Neural-Network based optimization of wave functions of interacting electrons
PI: Jainendra Jain (Physics)
Level of effort appropriate for the proposed project: 1 year of graduate student funding post COMPS (stipend only) in FY 25-26.
Description
When confined to two dimensions under a strong perpendicular magnetic field, electrons form a novel, strongly correlated phase of matter—the fractional quantum Hall (FQH) liquid, where each electron’s motion is entwined with all others. This collective behavior has revealed many new concepts including exotic quasiparticles, such as fractionally charged anyons and non-Abelian Majorana modes that underpin fault-tolerant quantum-computing proposals (a program actively pursued by Microsoft).
In a simplified theoretical framework where electrons are strictly confined to the lowest kinetic energy level called Landau level (LL), the fractional quantum Hall liquid, despite its strongly correlated non-perturbative character, is well-understood in term of composite fermion (CF) theory. Realistic systems however exhibit Landau-level mixing, i.e. go outside the simplified framework, and sometimes, even small admixtures of higher levels can induce dramatic ground-state changes— an effect confirmed experimentally and widely believed to underlie the 5/2 puzzle. Recent deeplearning approaches (e.g. Psi-former based on self-attention networks) variationally approximate FQH states with LL mixing but stall at approximately 12 particles, since they must learn all correlations from scratch and thus require enormous parameter counts. Systems this small are not sufficient to capture many of the exotic phenomena associated with the FQHE, leaving their conclusions in doubt.
In this project, we will initialize our model on CF trial wavefunctions and fine-tune to capture only the residual LL mixing effects—a transfer-learning strategy that slashes parameter requirements and opens the door to much larger systems. Concretely, we will augment the CF backflow ansatz with a message-passing neural network that employs a particle-wise attention mechanism (as in Carleo et al.) to learn correlations beyond the CF paradigm. By building in the bulk of the known CF physics, this hybrid architecture will require only a modest number of trainable parameters and enable scalable variational Monte Carlo studies in JAX.
Some of the first phenomena we will explore include:
Destabilization of the FQH liquid — under enhanced screening by higher bands.
Emergence and stability of Majorana modes — in finite-width, screened systems.
Selection among topologically distinct candidate states — identifying which phases dominate under varying conditions.
Liquid-to-crystal transitions — as screening strength, well width, and filling factor change.
We anticipate that this transfer-learning–based framework will yield new insights into these open questions, support multiple high-impact publications, and culminate in an open-source toolkit adaptable not only to FQH problems with LL mixing but also to a broader class of strongly correlated electron systems.
List of specific areas of computational and/or data science expertise or skills
Familiarity with quantum mechanics, quantum condensed matter physics, fractional quantum Hall effect; experience with variational Monte Carlo techniques for finding ground states of interacting many-body systems; experience in constructing machine-learning–based ansatzes for many-body fermionic wavefunctions; combining this with knowledge of the fractional quantum Hall effect; expertise in JAX, including neural-network optimization and automatic differentiation.
Connection of the project to ICDS’s mission
This proposal fits into both AI and quantum science, and it also touches on quantum information / computation.