Pomeranchuk and other Instabilities in the t-t' Hubbard model at the Van Hove Filling

TL;DR

This paper analyzes the stability of the two-dimensional t-t' Hubbard model near Van Hove filling, revealing dominant Pomeranchuk and other instabilities depending on parameters, using the flow equation method.

Contribution

It provides a detailed stability phase diagram of the t-t' Hubbard model near Van Hove filling, identifying various Pomeranchuk and magnetic instabilities with respect to t' and electron concentration.

Findings

d_{x^2-y^2}-wave Pomeranchuk instability dominates for t' > -t/3

g-wave Pomeranchuk and p-wave triplet instabilities occur for t' < -t/3

An s^*-magnetic phase appears at higher temperatures

Abstract

We present a stability analysis of the two-dimensional t-t' Hubbard model for various values of the next-nearest-neighbor hopping t', and electron concentrations close to the Van Hove filling by means of the flow equation method. For t' > -t/3 a d_{x^2-y^2}-wave Pomeranchuk instability dominates (apart from antiferromagnetism at small t'). At t' < -t/3 the leading instabilities are a g-wave Pomeranchuk instability and p-wave particle-hole instability in the triplet channel at temperatures T < 0.15t, and an s^*-magnetic phase for T > 0.15t; upon increasing the electron concentration the triplet analog of the flux phase occurs at low temperatures. Other weaker instabilities are found also.