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.
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Acknowledgments
This work was supported by the Department of Energy, Office of Basic Energy Sciences, Division of Materials Sciences and Engineering under Contract No. DE-FG02-08ER46542. S. B. was also supported by the National Science Foundation under grant number PHY-1314295. J.K.F. was also supported by the McDevitt Bequest at Georgetown.
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Balasubramanian, S., Freericks, J.K. Exact Time Evolution of the Asymmetric Hubbard Dimer. J Supercond Nov Magn 30, 97–102 (2017). https://doi.org/10.1007/s10948-016-3811-9
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DOI: https://doi.org/10.1007/s10948-016-3811-9