlations of various subsystems located at the center with the rest of the
lattice. We confirm that the entanglement entropy satisfies the area law at the
phase transition for fixed coordination number, i.e., it scales linearly with
the increasing size of the subsystems. On the other hand, the entanglement
entropy decreases as power-law with respect to the increasing coordination
number.Comment: accepted in Acta Phys. Pol. A (2020