Exact Time Evolution of the Asymmetric Hubbard Dimer
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 descr...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Springer US,
2017-01-12T18:00:53Z.
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| Subjects: | |
| Online Access: | Get fulltext |
| Summary: | 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. United States. Department of Energy. Office of Basic Energy Science. Division of Materials Sciences and Engineering.(Contract No. DE-FG02-08ER46542) National Science Foundation (U.S.) (Grant number PHY-1314295) |
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