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arXiv:2604.09798

Anyon molecules in fractional quantum Hall states

Taige Wang, Michael P. Zaletel

Published Apr 10, 2026• 0 citations
arXivHTMLPDF

Abstract

We use segment DMRG on the infinite cylinder to compute energies of charged excitations in gate-screened fractional quantum Hall states. For the $ν=1/3$ Laughlin, $ν=2/5$ Jain, and $ν=5/2$ anti-Pfaffian states, we find screening can bind like-charged anyons into molecules, with a strong dependence on filling-factor, gate distance, and fusion channel. In the Laughlin state, stable $\pm 2e/3$ molecules and larger clusters appear over a broad gate-distance window. The Jain state is molecular throughout the range we consider. In the anti-Pfaffian, binding is strongest on the hole side, where the charge-$e/2$ molecule is fused into the $ψ$ channel over a broad window of gate distances. In all three cases, screening suppresses long-range repulsion and exposes an intermediate-range attraction encoded in the oscillatory density tail of the fundamental anyon. We discuss consequences for addition spectra, interferometry, Wigner crystallization, anyon superconductivity, and entropy measurements.

DOI
10.48550/arxiv.2604.09798

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We use segment DMRG on the infinite cylinder to compute energies of charged excitations in gate-screened fractional quantum Hall states. For the ν=1/3ν=1/3ν=1/3 Laughlin, ν=2/5ν=2/5ν=2/5 Jain, and ν=5/2ν=5/2ν=5/2 anti-Pfaffian states, we find screening can bind like-charged anyons into molecules, with a strong dependence on filling-factor, gate distance, and fusion channel. In the Laughlin state, stable ±2e/3\pm 2e/3±2e/3 molecules and larger clusters appear over a broad gate-distance window. The Jain state is molecular throughout the range we consider. In the anti-Pfaffian, binding is strongest on the hole side, where the charge-e/2e/2e/2 molecule is fused into the ψψψ channel over a broad window of gate distances. In all three cases, screening suppresses long-range repulsion and exposes an intermediate-range attraction encoded in the oscillatory density tail of the fundamental anyon. We discuss consequences for addition spectra, interferometry, Wigner crystallization, anyon superconductivity, and entropy measurements.
The authors explore here the interesting ``chemistry'' of anyons -- collective excitations emerging from a large amount of correlated electrons -- in strongly interacting fractional quantum Hall fluids. Anyons can form clusters (``molecules'') because of the effective anyon-anyon interaction induced by tunable electron-electron interactions. Laughlin anyons form hydrogen molecule like bound states with short-range electron interactions, potentially explaining the mystery of the observed 2eee/3 effective charge at extremely low temperatures. In the non-Abelian Moore--Read phase, fusion channel dependent effective interactions lift the ``1/$\ensuremath{\psi}$'' degeneracy, enabling the possible energetic control of non-Abelian anyons. The authors also propose STM as a useful experimental tool for detecting the fingerprint of various configurations of anyon clusters.
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The quantum Hall effect has been the prototypical example for many emerging fields of Physics, including the study of topological phases of matter, topological order, and topological insulators. The objects of interest in this thesis are anyons, which are elementary excitations in fractional quantum Hall (FQH) fluids. Anyons are quasiparticles with fractional charge and fractional statistics. The latter prop- erty makes it a subject of immense interest due to application in fault-tolerant quantum computing. Here, we employ a perspective that anyons are the appro- priate degree of freedom to describe the relevant physics of FQH systems. This is because when a topological phase is assumed and the energy gap goes to infinity, anyons (“quasiholes”) are the only possible elementary excitations, since they are not energetically punished by the correspondng model Hamiltonian. With respect to a realistic Hamiltonian, however, this choice of degree of freedom depends on the exact effective interaction in the system. For example, while the Laughlin state is the model state at filling factor n + 1/3 (where n is some integer), when the effective electron-electron interaction is more long-ranged, the quasiholes of a Gaffnian state may be excited and become the better degree of freedom to describe physics in the same filling factor. This perspective results in a surprising observa- tion that a Laughlin quasihole may fractionalize under certain conditions, leading to a quasiparticle of charge e/6 that can potentially be detected in experiments. Another important aspect of anyons is their intrinsic spin and the corresponding spin-statistics relation, which must account for the fact that FQH anyons are not point particles, but objects with finite sizes and intricate internal structures. Our investigation leads to a rigorous derivation of the general spin-statistics relation for anyons in Abelian FQH phases. Furthermore, we show it is possible to fully capture the important features of the statistics by a conformal Hilbert space (CHS) description. Our analysis provides the necessary tools to study such geometric effects, which we use to investigate how disorder in a realistic system may affect different experimental schemes for measuring anyon statistics.
Understanding the nature of quasihole excitations, i.e., anyons that have fractional charge and fractional statistics, has been a challenging problem in condensed matter physics. Our theoretical approach to this problem has been to consider a quantum dot containing a few charged particles, Coulomb coupled to the incompressible fluid. The size of the dot and the separation distance of the dot from the incompressible state strongly influences the energetics of the Laughlin quasiholes. Photoluminescence (PL) spectroscopy studies of this system have previously been able to probe these quasiholes that have confirmed our estimates of the Laughlin quasihole energies. Turning to the Pfaffian state, we now observe that such a theoretical approach is also able to provide valuable information about the Pfaffian quasiholes, viz., the energy dispersion, the charge density distribution and the quasihole energy. The energy dispersion of e/4 quasiholes derived here, clearly reflect the interaction between the quantum dot and the incompressible Pfaffian state. PL spectroscopy experiments on the 5/2 Pfaffian-Laughlin state could perhaps shed light on the energetics we found here of these elusive quasiparticles.
The lowest-Landau-level anyon model becomes nonperiodic in the statistics parameter when the finite size of the attached flux tubes is taken into account. The finite-size effects cause the inverse proportional relation between the critical filling factor and the statistics parameter to be nonperiodically continued in the screening regime, where the fluxes are anti-parallel to the external magnetic field -- at critical filling, the external magnetic field is entirely screened by the mean magnetic field associated with the flux tubes. A clustering argument is proposed to select particular values of the statistics parameter. In this way, IQHE and FQHE fillings are obtained in terms of gapped nondegenerate LLL-anyonic wave functions. Jain's series are reproduced without the need to populate higher Landau levels. New FQHE series are proposed, like, in particular, the particle-hole complementary series of the Laughlin one. For fast-rotating Bose-Einstein condensates, a corresponding clustering argument yields particular fractional filling series.
We study phases of itinerant anyons when hole-doping Laughlin-like states in fractional Chern insulators (FCIs). In light of the recent observation of time-reversal-broken superconductivity near FCIs in van der Waals materials, a theoretical understanding of doped fractional quantum Hall states on a lattice has been developed by Shi and Senthil [Phys. Rev. X 15, 031069], reviving old ideas about "anyon superconductivity". We test these ideas analytically within an effective parton mean-field theory and numerically with variational Monte Carlo, pointing out that the predicted state depends on whether the Laughlin order at ν=1/mν=1/mν=1/m is described by a U(1), or an SU(m) Chern-Simons field, the latter implying a symmetry between the m parton species. Our results demonstrate that the interplay between band Berry curvature and effective anyon dispersion has crucial implications for which anyonic phase is realized. In the experimentally relevant scenario of hole-doping the ν=1/3ν=1/3ν=1/3 fermionic FCI, our results uncover a mechanism for the formation of an anyon superconducting state of half-integer central charge in the case when the energetically cheapest excitations are the fundamental 1/3 charge anyons, bypassing the need for these anyons to pair into charge-2/3 composites, which has generally been assumed in similar anyon superconductivity constructions.