We present a variational Monte Carlo (VMC) study of spontaneous Fermi-surface symmetry breaking in the $t\text{−}J$ model. We find that the variational energy of a Gutzwiller projected Fermi sea is lowered by allowing for a finite asymmetry between the $x$ and the $y$ directions. However, the best variational state remains a pure superconducting state with $d$-wave symmetry, as long as the underlying lattice is isotropic. Our VMC results are in good overall agreement with slave boson mean field theory (SBMFT) and renormalized mean field theory (RMFT), although apparent discrepancies do show up in the half-filled limit, revealing some limitations of mean field theories. VMC and complementary RMFT calculations also confirm the SBMFT predictions that many-body interactions can enhance any anisotropy in the underlying crystal lattice. Thus, our results may be of consequence for the description of strongly correlated superconductors with an anisotropic lattice structure.

• Received 25 July 2006

DOI:https://doi.org/10.1103/PhysRevB.74.165109