Possible Ordered States in the 2D Extended Hubbard Model

TL;DR

This paper investigates possible ordered states in the 2D extended Hubbard model near half filling, analyzing mean field phase diagrams and the effects of fluctuations, revealing conditions for coexistence of various ordered phases.

Contribution

It provides a comprehensive analysis of ordered states in the 2D extended Hubbard model, including mean field phase diagrams and fluctuation effects, highlighting conditions for coexistence of superconductivity, SDW, CDW, and ferromagnetism.

Findings

Coexistence of d-wave superconductivity, SDW, and π-triplet pairs for V<0.

Coexistence of CDW, SDW, and ferromagnetism for V>0.

Superconductivity can arise for U>0 and V≥0 due to fluctuations, with different symmetries depending on U and V.

Abstract

Possible ordered states in the 2D extended Hubbard model with on-site (U>0) and nearest-neighbor (V) interaction are examined near half filling, with emphasis on the effect of finite V. First, the phase diagram at absolute zero is determined in the mean field approximation. For $V<0$, a state where d_{x^{2}-y^{2}}-wave superconductivity (dSC), commensurate spin-density-wave (SDW) and $\pi$-triplet pair coexist is seen to be stabilized. Here, the importance of $\pi$-triplet pair on the coexistence of dSC and SDW is indicated. This coexistent state is hampered by the phase separation (PS), which is generally expected to occur in the presence of finite-range attractive interaction, but survives. For V>0, a state where commensurate charge-density-wave (CDW), SDW and ferromagnetism (FM) coexist is seen to be stabilized. Here, the importance of FM on the coexistence of CDW and SDW is indicated. Next, in order to examine the effects of fluctuation on each mean field ordered state, the renormalization group method for the special case that the Fermi level lies just on the saddle points, ($\pi$,0) and (0,$\pi$), is applied. The crucial difference from the mean field result is that superconductivity can arise even for U>0 and $V\geq0$, where the superconducting gap symmetry is d_{x^{2}-y^{2}}-wave for U>4V and s-wave for U<4V. Finally, the possibilities that the mean field coexistent states survive in the presence of fluctuation are discussed.