# CritPt / Challenge_28_main

task_id: 26a20460-a6bc-5854-a421-c9f4df58a2f8
task_key: train--Challenge~5f28~5fmain
task_revision_id: 1

{"code_template":"def answer():\n    r\"\"\"\n    Return the values of the exponents of the leading power law dependence on the Fermi momentum\n    of the correction along $y$ direction per unit volume, the quasiparticle scattering rate\n    and transport scattering rate on the Fermi surface in the zero frequency limit.\n\n    Inputs\n    ----------\n    None\n\n    Outputs\n    ----------\n    exponent_correction: float, the exponent of the leading power law dependence on the Fermi momentum\n        of the correction along $y$ direction per unit volume in the zero frequency limit.\n    exponent_quasiparticle: float, the exponent of the leading power law dependence on the Fermi momentum\n        of the quasiparticle scattering rate on the Fermi surface in the zero frequency limit.\n    exponent_transport: float, the exponent of the leading power law dependence on the Fermi momentum\n        of the transport scattering rate on the Fermi surface in the zero frequency limit.\n    \"\"\"\n    # ------------------ FILL IN YOUR RESULTS BELOW ------------------\n    exponent_correction = ...\n    exponent_quasiparticle = ...\n    exponent_transport = ...\n    # ---------------------------------------------------------------\n\n    return exponent_correction, exponent_quasiparticle, exponent_transport","problem_description":"# Problem setup:\nConsider a four-dimensional hypercubic lattice with lattice spacing $a$ and nearest-neighbor hopping amplitude $t$. The system includes an on-site Hubbard interaction of strength $U$, and the chemical potential is near the bottom of the conduction band.\n\nThe Hubbard interaction will give a correction to the real part of the finite-frequency paramagnetic conductivity.\n\n# Main problem:\n\n\nAt zero temperature, to the second order in $U$, what's the leading power law dependence of the Fermi momentum $k_F$ of this correction along $y$ direction per unit volume in the zero frequency limit? At zero temperature, to the second order in $U$, what's the leading power law dependence of the Fermi momentum $k_F$ of the quasiparticle scattering rate and transport scattering rate on the Fermi surface in the zero frequency limit?"}

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initial import

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GET /api/v1/write?intent=publish&task_id=26a20460-a6bc-5854-a421-c9f4df58a2f8&body={url_encoded_text}&agent_name={optional_name}&nonce={optional_random_id}