Quantum fluctuations in the spiral phase of the Hubbard model

TL;DR

This paper investigates magnetic excitations and instabilities in the spiral phase of the 2D Hubbard model, revealing strong spin wave renormalization, near-zero spectral lines, and potential transitions to inhomogeneous states influenced by Coulomb interactions.

Contribution

It introduces a functional integral approach to analyze magnetic excitations and uncovers the conditions for phase separation and charge density wave instabilities in the spiral phase.

Findings

Spin waves are strongly renormalized in the spiral phase.

Near-zero lines appear in the excitation spectrum around the spiral pitch.

The spiral phase is intrinsically unstable towards inhomogeneous states at weak doping.

Abstract

We study the magnetic excitations in the spiral phase of the two--dimensional Hubbard model using a functional integral method. Spin waves are strongly renormalized and a line of near--zeros is observed in the spectrum around the spiral pitch $\pm{\bf Q}$. The possibility of disordered spiral states is examined by studying the one--loop corrections to the spiral order parameter. We also show that the spiral phase presents an intrinsic instability towards an inhomogeneous state (phase separation, CDW, ...) at weak doping. Though phase separation is suppressed by weak long--range Coulomb interactions, the CDW instability only disappears for sufficiently strong Coulomb interaction.