Exact Time Evolution of the Asymmetric Hubbard Dimer
Author(s)Freericks, J. K.; Balasubramanian, Shankar N.
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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.
DepartmentMassachusetts Institute of Technology. Department of Physics
Journal of Superconductivity and Novel Magnetism
Balasubramanian, Shankar, and J. K. Freericks. “Exact Time Evolution of the Asymmetric Hubbard Dimer.” Journal of Superconductivity and Novel Magnetism (September 29, 2016).
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