Imaginary-chemical-potential quantum Monte Carlo method for Hubbard molecules

We generalize the imaginary-chemical-potential quantum Monte Carlo (QMC) method proposed by Dagotto et al. [Phys. Rev. B 41, R811 (1990)] to systems without particle-hole symmetry. The generalized method is tested by comparing the results of the QMC simulations and exact diagonalization on small Hubbard molecules, such as tetrahedron and truncated tetrahedron. Results of the application of the method to the ${\mathrm{C}}_{60}$ Hubbard molecule are discussed.

Figure 1

Fit of real (squares) and imaginary (circles) parts of determinant ratios according to Eq. (12) for a tetrahedron molecule.

Figure 2

Fits of ICPQMC data for a tetrahedron molecule at low temperatures for electron (a) and hole (b) doping. NLF forms for (a) and (b) are given by Eqs. (14, 15). ED results are also shown for comparison.

Figure 3

Fits of the real (squares) and imaginary (circles) parts of determinant ratios according to Eq. (12) for a ${\mathrm{C}}_{60}$ molecule.

Figure 4

Fits of ICPQMC data for a ${\mathrm{C}}_{60}$ molecule at low temperatures for electron and hole doping. Here e. (h.) denotes electron (hole) doping. For the behavior of ICPQMC sign average near half-filling, see Fig. 2 of Ref. 1.