NDLI: Exact Time Evolution of the Asymmetric Hubbard Dimer

Content Provider	Springer Nature Link
Author	Balasubramanian, Shankar Freericks, J. K.
Copyright Year	2016
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.
Starting Page	97
Ending Page	102
Page Count	6
File Format	PDF
ISSN	15571939
Journal	Journal of Superconductivity and Novel Magnetism
Volume Number	30
Issue Number	1
e-ISSN	15571947
Language	English
Publisher	Springer US
Publisher Date	2016-09-29
Publisher Place	New York
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Hubbard dimer Exact time dynamics Field-induced polarization Modulation spectroscopy Strongly Correlated Systems, Superconductivity Magnetism, Magnetic Materials Condensed Matter Physics Characterization and Evaluation of Materials
Content Type	Text
Resource Type	Article
Subject	Electronic, Optical and Magnetic Materials Condensed Matter Physics

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1	Ministry of Education (GoI), Department of Higher Education	Sanctioning Authority	https://www.education.gov.in/ict-initiatives
2	Indian Institute of Technology Kharagpur	Host Institute of the Project: The host institute of the project is responsible for providing infrastructure support and hosting the project	https://www.iitkgp.ac.in
3	National Digital Library of India Office, Indian Institute of Technology Kharagpur	The administrative and infrastructural headquarters of the project	Dr. B. Sutradhar bsutra@ndl.gov.in
4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
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