Checkerboard order in the t--J model on the square lattice

TL;DR

This paper investigates checkerboard charge order in the t-J model on a square lattice, proposing it as a possible explanation for STM observations in underdoped cuprates, and compares mean-field and variational Monte Carlo results.

Contribution

It demonstrates the emergence of checkerboard patterns from a bond-order-wave instability in the t-J model using both mean-field and variational Monte Carlo methods.

Findings

Charge modulation is much smaller than bond-order modulation.

Mean-field estimates of order parameters are significantly reduced by variational Monte Carlo.

Checkerboard pattern appears at doping around 1/8.

Abstract

We propose that the inhomogeneous patterns seen by STM in some underdoped superconducting cuprates could be related to a bond-order-wave instability of the staggered flux state, one of the most studied "normal" state proposed to compete with the d-wave RVB superconductor. A checkerboard pattern is obtained by a Gutzwiller renormalized mean-field theory of the t-J model for doping around 1/8. It is found that the charge modulation is always an order of magnitude smaller than the bond-order modulations. This is confirmed by an exact optimization of the wavefunction by a variational Monte Carlo scheme. The numerical estimates of the order parameters are however found to be strongly reduced w.r.t their mean-field values.