Coexistence between checkerboarded charge and striped spin in two-dimensional Hubbard model

Abstract

We have performed a variational Monte Carlo (VMC) simulation on a two-dimensional t–t′–t″–U Hubbard model to examine the stability of a 4×4 checkerboard state, which has been observed recently by scanning tunneling microscopy (STM) in Bi2Sr2CaCu2O8−δ and Ca2−xNaxCuO2Cl2 (Na–CCOC). In our VMC calculation, the checkerboard mean field wave function for the coexisting checkerboarded charge density wave in a striped spin density wave was used. We chose the transfer energies t′ and t″ suitable for Bi-based cuprate at the underdoping. The variational energy of the checkerboard state with 4×4 period comparable with that of the 4-period stripe state was obtained. It is important for stabilization of the checkerboard state that a Fermi surface around each of k=(π,0) and (0,π) points consists of two parallel flat section.