2 research outputs found
Hyperbolic Deformation on Quantum Lattice Hamiltonians
A group of non-uniform quantum lattice Hamiltonians in one dimension is
introduced, which is related to the hyperbolic -dimensional space. The
Hamiltonians contain only nearest neighbor interactions whose strength is
proportional to , where is the lattice index and where
is a deformation parameter. In the limit 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 Heisenberg spin chain by use of the
density matrix renormalization group (DMRG) method. It is shown that the ground
state is dimerized when is finite. Spin correlation function show
exponential decay, and the boundary effect decreases with increasing .Comment: 5 pages, 4 figure
Phase Transition of the Ising model on a Hyperbolic Lattice
The matrix product structure is considered on a regular lattice in the
hyperbolic plane. The phase transition of the Ising model is observed on the
hyperbolic lattice by means of the corner-transfer-matrix
renormalization group (CTMRG) method. Calculated correlation length is always
finite even at the transition temperature, where mean-field like behavior is
observed. The entanglement entropy is also always finite.Comment: 4 pages, 3 figure