Spin and charge order in doped Hubbard model: long-wavelength collective modes

TL;DR

This paper uses advanced quantum Monte Carlo methods to study the ground state of the doped 2D Hubbard model, revealing incommensurate spin density waves, charge order evolution, and the disappearance of SDW at high doping.

Contribution

It introduces large-scale constrained path auxiliary-field quantum Monte Carlo simulations to analyze spin and charge correlations in the doped Hubbard model, uncovering new collective mode behaviors.

Findings

Incommensurate SDW state at intermediate doping

Charge order evolves into stripe-like states with increased interaction

SDW order vanishes beyond a critical doping

Abstract

Determining the ground state properties of the two-dimensional Hubbard model has remained an outstanding problem. Applying recent advances in constrained path auxiliary-field quantum Monte Carlo techniques and simulating large rectangular periodic lattices, we calculate the long-range spin and charge correlations in the ground state as a function of doping. At intermediate interaction strengths, an incommensurate spin density wave (SDW) state is found, with antiferromagnetic order and essentially homogeneous charge correlation. The wavelength of the collective mode decreases with doping, as does its magnitude. The SDW order vanishes beyond a critical doping. As the interaction is increased, the holes go from a wave-like to a particle-like state, and charge ordering develops which eventually evolves into stripe-like states.