Effective Models for Dynamically Screened Interactions
(2025) PHYM01 20242Mathematical Physics
Department of Physics
- Abstract
- This master’s thesis project explores different methods for determining an effective electron-electron interaction strength to model dynamic interactions in the Anderson impurity model, an important model within the field of many-body quantum mechanics. The Anderson model describes an impurity atom which is embedded in a metal, with which in can exchange electrons. In this project, different observables for the dynamic Anderson model are estimated using continuous time quantum Monte Carlo simulations, and values for the imaginary time Green’s function are then used to develop various methods for obtaining the effective interaction strength. The main methods explored are neural networks and Bayesian parameter estimation. The accuracy of... (More)
- This master’s thesis project explores different methods for determining an effective electron-electron interaction strength to model dynamic interactions in the Anderson impurity model, an important model within the field of many-body quantum mechanics. The Anderson model describes an impurity atom which is embedded in a metal, with which in can exchange electrons. In this project, different observables for the dynamic Anderson model are estimated using continuous time quantum Monte Carlo simulations, and values for the imaginary time Green’s function are then used to develop various methods for obtaining the effective interaction strength. The main methods explored are neural networks and Bayesian parameter estimation. The accuracy of these effective models is evaluated by comparing their predictions of other observables, such as the double occupancy density and the kinetic energy. The results indicate that several of these methods could be utilized to make accurate predictions within certain domains of parameter space. The predictions made by the neural network and Bayesian inference methods were deemed to have a similar accuracy, which varied slightly for different temperatures. (Less)
- Popular Abstract
- Simplifying Complex Quantum Systems with AI and Statistics
Accurate models for quantum mechanical systems are often very complicated. But could it be possible to remove some of this complexity and create simpler models, while still capturing the underlying physics? This project explores how methods from computer science can help physicists build such simplified models, making it easier to study, understand and predict the behaviour of complex quantum systems.
The idea of removing extraneous complexity through effective theories is a cornerstone of physics. For example, to understand how the sound of a person speaking propogates through a room, we don’t need to track the position and velocity of every individual air molecule. Instead,... (More) - Simplifying Complex Quantum Systems with AI and Statistics
Accurate models for quantum mechanical systems are often very complicated. But could it be possible to remove some of this complexity and create simpler models, while still capturing the underlying physics? This project explores how methods from computer science can help physicists build such simplified models, making it easier to study, understand and predict the behaviour of complex quantum systems.
The idea of removing extraneous complexity through effective theories is a cornerstone of physics. For example, to understand how the sound of a person speaking propogates through a room, we don’t need to track the position and velocity of every individual air molecule. Instead, we can rely on a much simpler description, an effective theory, based on concepts like air pressure and wave speed. While such a model isn't perfectly precise, it offers impressive predictive power at a fraction of the complexity. In other words, it gives you a lot of insight for a relatively small investment.
In the same spirit, this project investigates whether a model of a complicated quantum system can be simplified while still capturing the most important behaviour. The system I studied involves a single atom embedded in a metal. Electrons from the surrounding metal can hop onto and off the atom. When two electrons occupy the same site, they repel each other. However, this repulsive interaction isn’t constant but dynamic, i.e. the strength of the interaction is time-dependent. This makes the system difficult to model and simulate.
The goal of the project was to see whether this dynamic behavior could be captured using just one effective variable that summarises the full interaction. Measurement data from both the dynamic and effective model was generated using probability based computer simulations. This data was used to tune different effective models, which were based on methods from computer science. Two different approaches were explored:
● A neural network, a form of artificial intelligence that learns patterns from data and can
predict outcomes based on previous examples.
● A Bayesian inference method, a statistical technique that combines data from
simulations with prior physical knowledge to make informed estimates about model
parameters.
Both methods succeeded in predicting the key quantities with high accuracy in certain domains. Surprisingly, the simpler theory generated by the Bayesian method performed just as well as the more complex neural network. This suggests that the underlying physics may be represented well by a relatively simple relationship.
This project shows that it is possible to create a simpler model of a complicated quantum system that still captures the essential physics. It also shows that modern tools from computer science can help us find that model efficiently, proving that such tools can aid physicists in building new theories for understanding our universe. (Less)
Please use this url to cite or link to this publication:
http://lup.lub.lu.se/student-papers/record/9188275
- author
- Pauli, Anton LU
- supervisor
- organization
- course
- PHYM01 20242
- year
- 2025
- type
- H2 - Master's Degree (Two Years)
- subject
- language
- English
- id
- 9188275
- date added to LUP
- 2025-05-15 14:35:02
- date last changed
- 2025-05-15 14:35:02
@misc{9188275,
abstract = {{This master’s thesis project explores different methods for determining an effective electron-electron interaction strength to model dynamic interactions in the Anderson impurity model, an important model within the field of many-body quantum mechanics. The Anderson model describes an impurity atom which is embedded in a metal, with which in can exchange electrons. In this project, different observables for the dynamic Anderson model are estimated using continuous time quantum Monte Carlo simulations, and values for the imaginary time Green’s function are then used to develop various methods for obtaining the effective interaction strength. The main methods explored are neural networks and Bayesian parameter estimation. The accuracy of these effective models is evaluated by comparing their predictions of other observables, such as the double occupancy density and the kinetic energy. The results indicate that several of these methods could be utilized to make accurate predictions within certain domains of parameter space. The predictions made by the neural network and Bayesian inference methods were deemed to have a similar accuracy, which varied slightly for different temperatures.}},
author = {{Pauli, Anton}},
language = {{eng}},
note = {{Student Paper}},
title = {{Effective Models for Dynamically Screened Interactions}},
year = {{2025}},
}