  Ground state of the one-dimensional transverse field Ising model is
investigated under the hyperbolic deformation, where the energy scale of j-th
bond is proportional to the function \cosh ( j \lambda ) that contains a
parameter \lambda. Although the Hamiltonian is position dependent, the ground
state is nearly uniform and finitely correlated. We observe the energy cross
over between the ordered and disordered state with respect to the transverse
field. The model shows first order phase transition, and the discontinuities in
the magnetization and entanglement entropy at the transition point detect the
Ising universality.
