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Abstract: The phase diagram for the interacting fermions in weak coupling is describedby the perturbative renormalization group equations. Due to the lack ofanalytic solutions for these coupled non-linear differential equations, it israther subtle to tell which couplings are relevant or irrelevant. We propose apowerful classification scheme to build up the hierarchy of the relevantcouplings by a scaling Ansatz found numerically. To demonstrate its superiorityover the conventional classification for the relevant couplings, we apply thisscheme to a controversial phase transition in the two-leg ladder and show thatit should be a non-trivial crossover instead. The scaling Ansatz we proposehere can classify the relevant couplings in hierarchical order without anyambiguity and can improve significantly how we interpret the numerical outcomesin general renormalization group methods.



Autor: Hong-Yan Shih, Wen-Min Huang, Sze-Bi Hsu, Hsiu-Hau Lin

Fuente: https://arxiv.org/



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