Hyperbolic Deformation on Quantum Lattice Hamiltonians

Details Hyperbolic Deformation on Quantum Lattice Hamiltonians Hyperbolic Deformation on Quantum Lattice Hamiltonians

2008-08-28

arxiv.org/abs/0808.3858v2

J.Phys.Soc.Jap.78:014001,2009

Physics

Quantum Physics

5 pages, 4 figures

Scientific paper

10.1143/JPSJ.78.014001

A 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 $\cosh j \lambda$, where $j$ is the lattice index and where $\lambda \ge 0$ is a deformation parameter. In the limit $\lambda \to 0$ 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 $\lambda$ is finite. Spin correlation function show exponential decay, and the boundary effect decreases with increasing $\lambda$.

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