Hyperbolic Deformation on Quantum Lattice Hamiltonians
| dc.creator | Ueda, Hiroshi | |
| dc.creator | Nishino, Tomotoshi | |
| dc.date | 2008-08-28 | |
| dc.date | 2008-09-03 | |
| dc.date.accessioned | 2026-07-07T12:40:16Z | |
| dc.date.available | 2026-07-07T12:40:16Z | |
| dc.description | 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 $\cosh j λ$, 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 $λ$. | |
| dc.description | 5 pages, 4 figures | |
| dc.identifier | https://arxiv.org/abs/0808.3858 | |
| dc.identifier | http://arxiv.org/abs/0808.3858 | |
| dc.identifier | J.Phys.Soc.Jap.78:014001,2009 | |
| dc.identifier | doi:10.1143/JPSJ.78.014001 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/219393 | |
| dc.subject | Quantum Physics | |
| dc.subject | Statistical Mechanics | |
| dc.subject | General Relativity and Quantum Cosmology | |
| dc.title | Hyperbolic Deformation on Quantum Lattice Hamiltonians | |
| dc.type | text |