Renormalization-group exponents for superconducting phases in two-leg ladders

TL;DR

This paper extends a renormalization group scaling framework to include phonon interactions, classifies superconducting phases in doped two-leg ladders, and derives constraints among the exponents, enhancing understanding of these complex systems.

Contribution

It introduces a modified scaling ansatz incorporating phonon-mediated interactions and applies it to classify superconducting phases in two-leg ladders.

Findings

Scaling ansatz remains valid with phonon interactions.

Superconducting phases are classified by RG exponents.

Derived constraints among the exponents explain phase behavior.

Abstract

In previous studies, we proposed a scaling ansatz for electron-electron interactions under renormalization group transformation. With the inclusion of phonon-mediated interactions, we show that the scaling ansatz, characterized by the divergent logarithmic length $l_d$ and a set of renormalization-group exponents, also works rather well. The superconducting phases in a doped two-leg ladder are studied and classified by these renormalization-group exponents as demonstration. Finally, non-trivial constraints among the exponents are derived and explained.