Possible Phases of the Two-Dimensional t-t' Hubbard Model

TL;DR

This paper analyzes the stability of various symmetry-broken phases in the 2D t-t' Hubbard model, revealing numerous phases including known and novel instabilities, through a numerical approach based on flow equations.

Contribution

It introduces a comprehensive stability analysis of the 2D t-t' Hubbard model, identifying both known and new phases using a flow equations method.

Findings

Multiple symmetry-broken phases identified, including antiferromagnetism and d-wave superconductivity.

Discovery of new phases such as triplet flux phase and p-wave particle-hole instability.

Numerical results suggest complex phase diagram with diverse instabilities.

Abstract

We present a stability analysis of the 2D t-t' Hubbard model on a square lattice for various values of the next-nearest-neighbor hopping t' and electron concentration. Using the free energy expression, derived by means of the flow equations method, we have performed numerical calculation for the various representations under the point group C_{4\nu} in order to determine at which temperature symmetry broken phases become more favorable than the symmetric phase. A surprisingly large number of phases has been observed. Some of them have an order parameter with many nodes in k-space. Commonly discussed types of order found by us are antiferromagnetism, d_{x^2-y^2}-wave singlet superconductivity, d-wave Pomeranchuk instability and flux phase. A few instabilities newly observed are a triplet analog of the flux phase, a particle-hole instability of p-type symmetry in the triplet channel which gives rise to a phase of magnetic currents, an s*-magnetic phase, a g-wave Pomeranchuk instability and the band splitting phase with p-wave character. Other weaker instabilities are found also. A comparison with experiments is made.