Dynamical Exchange-correlation Field in Low-dimensional Model Systems
(2024) FYSM63 20241Department of Physics
Mathematical Physics
- Abstract
- Recently, a new formalism for calculating the Green function of many-particle systems was introduced, in which the self-energy is replaced by a dynamical exchange-correlation potential. The dynamical exchange-correlation potential is an exact generalization of the Slater Xalpha exchange potential proposed in 1951, which includes the effects of correlations. It may be regarded as the counterpart of the Kohn-Sham potential in ground-state density-functional theory, providing in principle access to one-particle excitation spectra measured in (inverse) photoemission experiments.
The exchange-correlation potential and its associated hole have been previously investigated for the homogeneous electron gas within the random-phase approximation... (More) - Recently, a new formalism for calculating the Green function of many-particle systems was introduced, in which the self-energy is replaced by a dynamical exchange-correlation potential. The dynamical exchange-correlation potential is an exact generalization of the Slater Xalpha exchange potential proposed in 1951, which includes the effects of correlations. It may be regarded as the counterpart of the Kohn-Sham potential in ground-state density-functional theory, providing in principle access to one-particle excitation spectra measured in (inverse) photoemission experiments.
The exchange-correlation potential and its associated hole have been previously investigated for the homogeneous electron gas within the random-phase approximation using the so-called plasmon-pole approximation. In this thesis, as a benchmark the exchange-correlation potential and hole have been calculated within the full random-phase approximation without resort to the plasmon-pole approximation for both the three- and two-dimensional electron gas.
The dynamical exchange-correlation potential formalism has also been extended to the Hubbard model in the arbitrary dimension within the random-phase approximation. Particularly, the results it yields have been evaluated and compared to the exact one for the Hubbard dimer (Less) - Popular Abstract
- Have you ever wondered about the remarkable properties of materials like Gallium arsenide (GaAs), which seem to possess magical abilities like superconductivity and magnetism? Scientists are captivated by these surface materials and are diving deep into their mysteries. In labs around the world, researchers are conducting experiments to measure various properties and compare them with what theory predicts.
One fascinating aspect they're exploring involves something called the one-particle Green function. Think of it as a kind of magic formula that tells us the probability of particles making specific transitions between different states. It's like peeking into the quantum world and witnessing particles in action!
To understand these... (More) - Have you ever wondered about the remarkable properties of materials like Gallium arsenide (GaAs), which seem to possess magical abilities like superconductivity and magnetism? Scientists are captivated by these surface materials and are diving deep into their mysteries. In labs around the world, researchers are conducting experiments to measure various properties and compare them with what theory predicts.
One fascinating aspect they're exploring involves something called the one-particle Green function. Think of it as a kind of magic formula that tells us the probability of particles making specific transitions between different states. It's like peeking into the quantum world and witnessing particles in action!
To understand these Green functions, scientists use clever techniques like Feynman diagrams and quantum Monte Carlo simulations. But as they seek higher accuracy, traditional methods face challenges. It's like trying to solve a really tricky puzzle – sometimes, you need a new approach.
Enter density functional theory – a game-changer that simplified quantum mechanics computations. Building on this, researchers are now developing a new approach called the dynamical exchange-correlation field formalism. It's like upgrading from an old model of a car to a sleek new version – more efficient and powerful!
This new approach, based on the random-phase approximation, holds promise for developing a local density approximation. By studying the behavior of electrons in three-dimensional and two-dimensional electron gases, scientists are uncovering exciting insights into the world of quantum mechanics.
And it doesn't stop there! They're also applying this approach to explore the behavior of materials at the atomic level. Imagine being able to understand and control the behavior of materials like never before – it's like having a superpower in the palm of your hand!
So, next time you hear about GaAs or other surface materials that can be described by these models, remember – there's a whole world of discovery happening behind the scenes, fueled by curiosity and innovation. (Less)
Please use this url to cite or link to this publication:
http://lup.lub.lu.se/student-papers/record/9168145
- author
- Xu, Jinxiang LU
- supervisor
-
- Ferdi Aryasetiawan LU
- Zhen Zhao LU
- organization
- course
- FYSM63 20241
- year
- 2024
- type
- H2 - Master's Degree (Two Years)
- subject
- keywords
- dynamical exchange-correlation field formalism, exchange, correlation, Green function, three-dimensional electron gas, two-dimensional electron gas, Hubbard model, Hubbard dimer, random-phase approximation, sum rule, Hatree-Fock approximation.
- language
- English
- id
- 9168145
- date added to LUP
- 2024-06-26 08:27:52
- date last changed
- 2024-06-26 08:27:52
@misc{9168145,
abstract = {{Recently, a new formalism for calculating the Green function of many-particle systems was introduced, in which the self-energy is replaced by a dynamical exchange-correlation potential. The dynamical exchange-correlation potential is an exact generalization of the Slater Xalpha exchange potential proposed in 1951, which includes the effects of correlations. It may be regarded as the counterpart of the Kohn-Sham potential in ground-state density-functional theory, providing in principle access to one-particle excitation spectra measured in (inverse) photoemission experiments.
The exchange-correlation potential and its associated hole have been previously investigated for the homogeneous electron gas within the random-phase approximation using the so-called plasmon-pole approximation. In this thesis, as a benchmark the exchange-correlation potential and hole have been calculated within the full random-phase approximation without resort to the plasmon-pole approximation for both the three- and two-dimensional electron gas.
The dynamical exchange-correlation potential formalism has also been extended to the Hubbard model in the arbitrary dimension within the random-phase approximation. Particularly, the results it yields have been evaluated and compared to the exact one for the Hubbard dimer}},
author = {{Xu, Jinxiang}},
language = {{eng}},
note = {{Student Paper}},
title = {{Dynamical Exchange-correlation Field in Low-dimensional Model Systems}},
year = {{2024}},
}