Error estimates and specification parameters for functional renormalization

David Schnoerr; Igor Boettcher; Jan M. Pawlowski; Christof Wetterich

doi:10.1016/j.aop.2013.03.013

Error estimates and specification parameters for functional renormalization

David Schnoerr, Igor Boettcher, Jan M. Pawlowski, Christof Wetterich

Research output: Contribution to journal › Article › peer-review

Abstract

We present a strategy for estimating the error of truncated functional flow equations. While the basic functional renormalization group equation is exact, approximated solutions by means of truncations do not only depend on the choice of the retained information, but also on the precise definition of the truncation. Therefore, results depend on specification parameters that can be used to quantify the error of a given truncation. We demonstrate this for the BCS–BEC crossover in ultracold atoms. Within a simple truncation the precise definition of the frequency dependence of the truncated propagator affects the results, indicating a shortcoming of the choice of a frequency independent cutoff function.

Original language	English
Pages (from-to)	83 - 99
Number of pages	17
Journal	Annals of Physics
Volume	334
DOIs	https://doi.org/10.1016/j.aop.2013.03.013
Publication status	Published - Jul 2013

Keywords / Materials (for Non-textual outputs)

BCS–BEC crossover

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10.1016/j.aop.2013.03.013

http://www.sciencedirect.com/science/article/pii/S0003491613000626

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title = "Error estimates and specification parameters for functional renormalization",

abstract = "We present a strategy for estimating the error of truncated functional flow equations. While the basic functional renormalization group equation is exact, approximated solutions by means of truncations do not only depend on the choice of the retained information, but also on the precise definition of the truncation. Therefore, results depend on specification parameters that can be used to quantify the error of a given truncation. We demonstrate this for the BCS–BEC crossover in ultracold atoms. Within a simple truncation the precise definition of the frequency dependence of the truncated propagator affects the results, indicating a shortcoming of the choice of a frequency independent cutoff function.",

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T1 - Error estimates and specification parameters for functional renormalization

AU - Schnoerr, David

AU - Boettcher, Igor

AU - Pawlowski, Jan M.

AU - Wetterich, Christof

PY - 2013/7

Y1 - 2013/7

N2 - We present a strategy for estimating the error of truncated functional flow equations. While the basic functional renormalization group equation is exact, approximated solutions by means of truncations do not only depend on the choice of the retained information, but also on the precise definition of the truncation. Therefore, results depend on specification parameters that can be used to quantify the error of a given truncation. We demonstrate this for the BCS–BEC crossover in ultracold atoms. Within a simple truncation the precise definition of the frequency dependence of the truncated propagator affects the results, indicating a shortcoming of the choice of a frequency independent cutoff function.

AB - We present a strategy for estimating the error of truncated functional flow equations. While the basic functional renormalization group equation is exact, approximated solutions by means of truncations do not only depend on the choice of the retained information, but also on the precise definition of the truncation. Therefore, results depend on specification parameters that can be used to quantify the error of a given truncation. We demonstrate this for the BCS–BEC crossover in ultracold atoms. Within a simple truncation the precise definition of the frequency dependence of the truncated propagator affects the results, indicating a shortcoming of the choice of a frequency independent cutoff function.

KW - BCS–BEC crossover

U2 - 10.1016/j.aop.2013.03.013

DO - 10.1016/j.aop.2013.03.013

M3 - Article

SN - 0003-4916

VL - 334

SP - 83

EP - 99

JO - Annals of Physics

JF - Annals of Physics

ER -

Error estimates and specification parameters for functional renormalization

Abstract

Keywords / Materials (for Non-textual outputs)

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