A note on “On Anyon Superconductivity” - LLMs coming for Physics, too
https://home.uchicago.edu/dtson/papers/cwwh_note.pdf
After the headlines made on AI tackling math problems, Anthropic now came for one of the seminal condensed matter physics papers.
> Abstract
> In their 1989 paper On anyon superconductivity, Chen, Wilczek, Witten and Halperin (CWWH) computed, in the random-phase approximation (RPA), the electromagnetic response of a gas of anyons with statistical parameter θ = π(1 − 1/n), treated as fermions filling n Landau levels of a fictitious magnetic field. At the end of their Appendix A they report that one ingredient of the response function, the quantity Σ3, acquires corrections of order q 4 that current conservation forbids; they call this “something of an embarrassment” and suspect their treatment of the electromagnetic contact interaction. We show that no such corrections exist: the sum defining Σ3 is identically equal to n, as a direct consequence of the single-particle f-sum rule for each filled Landau level. The RPA response function of CWWH is therefore exactly current-conserving, and their treatment of the contact term is correct. We identify the probable origin of the discrepancy as a dropped factor 1/2! in the second-order term of a Laguerre-polynomial expansion; this single slip reproduces their erroneous coefficient n(n − 1)(n − 2)/6 exactly.
Chen, Wilczek, Witten, and Halperin are some pretty big names in the field.
Even though it's _just_ catching a missing factor, it fits the current narrative that the field is changing.
Noting that Anthropic is listed as the sole author, the acknowledgments are fitting:
> Acknowledgments
> I am grateful to Dam Thanh Son for providing the prompts that led to this note: for drawing my attention to the “embarrassment” of Appendix A of CWWH, for asking whether it could be resolved and what the source of the error might be, and for asking whether the point had ever been taken up in the literature.
https://stacker.news/items/1583150
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"content": "A note on “On Anyon Superconductivity” - LLMs coming for Physics, too\nhttps://home.uchicago.edu/dtson/papers/cwwh_note.pdf\n\nAfter the headlines made on AI tackling math problems, Anthropic now came for one of the seminal condensed matter physics papers.\n\n\u003e Abstract \n\n\u003e In their 1989 paper On anyon superconductivity, Chen, Wilczek, Witten and Halperin (CWWH) computed, in the random-phase approximation (RPA), the electromagnetic response of a gas of anyons with statistical parameter θ = π(1 − 1/n), treated as fermions filling n Landau levels of a fictitious magnetic field. At the end of their Appendix A they report that one ingredient of the response function, the quantity Σ3, acquires corrections of order q 4 that current conservation forbids; they call this “something of an embarrassment” and suspect their treatment of the electromagnetic contact interaction. We show that no such corrections exist: the sum defining Σ3 is identically equal to n, as a direct consequence of the single-particle f-sum rule for each filled Landau level. The RPA response function of CWWH is therefore exactly current-conserving, and their treatment of the contact term is correct. We identify the probable origin of the discrepancy as a dropped factor 1/2! in the second-order term of a Laguerre-polynomial expansion; this single slip reproduces their erroneous coefficient n(n − 1)(n − 2)/6 exactly.\n\nChen, Wilczek, Witten, and Halperin are some pretty big names in the field.\n\nEven though it's _just_ catching a missing factor, it fits the current narrative that the field is changing.\n\nNoting that Anthropic is listed as the sole author, the acknowledgments are fitting:\n\n\u003e Acknowledgments \n\n\u003e I am grateful to Dam Thanh Son for providing the prompts that led to this note: for drawing my attention to the “embarrassment” of Appendix A of CWWH, for asking whether it could be resolved and what the source of the error might be, and for asking whether the point had ever been taken up in the literature.\n\nhttps://stacker.news/items/1583150",
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