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pubs.acs.org/JCTCArticleA Similarity Renormalization Group Approach to Greens Function Methods Antoine Marie* and PierreFrancois Loos* Cite This: J. Chem. Theory Comput. 2023, 19, 39433957Downloaded via 37.65.50.187 on July 17, 2023 at 07:14:40 (UTC). See https://pubs.acs.org/sharingguidelines for options on how to legitimately share published articles.ACCESSRead OnlineMetrics & MoreArticle Recommendationss Supporting Information *ABSTRACT: The family of Greens function
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Identify the system of interest and its Hamiltonian.
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Choose a suitable cutoff that defines high-energy and low-energy degrees of freedom.
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Perform a Rayleigh-Schrodinger perturbation expansion if necessary.
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Rescale the Hamiltonian to incorporate the renormalization group transformations.
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Iteratively integrate out the high-energy degrees of freedom.
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Adjust the parameters of the Hamiltonian to maintain the same low-energy physics.
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Check the fixed points of the renormalization group flow and analyze their stability.
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Repeat the process until convergence is achieved or a desired scale is reached.

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Academics and students preparing for advanced studies in theoretical physics.
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A similarity renormalization group is a mathematical framework used in theoretical physics to analyze systems with many degrees of freedom by systematically integrating out short-range fluctuations and focusing on long-range behavior.
In the context of physics, researchers and theorists who are performing detailed studies and calculations involving many-body systems or critical phenomena may be seen as the ones who 'file' or utilize a similarity renormalization group approach.
To 'fill out' or apply a similarity renormalization group, one typically specifies the initial Hamiltonian or action of the system, identifies relevant parameters, and systematically performs transformations to derive effective theories for the long-range interactions.
The purpose of a similarity renormalization group is to simplify complex interactions in a physical system by removing short-range details and revealing the universal behavior or critical properties of the system.
Information usually reported includes the initial parameters of the system, the transformation methods used, fixed points, scaling behaviors, and any relevant observables that pertain to the effective theory derived from the renormalization group analysis.
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