Sandro Sorella

Nature and strength of interlayer binding in graphite.

We compute the interlayer bonding properties of graphite using an ab initio many-body theory. We carry out variational and diffusion quantum Monte Carlo calculations and find an equilibrium interlayer binding energy in good agreement with most recent experiments. We also analyze the behavior of the total energy as a function of interlayer separation at large distances comparing the results with the predictions of the random phase approximation.

Electron Localization in the Insulating State

The insulating state of matter is characterized by the excitation spectrum, but also by qualitative features of the electronic ground state. The insulating ground wavefunction in fact: (i) sustains macroscopic polarization, and (ii) is localized. We give a sharp definition of the latter concept, and we show how the two basic features stem from essentially the same formalism. Our approach to localization is exemplified by means of a two--band Hubbard model in one dimension. In the noninteracting limit the wavefunction localization is measured by the spread of the Wannier orbitals.

Correlated geminal wave function for molecules: An efficient resonating valence bond approach

We show that a simple correlated wave function, obtained by applying a Jastrow correlation term to an antisymmetrized geminal power, based upon singlet pairs between electrons, is particularly suited for describing the electronic structure of molecules, yielding a large amount of the correlation energy. The remarkable feature of this approach is that, in principle, several resonating valence bonds can be dealt simultaneously with a single determinant, at a computational cost growing with the number of electrons similar to more conventional methods, such as Hartree-Fock or density functional theory. Moreover we describe an extension of the stochastic reconfiguration method, which was recently introduced for the energy minimization of simple atomic wave functions. Within this extension the atomic positions can be considered as further variational parameters, which can be optimized together with the remaining ones. The method is applied to several molecules from Li(2) to benzene by obtaining total energies, bond lengths and binding energies comparable with much more demanding multiconfiguration schemes.

Long-Range Néel Order in the Triangular Heisenberg Model

We have studied the Heisenberg model on the triangular lattice using several Quantum Monte Carlo (QMC) techniques (up to 144 sites), and exact diagonalization (ED) (up to 36 sites). By studying the spin gap as a function of the system size we have obtained a robust evidence for a gapless spectrum, confirming the existence of long range Neel order. Our best estimate is that in the thermodynamic limit the order parameter m= 0.41 +/- 0.02 is reduced by about 59% from its classical value and the ground state energy per site is e0=-0.5458 +/- 0.0001 in unit of the exchange coupling. We have identified the important ground state correlations at short distance.

Semi-Metal-Insulator Transition of the Hubbard Model in the Honeycomb Lattice

Using quantum Monte Carlo and finite-size scaling for the Hubbard model, we find evidence of a zero-temperature transition between the nonmagnetic semi-metal and an antiferromagnetic insulator in the 2D honeycomb lattice for a nontrivial value of U/t?=?4.5???0.5. The corresponding transition in Hartree-Fock mean field is at U/t?=?2.23, which indicates the importance of quantum fluctuations. This represents the first example of Mott-Hubbard transition in a 2D bipartite lattice. Similar transitions are predicted for special lattices in higher dimensions, in particular for the 3D diamond lattice.

Geminal wave functions with Jastrow correlation: A first application to atoms

We introduce a simple generalization of the well-known geminal wave function already applied in quantum chemistry to atoms and small molecules. The main feature of the proposed wave function is the presence of the antisymmetric geminal part together with a Jastrow factor. Both the geminal and the Jastrow play a crucial role in determining the remarkable accuracy of the many-body state: the former permits the correct treatment of the nondynamic correlation effects; the latter allows the wave function to fulfill the cusp conditions and makes the geminal expansion rapidly converge to the lowest possible variational energies. This ansatz is expected to provide a substantial part of the correlation energy for general complex atomic and molecular systems. The antisymmetric geminal term can be written as a single determinant even in the polarized cases. In general, therefore, the computational effort to sample this correlated wave function is not very demanding, the scaling of the algorithm with the number of at...

Weak binding between two aromatic rings: Feeling the van der Waals attraction by quantum Monte Carlo methods

We report a systematic study of the weak chemical bond between two benzene molecules. We first show that it is possible to obtain a very good description of the C(2) dimer and the benzene molecule by using pseudopotentials for the chemically inert 1s electrons and a resonating valence bond wave function as a variational ansatz, expanded on a relatively small Gaussian basis set. We employ an improved version of the stochastic reconfiguration technique to optimize the many-body wave function, which is the starting point for highly accurate simulations based on the lattice regularized diffusion Monte Carlo method. This projection technique provides a rigorous variational upper bound for the total energy, even in the presence of pseudopotentials, and substantially improves the accuracy of the trial wave function, which already yields a large fraction of the dynamical and nondynamical electron correlation. We show that the energy dispersion of two benzene molecules in the parallel displaced geometry is significantly deeper than the face-to-face configuration. However, contrary to previous studies based on post-Hartree-Fock methods, the binding energy remains weak ( approximately 2 kcal/mol) also in this geometry, and its value is in agreement with the most accurate and recent experimental findings [H. Krause et al., Chem. Phys. Lett. 184, 411 (1991)].

Superconductivity in the two-dimensional t-J model

Using computational techniques, it is shown that pairing is a robust property of hole-doped antiferromagnetic insulators. In one dimension and for two-leg ladder systems, a BCS-like variational wave function with long-bond spin singlets and a Jastrow factor provides an accurate representation of the ground state of the t-J model, even though strong quantum fluctuations destroy the off-diagonal superconducting long-range order in this case. However, in two dimensions it is argued-and numerically confirmed using several techniques, especially quantum Monte Carlo-that quantum fluctuations are not strong enough to suppress superconductivity.

A Novel Technique for the Simulation of Interacting Fermion Systems

A new method for the simulation of ground-state properties of interacting fermions is introduced. A trial wave function, which is assumed to be a Slater determinant, is propagated to large imaginary times. The quantum many-body propagator is represented by a coherent superposition of single-particle propagators by means of a Hubbard-Stratonovich transformation. The resulting functional integral is performed by stochastic methods based on Langevin dynamics. Numerical stability is achieved by orthonormalizing the propagating single-particle orbitals entering the Slater determinant. The problem of the positiveness of the statistical weight is addressed and solved in most cases. Illustrative examples are given for the 1D and 2D Hubbard models.

Generalized Lanczos algorithm for variational quantum Monte Carlo

We show that the standard Lanczos algorithm can be efficiently implemented statistically and self-consistently improved, using the stochastic reconfiguration method, which has been recently introduced to stabilize the Monte Carlo sign problem instability. With this scheme a few Lanczos steps over a given variational wave function are possible even for large size as a particular case of a more general and more accurate technique that allows to obtain lower variational energies. This method has been tested extensively for a strongly correlated model like the