Pith. sign in

REVIEW 3 major objections 5 minor 66 references

Simulating Composite Fermion Excitons by Density Functional Theory and Monte Carlo on a Disk

T0 review · 3 major / 5 minor · reviewed 2026-08-11 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read Composite-fermion excitons constructed on a disk reproduce the $\nu=1/3$ magnetoroton dispersion in density functional theory, Monte Carlo, and exact diagonalization, and their spectral function places the chiral spin $-2$ graviton at…

desk verdict Solid CF-exciton dispersion calculation on the disk; the chiral graviton spectral function is a restricted-basis projection and should not be sold as a spectral measurement. read the letter →

arxiv 2412.02320 v1 pith:LACTKPA6 submitted 2024-12-03 cond-mat.str-el cond-mat.mes-hall

Yi Yang , Songyang Pu , Yayun Hu , Zi-Xiang Hu This is my paper · ORCID
classification cond-mat.str-elcond-mat.mes-hall
keywords fractionalquantumHalleffectcompositefermionexcitonmagnetorotonchiralgravitondensityfunctionaltheoryMonteCarlodiskgeometryν=1/3state
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

The paper constructs neutral excitations of the fractional quantum Hall state at filling $\nu=1/3$ as single composite-fermion excitons in disk geometry, and simulates them with density functional theory and variational Monte Carlo. The three numerical methods give consistent magnetoroton dispersions, with a matching roton minimum and a neutral gap near $0.008$ in units of $e^2/\epsilon l$. The paper then evaluates a spectral function over this exciton branch and finds a single peak at angular-momentum transfer $\Delta M=2$, which it identifies with the chiral spin $-2$ graviton mode; the particle-hole conjugate state at $\nu=2/3$ shows the opposite chirality. If correct, the work provides a practical route to neutral collective excitations and their geometric 'graviton' content for a broad class of fractional quantum Hall states in a geometry that includes a physical edge.

What carries the argument

The central object is the single composite-fermion exciton in disk geometry: an antisymmetrized product of composite-fermion orbitals in an effective magnetic field, in which one fermion is removed from the top occupied $\Lambda$-level orbital and placed into the first unoccupied $\Lambda$-level orbital, followed by projection onto the lowest Landau level. The machinery includes composite-fermion density functional theory with a density-dependent effective magnetic field and a local-density exchange-correlation energy; a projected trial wave function sampled by Monte Carlo; and a spectral function $I_\sigma(M)$ restricted to the exciton branch, built from operators $\hat O_\pm$ that change two-body relative angular momentum by $\pm2$. The scaling $k=\Delta M/\sqrt{6N_e}$ collapses data for different particle numbers onto one dispersion curve, and the $\Delta M=2$ selection rule in $I_\pm$ isolates the chiral graviton.

What would settle it

An exact diagonalization of the same $\nu=1/3$ disk with $N_e$ up to about 12, computing the spectral function over all eigenstates rather than the single-exciton branch, would falsify the claim if it found a comparable peak in $I_+(M)$ at $\Delta M=2$ or additional spin-2 resonances at other $\Delta M$ values.

Watch

Extended reading notes

Core claim

The central claim is that the magnetoroton mode of the $\nu=1/3$ state can be faithfully described as a single composite-fermion exciton, one composite fermion promoted from the highest occupied angular-momentum orbital of the lowest $\Lambda$ level to an orbital of the first empty $\Lambda$ level. Energy differences computed from this one-exciton ansatz, using self-consistent composite-fermion density functional theory, Monte Carlo sampling of the projected wave function, and exact diagonalization, all collapse onto the same dispersion curve when plotted against $k=\Delta M/\sqrt{6N_e}$. The same exciton wave functions, fed into the spectral function $I_\sigma(M)$, yield exactly one nonzero peak, in $I_-(M)$ at $\Delta M=2$ for $\nu=1/3$ and in $I_+(M)$ at $\Delta M=2$ for $\nu=2/3$, which the paper reads as the chiral graviton with spin $-2$ and spin $+2$, respectively. The paper presents the three-method agreement, the consistency of the roton minimum, and the selective $\Delta M=2$ peak as evidence that the single-exciton branch carries the graviton spectral weight.

Load-bearing premise

The load-bearing assumption is that a single composite-fermion exciton, one hole in the highest occupied $\Lambda$ level and one particle in the first empty $\Lambda$ level, faithfully represents the magnetoroton and carries the entire chiral graviton spectral weight.

Editorial extensions

If this is right

  • For the $\nu=1/3$ state, the magnetoroton dispersion and its roton minimum can be obtained in disk geometry without exact diagonalization, so bulk neutral gaps become accessible for systems of 50--100 electrons.
  • The chiral graviton mode of the $\nu=1/3$ state has spin $-2$ and appears in the exciton spectral function at $\Delta M=2$; the $\nu=2/3$ state has the opposite chirality, spin $+2$.
  • The scaling $k=\Delta M/\sqrt{6N_e}$ makes data from different system sizes collapse onto one curve, allowing thermodynamic-limit extrapolation of the graviton peak and the neutral gap.
  • The same construction extends to the entire sequence $\nu=n/(2n\pm1)$ and to higher-$\Lambda$-level excitations, including spin-4 composite-fermion excitons.
  • The method gives a route to neutral collective excitations in disk geometry, which naturally includes edge and confinement effects absent in closed-geometry calculations.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • Because the spectral function is restricted to the single-exciton branch, the zeros of $I_+(M)$ and the absence of other resonances in $I_-(M)$ reflect the ansatz as much as the physics; a full many-body spectrum under Coulomb interaction may contain additional chiral graviton resonances, as the paper itself notes.
  • If the single-exciton description holds, the calculated spectral function could be compared directly with polarized Raman scattering intensities, giving a quantitative prediction for the graviton peak's position and chirality as a function of filling factor.
  • The long-wavelength discrepancy between density functional theory and Monte Carlo, attributed to the lack of lowest-Landau-level projection in the DFT treatment, suggests that a projection-corrected functional would bring the two dispersions into agreement there as well.
  • Varying the confining background potential in the disk would test whether the roton minimum and the $\Delta M=2$ peak are robust against edge details.
Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 5 minor

Summary. This paper studies neutral collective excitations of the ν=1/3 fractional quantum Hall state in disk geometry using composite fermion (CF) excitons. The authors construct single CF exciton wave functions in the disk, implement them in a CF density functional theory (DFT) framework and in variational Monte Carlo (MC), and compare the resulting magnetoroton dispersion with exact diagonalization (ED). The ground-state energies extrapolate to values consistent with previous literature. The paper further defines a spectral function Iσ(M) from the single-CF-exciton branch and interprets a peak at ΔM=2 as a chiral graviton mode with spin −2 for ν=1/3 and spin +2 for the particle-hole conjugate ν=2/3 state.

Significance. The methodological contribution—constructing CF excitons on a disk and benchmarking their dispersion against DFT, MC, and ED—is valuable and likely extendable to other Jain sequence states. The agreement between the three methods for the roton minimum and the thermodynamic extrapolation of the ground-state energy are credible and carefully presented. However, the graviton identification rests on a spectral function that, as the authors acknowledge, sums over the restricted single-exciton branch rather than over all eigenstates. This limitation, combined with the paper's own discussion of multiple chiral graviton modes under Coulomb interactions, means the central claim of 'confirming' the chiral graviton is not yet supported. The paper would benefit from either a full-Hilbert-space spectral function calculation (e.g., ED for small systems) or a more cautious interpretation.

major comments (3)
  1. [Sec. IV, Eq. (11)] The spectral function Iσ(M) in Eq. (11) sums only over the single-CF-exciton trial states, not over eigenstates of the full Hamiltonian, as the paper explicitly notes. The resulting sharp peak in I−(M) at ΔM=2 and exact zeros elsewhere are therefore properties of this variational subspace, not of the physical spectrum. This undermines the statement in Sec. IV that the peak 'confirms the presence of a chiral graviton mode,' especially because Sec. V acknowledges that Coulomb interactions may generate multiple chiral graviton modes and numerous resonance peaks. A full spectral function calculation (e.g., ED on small systems) or a clear reframing of the result as a variational approximation is needed.
  2. [Sec. IV, Figs. 5 and 6] No statistical error bars are reported for the Monte Carlo spectral function values, nor for the thermodynamic-limit extrapolation of the peak heights shown in the inset of Fig. 5. Given that the graviton claim rests entirely on the location and amplitude of this peak, the authors should provide uncertainty estimates to establish that the peak is significant and not a statistical fluctuation.
  3. [Sec. II A] The CF exciton states are not constructed with a definite center-of-mass (COM) angular momentum, as the paper states. Since the operators O± in Eq. (12) conserve COM angular momentum, the matrix elements in Eq. (11) couple only to the zero-COM component of each trial state. The authors should either project the trial states to zero COM angular momentum or quantify the weight of the zero-COM component to ensure that the spectral function is not contaminated by COM motion.
minor comments (5)
  1. [Abstract] Abstract contains a typo: 'rescontruction' should be 'reconstruction'.
  2. [Sec. II B] In Sec. II B, 'quastiparticle' should be 'quasiparticle'.
  3. [Sec. IV] In Sec. IV, 'paricles' should be 'particles'.
  4. [Sec. III] The phrase 'identical roton minimum' in Sec. III is stronger than the small-system ED data can support; suggest 'consistent roton minimum' throughout.
  5. [Sec. IV] The normalization of Iσ(M) (by ⟨Ψ1/3|O†σ Oσ|Ψ1/3⟩) should be defined more explicitly, and the effect of this normalization on the peak amplitude and its thermodynamic scaling should be discussed.

Circularity Check

1 steps flagged · score 3.0 of 10

Mild circularity in the graviton spectral-function claim: Eq. (11) is defined over the CF-exciton trial branch, so the ΔM=2 peak and the zeros are kinematically forced by angular momentum selection, while the dispersion claim remains independently benchmarked against ED.

  1. self definitional [Section IV, Eq. (11) and Fig. 5]
    "We evaluate the spectral function as a function of the total angular momentum for the full CF exciton branch rather than as a function of energy for all eigenstates, which makes Eq. (11) different from its original definition in Ref. 25. ... As shown in Fig. 5, I−(M) exhibits a pronounced peak at ∆M = 2, indicating the presence of a spin −2 “graviton” excitation."

    Because Eq. (11) sums only over the single-CF-exciton states |Ψ_m_exciton⟩, whose angular momenta are Mm = Mgs − (Ne−1−m), and the operators O± in Eq. (12) change angular momentum by ±2, angular momentum conservation forces every nonzero matrix element to sit at ΔM=2 for I− and forbids all weight for I+ (with I+ also vanishing by O+ annihilating the Laughlin state). Thus the reported peak location and the zeros are a selection-rule consequence of the restricted definition of Iσ, not a property of the full excitation spectrum. The paper explicitly concedes that Eq. (11) differs from the original full-eigenstate definition in Ref. 25, and Sec. V concedes that Coulomb interactions may produce multiple chiral graviton peaks.

full rationale

The magnetoroton dispersion claim is largely self-contained: DFT and MC exciton energies are benchmarked against exact diagonalization in Fig. 4, and the DFT LDA parameters (Appendix A) were fitted to prior ground-state data rather than to the roton minimum or neutral gap, so the dispersion comparison is an independent test. The main circularity is confined to the spectral-function analysis, where Eq. (11) is deliberately restricted to the CF-exciton branch, making the ΔM=2 peak and the zeros kinematically predetermined by angular momentum alone; the nonzero amplitude is still a genuine Monte Carlo overlap, so the reduction is partial. Self-citations to the CF-DFT framework (Ref. 44) and the IQHE-FQHE correspondence (Ref. 52) are methodological support rather than load-bearing justification for the central results, and the paper's Sec. V caveat about multiple chiral graviton modes under Coulomb interactions is an honest limitation. Overall, the central dispersion result is independently benchmarked, and the graviton claim has a real computed amplitude despite its restricted-basis definition.

Assumptions & free parameters 5 free parameters · 5 assumptions · 0 invented entities

The paper introduces no new physical entities. The main parameters are the four LDA coefficients fitted in prior work and the unspecified CF kinetic-energy scale. The axioms are standard domain assumptions of composite-fermion theory and its DFT formulation, plus the single-exciton ansatz.

free parameters (5)
  • LDA coefficient a = -0.78213
    Fitted to reproduce FQH ground-state energies in prior work (Hu & Jain 2019); used in the exchange-correlation energy functional in Eq. (5).
  • LDA coefficient b = 0.2774
    Fitted LDA parameter for the CF exchange-correlation functional, Appendix A.
  • LDA coefficient f = 0.33
    Fitted LDA parameter for the CF exchange-correlation functional, Appendix A.
  • LDA coefficient g = -0.04981
    Fitted LDA parameter for the CF exchange-correlation functional, Appendix A.
  • CF effective mass / cyclotron energy scale in DFT = not stated
    The kinetic energy operator in Eq. (B5) depends on ℏω_B (or the CF effective mass), but its numerical value or relation to the Coulomb scale is not given, which is needed to reproduce the DFT energies.
assumptions (5)
  • domain assumption Composite fermion mapping (electrons bound to two flux quanta) is valid for the Laughlin 1/3 state and Jain sequence.
    Used throughout to construct the ground state and exciton states in Section II.
  • domain assumption The LDA exchange-correlation functional for composite fermions is accurate for inhomogeneous electron densities in the disk.
    Adopted from Hu & Jain 2019; the DFT energies depend on this functional via Eq. (5).
  • domain assumption A single CF exciton (one hole in the 0ΛL and one particle in the 1ΛL) describes the magnetoroton mode.
    Central modeling choice in Section II.A; the validity is tested only indirectly by comparing energies with ED.
  • domain assumption The Jain-Kamilla projection is an accurate approximation to the full lowest-Landau-level projection for these trial wavefunctions.
    Used in the MC wavefunctions, Eq. (8) and Eq. (9).
  • domain assumption Constrained DFT is a valid formalism for excited states.
    Invoked in Section II.B to justify the DFT treatment of excitons.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Simulating Composite Fermion Excitons by Density Functional Theory and Monte Carlo on a Disk." pith.science (2026). https://pith.science/paper/LACTKPA6

@misc{pith2026241202320,
  author       = {Pith},
  title        = {Pith review of: Simulating Composite Fermion Excitons by Density Functional Theory and Monte Carlo on a Disk},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/LACTKPA6}},
  note         = {Machine review of arXiv:2412.02320}
}
abstract

The Kohn-Sham density functional method for the fractional quantum Hall (FQH) effect has recently been developed by mapping the strongly interacting electrons into an auxiliary system of weakly interacting composite fermions (CFs) that experience a density-dependent effective magnetic field. This approach has been successfully applied to explore the edge rescontruction, fractional charge and fractional braiding statistics of quasiparticle excitations. In this work, we investigate composite fermion excitons in the bulk of the disk geometry. By varying the separation of the quasiparticle-quasihole pairs and calculating their energy, we compare the dispersion of the magnetoroton mode with results from other numerical methods, such as exact diagonalization (ED) and Monte Carlo (MC) simulation. Furthermore, through an evaluation of the spectral function, we identify chiral ``graviton'' excitations: a spin $-2$ mode for the particle-like Laughlin state and a spin $2$ mode for the hole-like Laughlin state. This method can be extended to construct neutral collective excitations for other fractional quantum Hall states in disk geometry.

Figures

Figures reproduced from arXiv: 2412.02320 by the authors.

Figure 1
Figure 1. FIG. 1: A schematic cartoon of a single CF exciton on a [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2: The ground-state energy per electron at [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3: CF exciton density profiles calculated using DFT [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figures from the paper (3 more)
Figure 4
Figure 4. Figure 4: FIG. 4: CF exciton energy calculated using three different [PITH_FULL_IMAGE:figures/full_fig_p006_4.png]
Figure 5
Figure 5. Figure 5: FIG. 5: Spectral function obtained from MC simulations [PITH_FULL_IMAGE:figures/full_fig_p006_5.png]
Figure 6
Figure 6. Figure 6: FIG. 6: Spectral function obtained from MC simulations for [PITH_FULL_IMAGE:figures/full_fig_p007_6.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

66 extracted references · 28 canonical work pages

  1. [1]

    author D. C. Tsui , author H. L. Stormer , and author A. C. Gossard , journal Phys. Rev. Lett. volume 48 , pages 1559 ( year 1982 ), ://link.aps.org/doi/10.1103/PhysRevLett.48.1559

    doi:10.1103/physrevlett.48.1559 1982

  2. [2]

    author R. B. Laughlin , journal Phys. Rev. Lett. volume 50 , pages 1395 ( year 1983 ), ://link.aps.org/doi/10.1103/PhysRevLett.50.1395

    doi:10.1103/physrevlett.50.1395 1983

  3. [3]

    author X. G. Wen and author Q. Niu , journal Phys. Rev. B volume 41 , pages 9377 ( year 1990 ), ://link.aps.org/doi/10.1103/PhysRevB.41.9377

    doi:10.1103/physrevb.41.9377 1990

  4. [4]

    Wen , journal Advances in Physics volume 44 , pages 405 ( year 1995 ), ://doi.org/10.1080/00018739500101566

    author X.-G. Wen , journal Advances in Physics volume 44 , pages 405 ( year 1995 ), ://doi.org/10.1080/00018739500101566

    doi:10.1080/00018739500101566 1995

  5. [5]

    Arovas , author J

    author D. Arovas , author J. R. Schrieffer , and author F. Wilczek , journal Phys. Rev. Lett. volume 53 , pages 722 ( year 1984 ), ://link.aps.org/doi/10.1103/PhysRevLett.53.722

    doi:10.1103/physrevlett.53.722 1984

  6. [6]

    author F. D. M. Haldane and author E. H. Rezayi , journal Phys. Rev. B volume 31 , pages 2529 ( year 1985 ), ://link.aps.org/doi/10.1103/PhysRevB.31.2529

    work page doi:10.1103/physrevb.31.2529 1985

  7. [7]

    Yang , author Z.-X

    author B. Yang , author Z.-X. Hu , author Z. Papi c \' c , and author F. D. M. Haldane , journal Phys. Rev. Lett. volume 108 , pages 256807 ( year 2012 ), ://link.aps.org/doi/10.1103/PhysRevLett.108.256807

    doi:10.1103/physrevlett.108.256807 2012

  8. [8]

    Golkar , author D

    author S. Golkar , author D. X. Nguyen , and author D. T. Son , journal Journal of High Energy Physics volume 2016 , pages 21 ( year 2016 ), ISSN issn 1029-8479 , ://doi.org/10.1007/JHEP01(2016)021

    doi:10.1007/jhep01(2016)021 2016

Show all 66 references
  1. [10]

    author A. C. Balram and author S. Pu , journal The European Physical Journal B volume 90 , pages 124 ( year 2017 ), ISSN issn 1434-6036 , ://doi.org/10.1140/epjb/e2017-80177-5

    2017 doi

  2. [11]

    author S. M. Girvin , author A. H. MacDonald , and author P. M. Platzman , journal Phys. Rev. Lett. volume 54 , pages 581 ( year 1985 ), ://link.aps.org/doi/10.1103/PhysRevLett.54.581

    1985 doi

  3. [12]

    author S. M. Girvin , author A. H. MacDonald , and author P. M. Platzman , journal Phys. Rev. B volume 33 , pages 2481 ( year 1986 ), ://link.aps.org/doi/10.1103/PhysRevB.33.2481

    1986 doi

  4. [13]

    author I. D. Rodriguez , author A. Sterdyniak , author M. Hermanns , author J. K. Slingerland , and author N. Regnault , journal Phys. Rev. B volume 85 , pages 035128 ( year 2012 ), ://link.aps.org/doi/10.1103/PhysRevB.85.035128

    2012 doi

  5. [14]

    author F. D. M. Haldane , journal Phys. Rev. Lett. volume 107 , pages 116801 ( year 2011 ), ://link.aps.org/doi/10.1103/PhysRevLett.107.116801

    2011 doi

  6. [15]

    author J. K. Jain , title Composite Fermions ( publisher Cambridge University Press , year 2007 )

    2007

  7. [16]

    author P. M. Platzman and author S. He , journal Phys. Rev. B volume 49 , pages 13674 ( year 1994 ), ://link.aps.org/doi/10.1103/PhysRevB.49.13674

    1994 doi

  8. [17]

    author V. W. Scarola , author K. Park , and author J. K. Jain , journal Phys. Rev. B volume 61 , pages 13064 ( year 2000 ), ://link.aps.org/doi/10.1103/PhysRevB.61.13064

    2000 doi

  9. [18]

    author A. C. Balram , author G. J. Sreejith , and author J. K. Jain , title Splitting of girvin-macdonald-platzman density wave and the nature of chiral gravitons in fractional quantum hall effect ( year 2024 ), 2406.02730 , ://arxiv.org/abs/2406.02730

    2024 arXiv

  10. [19]

    Yang , title Quantum geometric fluctuations in fractional quantum hall fluids ( year 2024 ), 2411.05076 , ://arxiv.org/abs/2411.05076

    author B. Yang , title Quantum geometric fluctuations in fractional quantum hall fluids ( year 2024 ), 2411.05076 , ://arxiv.org/abs/2411.05076

    2024 arXiv

  11. [20]

    Liu , author T

    author Y. Liu , author T. Zhao , and author T. Xiang , journal Phys. Rev. B volume 110 , pages 195137 ( year 2024 ), ://link.aps.org/doi/10.1103/PhysRevB.110.195137

    2024 doi

  12. [21]

    Fierz and author W

    author M. Fierz and author W. E. Pauli , journal Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences volume 173 , pages 211 ( year 1939 ), ://doi.org/10.1098/rspa.1939.0140

    1939

  13. [22]

    author E. A. Bergshoeff , author O. Hohm , and author P. K. Townsend , journal Phys. Rev. Lett. volume 102 , pages 201301 ( year 2009 ), ://link.aps.org/doi/10.1103/PhysRevLett.102.201301

    2009 doi

  14. [23]

    author E. A. Bergshoeff , author J. Rosseel , and author P. K. Townsend , journal Phys. Rev. Lett. volume 120 , pages 141601 ( year 2018 ), ://link.aps.org/doi/10.1103/PhysRevLett.120.141601

    2018 doi

  15. [24]

    Liu , author A

    author Z. Liu , author A. Gromov , and author Z. Papi c \' c , journal Phys. Rev. B volume 98 , pages 155140 ( year 2018 ), ://link.aps.org/doi/10.1103/PhysRevB.98.155140

    2018 doi

  16. [25]

    Liou , author F

    author S.-F. Liou , author F. D. M. Haldane , author K. Yang , and author E. H. Rezayi , journal Phys. Rev. Lett. volume 123 , pages 146801 ( year 2019 ), ://link.aps.org/doi/10.1103/PhysRevLett.123.146801

    2019 doi

  17. [26]

    Voinea , author R

    author C. Voinea , author R. Fan , author N. Regnault , and author Z. Papić , title Regularizing 3d conformal field theories via anyons on the fuzzy sphere ( year 2024 ), 2411.15299 , ://arxiv.org/abs/2411.15299

    2024 arXiv

  18. [27]

    Zhu , author C

    author W. Zhu , author C. Han , author E. Huffman , author J. S. Hofmann , and author Y.-C. He , journal Phys. Rev. X volume 13 , pages 021009 ( year 2023 ), ://link.aps.org/doi/10.1103/PhysRevX.13.021009

    2023 doi

  19. [28]

    Pinczuk , author B

    author A. Pinczuk , author B. S. Dennis , author L. N. Pfeiffer , and author K. West , journal Phys. Rev. Lett. volume 70 , pages 3983 ( year 1993 ), ://link.aps.org/doi/10.1103/PhysRevLett.70.3983

    1993 doi

  20. [29]

    author H. D. M. Davies , author J. C. Harris , author J. F. Ryan , and author A. J. Turberfield , journal Phys. Rev. Lett. volume 78 , pages 4095 ( year 1997 ), ://link.aps.org/doi/10.1103/PhysRevLett.78.4095

    1997 doi

  21. [30]

    Kang , author A

    author M. Kang , author A. Pinczuk , author B. S. Dennis , author L. N. Pfeiffer , and author K. W. West , journal Phys. Rev. Lett. volume 86 , pages 2637 ( year 2001 ), ://link.aps.org/doi/10.1103/PhysRevLett.86.2637

    2001 doi

  22. [31]

    Kang , author A

    author M. Kang , author A. Pinczuk , author B. S. Dennis , author M. A. Eriksson , author L. N. Pfeiffer , and author K. W. West , journal Phys. Rev. Lett. volume 84 , pages 546 ( year 2000 ), ://link.aps.org/doi/10.1103/PhysRevLett.84.546

    doi

  23. [32]

    Ezawa , journal Phys

    author M. Ezawa , journal Phys. Rev. Lett. volume 120 , pages 026801 ( year 2018 ), ://link.aps.org/doi/10.1103/PhysRevLett.120.026801

    2018 doi

  24. [33]

    Du , author U

    author L. Du , author U. Wurstbauer , author K. W. West , author L. N. Pfeiffer , author S. Fallahi , author G. C. Gardner , author M. J. Manfra , and author A. Pinczuk , journal Science Advances volume 5 , pages eaav3407 ( year 2019 ), ://www.science.org/doi/abs/10.1126/sciad...

    2019 doi

  25. [34]

    Liu , author U

    author Z. Liu , author U. Wurstbauer , author L. Du , author K. W. West , author L. N. Pfeiffer , author M. J. Manfra , and author A. Pinczuk , journal Phys. Rev. Lett. volume 128 , pages 017401 ( year 2022 ), ://link.aps.org/doi/10.1103/PhysRevLett.128.017401

    2022 doi

  26. [35]

    author C. J. Mellor , author R. H. Eyles , author J. E. Digby , author A. J. Kent , author K. A. Benedict , author L. J. Challis , author M. Henini , author C. T. Foxon , and author J. J. Harris , journal Phys. Rev. Lett. volume 74 , pages 2339 ( year 1995 ), ://link.aps.org/d...

    1995 doi

  27. [36]

    author I. V. Kukushkin , author J. H. Smet , author D. Schuh , author W. Wegscheider , and author K. von Klitzing , journal Phys. Rev. Lett. volume 98 , pages 066403 ( year 2007 ), ://link.aps.org/doi/10.1103/PhysRevLett.98.066403

    2007 doi

  28. [37]

    author I. V. Kukushkin , author J. H. Smet , author V. W. Scarola , author V. Umansky , and author K. von Klitzing , journal Science volume 324 , pages 1044 ( year 2009 b ), ://www.science.org/doi/abs/10.1126/science.1171472

    2009 doi

  29. [38]

    Dujovne , author A

    author I. Dujovne , author A. Pinczuk , author M. Kang , author B. S. Dennis , author L. N. Pfeiffer , and author K. W. West , journal Phys. Rev. Lett. volume 90 , pages 036803 ( year 2003 ), ://link.aps.org/doi/10.1103/PhysRevLett.90.036803

    2003 doi

  30. [39]

    author C. F. Hirjibehedin , author I. Dujovne , author A. Pinczuk , author B. S. Dennis , author L. N. Pfeiffer , and author K. W. West , journal Phys. Rev. Lett. volume 95 , pages 066803 ( year 2005 ), ://link.aps.org/doi/10.1103/PhysRevLett.95.066803

    2005 doi

  31. [40]

    author T. D. Rhone , author D. Majumder , author B. S. Dennis , author C. Hirjibehedin , author I. Dujovne , author J. G. Groshaus , author Y. Gallais , author J. K. Jain , author S. S. Mandal , author A. Pinczuk , et al. , journal Phys. Rev. Lett. volume 106 , pages 096803 ( ...

    2011 doi

  32. [41]

    Liang , author Z

    author J. Liang , author Z. Liu , author Z. Yang , author Y. Huang , author U. Wurstbauer , author C. R. Dean , author K. W. West , author L. N. Pfeiffer , author L. Du , and author A. Pinczuk , journal Nature volume 628 , pages 78 ( year 2024 ), ISSN issn 1476-4687 , ://doi.o...

    2024 doi

  33. [42]

    author F. D. M. Haldane , author E. H. Rezayi , and author K. Yang , journal Phys. Rev. B volume 104 , pages L121106 ( year 2021 ), ://link.aps.org/doi/10.1103/PhysRevB.104.L121106

    2021 doi

  34. [43]

    author D. X. Nguyen and author D. T. Son , journal Phys. Rev. Res. volume 3 , pages 023040 ( year 2021 ), ://link.aps.org/doi/10.1103/PhysRevResearch.3.023040

    2021 doi

  35. [44]

    Hu and author J

    author Y. Hu and author J. K. Jain , journal Phys. Rev. Lett. volume 123 , pages 176802 ( year 2019 ), ://link.aps.org/doi/10.1103/PhysRevLett.123.176802

    2019 doi

  36. [45]

    Ferconi , author M

    author M. Ferconi , author M. R. Geller , and author G. Vignale , journal Phys. Rev. B volume 52 , pages 16357 ( year 1995 ), ://link.aps.org/doi/10.1103/PhysRevB.52.16357

    1995 doi

  37. [46]

    Heinonen , author M

    author O. Heinonen , author M. I. Lubin , and author M. D. Johnson , journal Phys. Rev. Lett. volume 75 , pages 4110 ( year 1995 ), ://link.aps.org/doi/10.1103/PhysRevLett.75.4110

    1995 doi

  38. [47]

    Zhang and author J.-R

    author Y.-H. Zhang and author J.-R. Shi , journal Chinese Physics Letters volume 32 , eid 037101 ( year 2015 ), ://cpl.iphy.ac.cn/EN/abstract/article_63772.shtml

    2015

  39. [48]

    Zhao , author M

    author J. Zhao , author M. Thakurathi , author M. Jain , author D. Sen , and author J. K. Jain , journal Phys. Rev. Lett. volume 118 , pages 196802 ( year 2017 ), ://link.aps.org/doi/10.1103/PhysRevLett.118.196802

    2017 doi

  40. [49]

    author J. K. Jain , journal Phys. Rev. Lett. volume 63 , pages 199 ( year 1989 a ), ://link.aps.org/doi/10.1103/PhysRevLett.63.199

    1989 doi

  41. [50]

    Yang , author Q

    author W.-Q. Yang , author Q. Li , author L.-P. Yang , and author Z.-X. Hu , journal Chinese Physics B volume 28 , pages 067303 ( year 2019 ), ://dx.doi.org/10.1088/1674-1056/28/6/067303

    2019 doi

  42. [51]

    Kaduk , author T

    author B. Kaduk , author T. Kowalczyk , and author T. Van Voorhis , journal Chemical Reviews volume 112 , pages 321 ( year 2012 ), ://doi.org/10.1021/cr200148b

    2012 doi

  43. [52]

    Pu , author G

    author S. Pu , author G. J. Sreejith , and author J. K. Jain , journal Phys. Rev. Lett. volume 128 , pages 116801 ( year 2022 ), ://link.aps.org/doi/10.1103/PhysRevLett.128.116801

    2022 doi

  44. [53]

    author J. K. Jain , journal Phys. Rev. B volume 40 , pages 8079 ( year 1989 b ), ://link.aps.org/doi/10.1103/PhysRevB.40.8079

    1989 doi

  45. [54]

    author G. S. Jeon , author K. L. Graham , and author J. K. Jain , journal Phys. Rev. Lett. volume 91 , pages 036801 ( year 2003 ), ://link.aps.org/doi/10.1103/PhysRevLett.91.036801

    2003 doi

  46. [55]

    author G. S. Jeon , author K. L. Graham , and author J. K. Jain , journal Phys. Rev. B volume 70 , pages 125316 ( year 2004 ), ://link.aps.org/doi/10.1103/PhysRevB.70.125316

    2004 doi

  47. [56]

    author J. K. Jain and author R. K. Kamilla , journal International Journal of Modern Physics B volume 11 , pages 2621 ( year 1997 a ), ://doi.org/10.1142/S0217979297001301

    1997 doi

  48. [57]

    author J. K. Jain and author R. K. Kamilla , journal Phys. Rev. B volume 55 , pages R4895 ( year 1997 b ), ://link.aps.org/doi/10.1103/PhysRevB.55.R4895

    1997 doi

  49. [58]

    Metropolis , author A

    author N. Metropolis , author A. W. Rosenbluth , author M. N. Rosenbluth , author A. H. Teller , and author E. Teller , journal The Journal of Chemical Physics volume 21 , pages 1087 ( year 1953 ), ISSN issn 0021-9606 , ://doi.org/10.1063/1.1699114

    1953 doi

  50. [59]

    Ciftja and author C

    author O. Ciftja and author C. Wexler , journal Phys. Rev. B volume 67 , pages 075304 ( year 2003 ), ://link.aps.org/doi/10.1103/PhysRevB.67.075304

    2003 doi

  51. [60]

    Yang and author Z.-X

    author Y. Yang and author Z.-X. Hu , journal Phys. Rev. B volume 107 , pages 115162 ( year 2023 ), ://link.aps.org/doi/10.1103/PhysRevB.107.115162

    2023 doi

  52. [61]

    Zhao , author D

    author J. Zhao , author D. N. Sheng , and author F. D. M. Haldane , journal Phys. Rev. B volume 83 , pages 195135 ( year 2011 ), ://link.aps.org/doi/10.1103/PhysRevB.83.195135

    2011 doi

  53. [62]

    Hu , author Z

    author Z.-X. Hu , author Z. Papić , author S. Johri , author R. Bhatt , and author P. Schmitteckert , journal Physics Letters A volume 376 , pages 2157 ( year 2012 ), ISSN issn 0375-9601 , ://www.sciencedirect.com/science/article/pii/S0375960112006111

    2012

  54. [63]

    author E. V. Tsiper and author V. J. Goldman , journal Phys. Rev. B volume 64 , pages 165311 ( year 2001 ), ://link.aps.org/doi/10.1103/PhysRevB.64.165311

    2001 doi

  55. [64]

    Wan , author E

    author X. Wan , author E. H. Rezayi , and author K. Yang , journal Phys. Rev. B volume 68 , pages 125307 ( year 2003 ), ://link.aps.org/doi/10.1103/PhysRevB.68.125307

    2003 doi

  56. [65]

    author M. R. Peterson and author J. K. Jain , journal Phys. Rev. B volume 68 , pages 195310 ( year 2003 ), ://link.aps.org/doi/10.1103/PhysRevB.68.195310

    2003 doi

  57. [66]

    author D. X. Nguyen , author F. D. M. Haldane , author E. H. Rezayi , author D. T. Son , and author K. Yang , journal Phys. Rev. Lett. volume 128 , pages 246402 ( year 2022 ), ://link.aps.org/doi/10.1103/PhysRevLett.128.246402

    2022 doi

  58. [67]

    author A. C. Balram and author J. K. Jain , journal Phys. Rev. B volume 93 , pages 235152 ( year 2016 ), ://link.aps.org/doi/10.1103/PhysRevB.93.235152

    2016 doi

Pith tools

Reviewed August 11, 2026 · model on record in the stance chip above.