Renormalization Group Analysis of a Fermionic Hot Spot Model

TL;DR

This paper applies renormalization group analysis to a fermionic hot spot model on the square lattice, exploring various interactions and instabilities, especially focusing on superconducting and density wave orders near hot spots.

Contribution

It introduces a comprehensive RG framework for hot spot models, analyzing all quartic interactions and instabilities, including effects of nesting and non-nesting conditions.

Findings

Non-nested hot spots with J, V interactions show competing d-wave superconductivity and incommensurate density waves.

Enhanced incommensurate density waves near experimental wavevectors with dominant d-form factor.

RG flow indicates specific dominant instabilities depending on nesting and interaction parameters.

Abstract

We present a renormalization group (RG) analysis of a fermionic "hot spot" model of interacting electrons on the square lattice. We truncate the Fermi surface excitations to linearly dispersing quasiparticles in the vicinity of eight hot spots on the Fermi surface, with each hot spot separated from another by the wavevector $(\pi, \pi)$. This motivated by the importance of these Fermi surface locations to the onset of antiferromagnetic order; however, we allow for all possible quartic interactions between the fermions, and also for all possible ordering instabilities. We compute the RG equations for our model, which depend on whether the hot spots are perfectly nested or not, and relate our results to earlier models. We also compute the RG flow of the relevant order parameters for both Hubbard and $J$, $V$ interactions, and present our results for the dominant instabilities in the nested and non-nested cases. In particular, we find that non-nested hot spots with $J$, $V$ interactions have competing singlet $d_{x^2-y^2}$ superconducting and $d$-form factor incommensurate density wave instabilities. We also investigate the enhancement of incommensurate density waves near experimentally observed wavevectors, and find dominant $d$-form factor enhancement for a range of couplings.