Variational study of a mobile hole in a two-dimensional quantum antiferromagnet using entangled-plaquette states

We study the properties of a mobile hole in the $t-J$ model on the square lattice by means of variational Monte Carlo simulations based on the entangled-plaquette ansatz. Our energy estimates for small lattices reproduce available exact results. We obtain values for the hole energy dispersion curve on large lattices in quantitative agreement with earlier findings based on the most reliable numerical techniques. Accurate estimates of the hole spectral weight are provided.

Figure 1

Hole energy dispersion curve for a lattice of $256$ sites with PBC at $\frac{J}{t}=2.0$. EPS estimates (triangles) are computed using square plaquettes of nine sites. QMC results (crosses) are also shown for comparison.[14]

Figure 2

Hole energy dispersion curve for a lattice of $256$ sites with PBC at $\frac{J}{t}=0.8$. EPS estimates (triangles) are computed using square plaquettes of nine sites. QMC results (crosses) are also shown for comparison.[14]

Figure 3

Hole energy dispersion curve for a lattice of $256$ sites with PBC at $\frac{J}{t}=0.4$. EPS estimates are computed using square plaquettes of four (circles) or nine (triangles) sites. GFMC results (crosses)[13] are also shown for comparison.

Figure 4

Hole spectral weight for a $16\times 16$ lattice with PBC at $\frac{J}{t}=0.4$. The dashed line is a guide to the eye.