Machine Learning for Correlated Matter

About

I am Jonas Rigo and I am currently a Postdoc in the Computational Quantum Science group led by Markus Schmitt. Our group focuses on the study of complex quantum systems with Machine Learning techniques, and my personal research interests lie particularly in correlated matter.

In my research I leverage machine learning techniques to tackle the challenges of quantum many-body systems. My work involves developing effective models to simplify and accurately represent these systems, as well as utilizing neural quantum states to explore equilibrium and non-equilibrium quantum systems.

By combining these approaches, I aim to advance our understanding of both equilibrium and non-equilibrium properties of quantum systems, potentially paving the way for innovations in quantum devices and discoveries in quantum mechanics. If this piqued your interest, find out more below.

I am always open for students seeking an internship or a graduation project. Feel free to contact me or take a look at our group website.

Research Topics

• Effective Models
• Neural Quantum States

To learn more about my research topics, you can watch the recording of my presentation at Science online+ (in German).

Contact

Jonas Rigo

PGI-8

Building 02.18 / Room 2003

+49 2461/61-96989

E-Mail

Effective Models

In the study of solids, the microscopic models describing the underlying quantum many-body systems are often well known, as the crystal structures of solids can be empirically measured. However, the complexity of these models increases rapidly with the number of degrees of freedom (such as occupied orbitals of atoms), making brute force solutions analytically and/or numerically intractable for many realistic scenarios of interest. The challenge in many-body theory, therefore, lies not in writing down the bare model, but in solving it.

In many cases, it is unnecessary to consider all degrees of freedom of the system because only a relatively small subset actively controls the phenomena of interest. Thus, effective models can be devised that faithfully capture these phenomena while focusing only on the active degrees of freedom. Such effective models have reduced complexity and increased expressiveness. Consequently, the challenge in many-body theory can be restated as finding the best solvable model that approximates the physics of interest accurately.

This situation is akin to the inverse problem encountered in statistical inference or machine learning, where the goal is to infer a probabilistic model from observed data. A prominent example is large language models, which describe the probability of sentences in a given language. In this spirit, I explore machine learning techniques to construct effective models from simulated or experimentally measured data.

I am particularly interested in the design and use of complex quantum nano-electronics devices with advanced functionality beyond the classical paradigm. For these devices, effective models are essential to understand their low-temperature correlated electron physics and quantum transport properties. My research aims to develop these models automatically using machine learning techniques.

Neural Quantum States

The fundamental ingredients of a many-body system or correlated matter are a lattice, particles that can occupy the lattice sites, and a model (or Hamiltonian) that defines the transitions between all possible configurations of the particles on the lattice. To understand the behavior of this system, we need to find which configuration of particles on the lattice is the most likely to occur. However, quantum mechanics allows the system to be in several different configurations at once. This phenomenon, known as superposition, makes quantum many-body physics a formidable challenge because we need to find not just the most likely configuration but the most likely combination of configurations. The object that quantifies which configurations coexist in a superposition, and to what degree, is the quantum many-body wave function.

The only way to study the quantum many-body wave function is to find a high-quality approximate representation. To this end, I leverage the representational power of modern neural networks, which have shown themselves capable of learning exceedingly complicated probability distributions, such as those found in natural language. The approximation of a quantum many-body wave function with a neural network is known as a Neural Quantum State (NQS). NQS are used to represent ground state (lowest energy) wave functions, excited state wave functions, or the time evolution of quantum systems.

My main interest lies in breaking new ground in the understanding of correlated fermion systems by accessing ground states and equilibrium-dynamic quantities through NQS. Beyond equilibrium properties, the realm of non-equilibrium time evolution is filled with open questions, such as how an isolated quantum system can transition into a thermalized state similar to those we experience daily. NQS offer a promising new avenue to pursue these questions.

By advancing the study of NQS, I aim to unlock deeper insights into the behaviour of complex quantum systems, potentially paving the way for new technologies and enhancing our understanding of the quantum world.