2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/219393A group of non-uniform quantum lattice Hamiltonians in one dimension is introduced, which is related to the hyperbolic $1 + 1$-dimensional space. The Hamiltonians contain only nearest neighbor interactions whose strength is proportional to $\cosh j λ$, where $j$ is the lattice index and where $λ\ge 0$ is a deformation parameter. In the limit $λ\to 0$ the Hamiltonians become uniform. Spacial translation of the deformed Hamiltonians is induced by the corner Hamiltonians. As a simple example, we investigate the ground state of the deformed $S = 1/2$ Heisenberg spin chain by use of the density matrix renormalization group (DMRG) method. It is shown that the ground state is dimerized when $λ$ is finite. Spin correlation function show exponential decay, and the boundary effect decreases with increasing $λ$.5 pages, 4 figuresQuantum PhysicsStatistical MechanicsGeneral Relativity and Quantum Cosmologytext