Classification of potential flows under renormalization grouptransformation

Sze-Bi Hsu; Bernold  Fiedler; Hsiu-Hau  Lin

doi:10.3934/dcdsb.2016.21.437

Article Contents

2016, Volume 21, Issue 2: 437-446. Doi: 10.3934/dcdsb.2016.21.437

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Classification of potential flows under renormalization group transformation

1.
Department of Mathematics, National Tsing Hua University, National Center of Theoretical Science, Hsinchu 300
2.
Institute of Mathematics, Free University Berlin, Arnimallee 3, D-14195 Berlin
3.
Department of Physics and The National Center for Theoretical Science, National Tsing Hua University, Hsinchu 30013

Received: November 30, 2014

Revised: April 30, 2015

Published: February 2016

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Abstract

Competitions between different interactions in strongly correlated electron systems often lead to exotic phases. Renormalization group is one of the powerful techniques to analyze the competing interactions without presumed bias. It was recently shown that the renormalization group transformations to the one-loop order in many correlated electron systems are described by potential flows. Here we prove several rigorous theorems in the presence of renormalization-group potential and find the complete classification for the potential flows. In addition, we show that the relevant interactions blow up at the maximal scaling exponent of unity, explaining the puzzling power-law Ansatz found in previous studies. The above findings are of great importance in building up the hierarchy for relevant couplings and the complete classification for correlated ground states in the presence of generic interactions.

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Mathematics Subject Classification: 34, 37.

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