Adrien KAHN

PhD Student

Resarch activities at CPHT: Condensed Matter

Research interests: Correlated Quantum Systems, Variational Optimization, Machine Learning

Thesis:  "Neural Network methods for Correlated Quantum Systems"

Advisor: Filippo Vicentini

Abstract

Simulating interacting quantum systems is particularly challenging because of the curse of dimensionality. In recent years, an approach inspired by machine learning has taken off, where the exponentially-large space is restricted to the subspace induced by a neural network with polynomially-few parameters. The parameters describing the ground-state or time-evolved state are then computed by solving an approximate optimisation problem. While this approach, known as Neural Quantum States, has delivered outstanding results in relatively short timescales, developments have focused on homogeneous systems. The objective of this PhD project is to focus on a particular class of quantum systems where a small 'impurity' is coupled to a large 'bath', and develop variational methods to study such systems. The objective is to leverage the particular structure of those problems, where the impurity must be represented with high precision but an effective description of the bath can be employed. Once a suitable numerical method has been developed, it will first be applied to the study of the Spin-Boson model, and later to the study of correlated electronic systems..