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- Title
Exact Time Evolution of the Asymmetric Hubbard Dimer.
- Authors
Balasubramanian, Shankar; Freericks, J.
- Abstract
We examine the time evolution of an asymmetric Hubbard dimer, which has a different on-site interaction on the two sites. The Hamiltonian has a time-dependent hopping term, which can be employed to describe an electric field (which creates a Hamiltonian with complex matrix elements), or it can describe a modulation of the lattice (which has real matrix elements). By examining the symmetries under spin and pseudospin, we show that the former case involves at most a 3 × 3 block-it can be mapped onto the time evolution of a time-independent Hamiltonian, so the dynamics can be evaluated analytically and exactly (by solving a nontrivial cubic equation). We also show that the latter case reduces to at most 2 × 2 blocks, and hence, the time evolution for a single Trotter step can be determined exactly, but the time evolution generically requires a Trotter product.
- Subjects
HUBBARD model; HAMILTONIAN systems; LANDAU-Zener formula; MODULATION spectroscopy; SYMMETRY (Physics)
- Publication
Journal of Superconductivity & Novel Magnetism, 2017, Vol 30, Issue 1, p97
- ISSN
1557-1939
- Publication type
Article
- DOI
10.1007/s10948-016-3811-9