Staggered Flux State in Two-Dimensional Hubbard Models

TL;DR

This study investigates the stability of a staggered flux state in the Hubbard model, revealing its prominence in strongly correlated, underdoped regimes and its potential role in pseudogap phenomena of high-Tc cuprates.

Contribution

It introduces a variational Monte Carlo approach with a configuration-dependent phase factor to analyze the staggered flux state's stability in the Hubbard model, highlighting its significance in certain parameter regimes.

Findings

SF state is more stable than the normal state in strongly correlated, underdoped regions.

The energy decrease is significant where Mott physics dominates.

Frustration t'/t is crucial for charge homogeneity and modeling cuprates.

Abstract

The stability and other properties of a staggered flux (SF) state or a correlated d-density wave state are studied for the Hubbard (t-t'-U) model on extended square lattices, as a low-lying state that competes with the d(x2-y2)-wave superconductivity (d-SC) and possibly causes the pseudogap phenomena in underdoped high-Tc cuprates and organic kappa-BEDT-TTF salts. In calculations, a variational Monte Carlo method is used. In the trial wave function, a configuration-dependent phase factor, which is vital to treat a current-carrying state for a large U/t, is introduced in addition to ordinary correlation factors. Varying U/t, t'/t, and the doping rate (delta) systematically, we show that the SF state becomes more stable than the normal state (projected Fermi sea) for a strongly correlated (U/t\gtrsim 5) and underdoped (delta\lesssim 0.16) area. The decrease in energy is sizable, particularly in the area where Mott physics prevails and the circular current (order parameter) is strongly suppressed. These features are consistent with those for the t-J model. The effect of the frustration t'/t plays a crucial role in preserving charge homogeneity and appropriately describing the behavior of hole- and electron-doped cuprates and kappa-BEDT-TTF salts. We argue that the SF state does not coexist with d-SC and is not a `normal state' from which d-SC arises. We also show that a spin current (flux or nematic) state is never stabilized in the same regime.