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arXiv:2512.00527 · PRX Intelligence

Dressing Composite Fermions with Artificial Intelligence

Mytraya Gattu

Published Oct 28, 2026• 0 citations
arXivHTMLPDF

Abstract

Recent variational studies have demonstrated that the strongly correlated ground states of the fractional quantum Hall (FQH) effect can be captured using machine learning approaches starting from no prior knowledge of the underlying physics. We introduce a complementary framework that instead starts from Jain's composite-fermion (CF) wave functions, which accurately describe FQH states as weakly interacting states of CFs at fillings ν = n / ( 2 p n + 1 ) in an idealized limit. As we move away from this idealized limit to one more in line with experimental reality, we expect CFs to become dressed much like the electrons of a noninteracting system, which are dressed by neutral excitations as the interaction is turned on adiabatically, as in Landau's Fermi-liquid theory. We model this dressing using a Feynman-Cohen-style backflow approach, implemented through symmetry-preserving neural networks, which we refer to as CF-Flow. CF-Flow achieves competitive accuracy with substantially greater computational efficiency and scales to systems of ≳ 26 electrons. At fillings ν = 1 / 3 and 2 / 5 , CF-Flow produces ground-state energies as functions of Landau-level mixing strength that are nearly indistinguishable from those obtained using the fixed-phase diffusion Monte Carlo (fp-DMC) method, with low local-energy standard deviations, even though the latter constrains the wave function phase to that of the lowest Landau level, thereby providing insight into why fp-DMC has been successful in giving an accurate quantitative account of several experiments. Finally, the symmetry-preserving architecture of CF-Flow enables access to excited states and computation of the transport gap at ν = 1 / 3 and ν = 2 / 5 . Within the FQH sectors studied, the extrapolated gap is well described by an exponential decrease with Landau-level mixing and approaches a finite value at large mixing strength.

DOI
10.1103/zq76-147c

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•May 1, 2012•0 citations
Recent variational studies have demonstrated that the strongly correlated ground states of the fractional quantum Hall (FQH) effect can be captured using machine learning approaches starting from no prior knowledge of the underlying physics. We introduce a complementary framework that instead starts from Jain's composite-fermion (CF) wave functions, which accurately describe FQH states as weakly interacting states of CFs at fillings ν = n / ( 2 p n + 1 ) in an idealized limit. As we move away from this idealized limit to one more in line with experimental reality, we expect CFs to become dressed much like the electrons of a noninteracting system, which are dressed by neutral excitations as the interaction is turned on adiabatically, as in Landau's Fermi-liquid theory. We model this dressing using a Feynman-Cohen-style backflow approach, implemented through symmetry-preserving neural networks, which we refer to as CF-Flow. CF-Flow achieves competitive accuracy with substantially greater computational efficiency and scales to systems of ≳ 26 electrons. At fillings ν = 1 / 3 and 2 / 5 , CF-Flow produces ground-state energies as functions of Landau-level mixing strength that are nearly indistinguishable from those obtained using the fixed-phase diffusion Monte Carlo (fp-DMC) method, with low local-energy standard deviations, even though the latter constrains the wave function phase to that of the lowest Landau level, thereby providing insight into why fp-DMC has been successful in giving an accurate quantitative account of several experiments. Finally, the symmetry-preserving architecture of CF-Flow enables access to excited states and computation of the transport gap at ν = 1 / 3 and ν = 2 / 5 . Within the FQH sectors studied, the extrapolated gap is well described by an exponential decrease with Landau-level mixing and approaches a finite value at large mixing strength.
The composite fermion (CF) theory gives both a phenomenological description for many fractional quantum Hall (FQH) states, as well as a microscopic construction for large scale numerical calculation of these topological phases. The fundamental postulate of mapping FQH states of electrons to integer quantum Hall (IQH) states of CFs, however, was not formally established. The Landau level (LL) projection needed for the microscopic calculations is in some sense uncontrolled and unpredictable. We rigorously derive the unitary relationship between electrons and the CFs, showing the latter naturally emerge from special interactions within a single LL, without resorting to any projection by hand. In this framework, all FQH states topologically equivalent to those described by the conventional CF theory (e.g., the Jain series) have exact model Hamiltonians that can be explicitly derived, and we can easily generalize to FQH states from interacting CFs. Our derivations reveal fundamental connections between the CF theory and the pseudopotential/Jack polynomial constructions, and argue that all Abelian CF states are physically equivalent to the IQH states, while a plethora of non-Abelian CF states can be systematically constructed and classified. We also discuss about implications to experiments and effective field theory descriptions based on the descriptions with CFs as elementary particles.
Single particle basis functions for composite fermions are obtained from which many-composite fermion states confined to the lowest electronic Landau level can be constructed in the standard manner, i.e. by building Slater determinants. This representation enables a Monte Carlo study of systems containing a large number of composite fermions, yielding new quantitative and qualitative information. The ground state energy and the gaps to charged and neutral excitations are computed for a number of fractional quantum Hall effect (FQHE) states, earlier off-limits to a quantitative investigation. The ground state energies are estimated to be accurate to ~0.1% and the gaps at the level of a few percent. It is also shown that at Landau level fillings smaller than or equal to 1/9 the FQHE is unstable to a spontaneous creation of excitons of composite fermions. In addition, this approach provides new conceptual insight into the structure of the composite fermion wave functions, resolving in the affirmative the question of whether it is possible to motivate the composite fermion theory entirely within the lowest Landau level, without appealing to higher Landau levels.
Fractional quantum Hall systems host strongly correlated topological phases with potential applications in topological quantum computation, yet identifying their microscopic ground states remains challenging because competing phases are often nearly degenerate and Landau-level mixing is difficult to treat. Here, we introduce a symmetry-adapted neural-network wavefunction that describes Abelian and non-Abelian states while incorporating all Landau levels. The method accurately captures composite-fermion liquids and the emergence of Wigner crystallization at low filling. When the first Landau level is partially filled, finite-size overlaps and entanglement spectra provide evidence consistent with 2ˉk1k+1\bar{2}^{k}1^{k+1}2ˉk1k+1-type parton phases at ν=4/3ν=4/3ν=4/3 and 7/57/57/5, while the ν=3/2ν=3/2ν=3/2 state exhibits anti-Pfaffian-like entanglement structure. These results demonstrate that neural-network wavefunctions offer a flexible framework for studying competing topological orders in fractional quantum Hall systems.
Pairing of composite fermions provides a possible mechanism for fractional quantum Hall effect at even denominator fractions and is believed to serve as a platform for realizing quasiparticles with non-Abelian braiding statistics. We present results from fixed-phase diffusion Monte Carlo calculations which predict that substantial Landau level mixing can induce a pairing of composite fermions at filling factors ν=1/2 and ν=1/4 in the l=-3 relative angular momentum channel, thereby destabilizing the composite-fermion Fermi seas to produce non-Abelian fractional quantum Hall states.
Strong correlation brings a rich array of emergent phenomena, as well as a daunting challenge to theoretical physics study. In condensed matter physics, the fractional quantum Hall effect is a prominent example of strong correlation, with Landau level mixing being one of the most challenging aspects to address using traditional computational methods. Deep learning real-space neural network wave function methods have emerged as promising architectures to describe electron correlations in molecules and materials, but their power has not been fully tested for exotic quantum states. In this work, we employ real-space neural network wave function techniques to investigate fractional quantum Hall systems. On both 1/3 and 2/5 filling systems, we achieve energies consistently lower than exact diagonalization results which only consider the lowest Landau level. We also demonstrate that the real-space neural network wave function can naturally capture the extent of Landau level mixing up to a very high level, overcoming the limitations of traditional methods. Our work underscores the potential of neural networks for future studies of strongly correlated systems and opens new avenues for exploring the rich physics of the fractional quantum Hall effect.
Materials exhibiting exotic quantum phenomena at a macroscopic level are of great interest because of its intrinsic value to Physics, and also because of its potential applications in technology. Strongly correlated electronic systems form interesting examples of these. Exploring them calls for a good understanding of its physics, and development of new tools that are applicable to their analysis. Robustness of the fractional quantum Hall effect (FQHE) makes it an ideal stage to study strongly correlated electron systems. The complexity of the FQHE problem stems directly from the strong interactions between the constituent particles and not from the specific nature of the material it is implemented in. This work attempts to gain a theoretical description of some of the less understood aspects of FQHE. FQHE in the lowest Landau level is well understood using the theory of weakly interacting emergent particles called composite fermions. Composite fermions formed in the second Landau level however appear to be strongly interacting. Of particular interest is the FQHE at 2 + 1/2 filling fraction, where the many body ground state is believed to be described by a paired state of composite fermions, represented by the Pfaffian wavefunction. Based on predicted properties of its excitations, there has been proposals for implementing topological quantum com- putations in this system. However a good understanding of the nature of these excitations is still lacking. This thesis introduces a class of many body wavefunctions called “bipartite composite fermion states” that provide a unified description of all excitations of the paired state at 5/2. In the bipartite composite fermion (BCF) picture, constituent composite fermions split into two partitions which are correlated to each other. Within each partition, they fill the lowest composite fermion Landau level of its partition. Properties of the BCF state can now be related to the properties of the individual partitions, which are well understood in terms of the composite fermion theory. In particular, we show that the excitations of BCF states are obtained by creating excitations in the individual partitions. The paired state with odd number of composite fermions should have an unpaired composite fermion. The BCF model predicts that this unpaired composite fermion behaves as an exciton in the quasiparticle and quasihole are in separate partitions. We confirm this prediction numerically in finite size systems. Generalizations of bipartite composite fermion functions to other filling fractions especially 2 + 4/7 and 2 + 3/5 are also studied. Idea of bipartite composite fermions can be generalized to the case of more partitions. Specifically, we look at tripartite composite fermion states which are similar to the bipartite states, except that these have three correlated partitions instead of two. Tripartite states have a filling fraction of ν = 3/5, and its particle hole conjugate is a candidate wavefunction for describing the ν = 2 + 2/5…