Exact Time Evolution of the Asymmetric Hubbard Dimer
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10948_2016_3811_ReferencePDF.pdf
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3.4 MB
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Checksum (MD5)
9711c5523b6938e3b906750ffdd2f3ca
Author(s)
Freericks, J. K.
Balasubramanian, Shankar N.
Date Issued
September 2016
Journal
Journal of Superconductivity and Novel Magnetism
Publisher
Springer US
Citation
Balasubramanian, Shankar, and J. K. Freericks. “Exact Time Evolution of the Asymmetric Hubbard Dimer.” Journal of Superconductivity and Novel Magnetism (September 29, 2016).
Version
Author's final manuscript
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.
MIT Department
Massachusetts Institute of Technology. Department of Physics
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Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
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DOI of Published Version
https://doi.org/10.1007/s10948-016-3811-9
