Absence of the d-Density Wave State in 2D Hubbard Model

TL;DR

This study uses the Dynamical Cluster Approximation to investigate the possibility of d-density wave order in the 2D Hubbard model, finding no evidence of a transition despite enhanced susceptibility in the pseudogap region.

Contribution

First DCA-based calculation showing the absence of DDW order in the 2D Hubbard model, challenging previous theories predicting such order.

Findings

No transition to DDW state observed.

DDW susceptibility is enhanced in the pseudogap region.

d-wave pairing susceptibility remains dominant.

Abstract

Using the Dynamical Cluster Approximation (DCA) we calculate the alternating circulating-current susceptibility and investigate the transition to the d-density wave (DDW) order in the two-dimensional Hubbard model. The 2 x 2 cluster used in the DCA calculation is the smallest that can capture d-wave order; therefore, due to the mean-field character of our calculation, we expect to overestimate d-wave transition temperatures. Despite this, we found no transition to the DDW state. In the pseudogap region the DDW susceptibility is enhanced, as predicted by the slave boson SU(2) theory, but it still is much smaller than the d-wave pairing susceptibility.