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Time-dependent density-functional theory and strongly correlated systems: insight from numerical studies
1Division of Mathematical Physics and European Theoretical Spectroscopy Facility (ETSF), Lund University, Lund, Sweden.
Physical Review Letters
|November 13, 2008
Summary
This study explores time-dependent density-functional theory for strongly correlated models out of equilibrium. Researchers reverse-engineered the exact exchange-correlation potential for Hubbard chains, offering insights into approximate potentials.
Area of Science:
- Condensed Matter Physics
- Quantum Many-Body Theory
- Computational Chemistry
Background:
- Time-dependent density-functional theory (TDDFT) is a powerful tool for studying quantum systems.
- Strongly correlated lattice models, like the Hubbard model, present significant challenges for theoretical treatment, especially out of equilibrium.
- Understanding the exact exchange-correlation (xc) potential is crucial for the accuracy of TDDFT.
Purpose of the Study:
- To illustrate the applicability of TDDFT to strongly correlated lattice models under non-equilibrium conditions.
- To reverse-engineer the exact xc potential for small Hubbard chains subjected to time-dependent fields.
- To develop and assess an approximate xc potential for the 1D Hubbard model.
Main Methods:
- Exact many-body time evolution was employed to simulate the system's dynamics.
- The exact xc potential was computationally derived (reverse-engineered) from the exact time evolution.
- An adiabatic local density approximation (ALDA) for the xc potential in the 1D Hubbard model was introduced and compared with exact results.
Main Results:
- The study successfully demonstrated the scope of TDDFT for out-of-equilibrium strongly correlated models.
- Exact xc potentials were obtained for small 1D Hubbard chains under time-dependent perturbations.
- The proposed ALDA showed promise in approximating the exact xc potential, providing insights into its behavior.
Conclusions:
- TDDFT can be effectively applied to challenging non-equilibrium strongly correlated systems.
- The reverse-engineering approach provides a benchmark for developing accurate approximate xc potentials.
- Further investigation into the v-representability of the 1D Hubbard model is warranted.
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