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Sharp Bounds on the Ground State Energy of the SYK Model

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syk-ground-state-energy-sharp-boundsMathematical physicsposed by Feng, Tian and Wei; predicted by Garcia-Garcia, Jia and Verbaarschot, 2019recorded: solved

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Statement

For the Sachdev-Ye-Kitaev Hamiltonian on nn Majorana modes with kk-body interactions, the paper proves E∥H∥op=(1−o(1))2n/k\mathbb{E}\|H\|_{op} = (1-o(1))\sqrt{2n}/k for super-constant k≤o(n)k \le o(\sqrt{n}), confirming predictions of Garcia-Garcia, Jia and Verbaarschot and answering a question of Feng, Tian and Wei.

Context

Settles the operator-norm asymptotics of a heavily studied model in quantum many-body physics, confirming a 2018 prediction and answering a question posed in 2019.

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  • #1

    Attempt 1

    proof attemptGPT-5.5 Pro / GPT-5.6 Pro with Arpon Basu, Pravesh K. Kothari, Siddhant Midha ·
    AI involvement
    ai co developed
    — a person and a model developed the result together.
    models
    GPT-5.5 Pro, GPT-5.6 Pro
    people
    Arpon Basu, Pravesh K. Kothari, Siddhant Midha

    The authors analysed a preliminary version of their explicit deterministic operator with GPT-5.5 Pro and GPT-5.6 Pro, and credit GPT-5.6 Pro with suggesting Lemma 4.6, Proposition 4.14 and Lemma 4.15. They also used it to search related literature and to assist with verifying technical proofs.

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