Jastrow Correlations Research Articles

Hidden Mott transition and large- U superconductivity in the two-dimensional Hubbard model

We consider the one-band Hubbard model on the square lattice by using variational and Green's function Monte Carlo methods, where the variational states contain Jastrow and backflow correlations on top of an uncorrelated wave function that includes BCS pairing and magnetic order. At half filling, where the ground state is antiferromagnetically ordered for any value of the on-site interaction $U$, we can identify a hidden critical point $U_{\rm Mott}$, above which a finite BCS pairing is stabilized in the wave function. The existence of this point is reminiscent of the Mott transition in the paramagnetic sector and determines a separation between a Slater insulator (at small values of $U$), where magnetism induces a potential energy gain, and a Mott insulator (at large values of $U$), where magnetic correlations drive a kinetic energy gain. Most importantly, the existence of $U_{\rm Mott}$ has crucial consequences when doping the system: We observe a tendency to phase separation into a hole-rich and a hole-poor region only when doping the Slater insulator, while the system is uniform by doping the Mott insulator. Superconducting correlations are clearly observed above $U_{\rm Mott}$, leading to the characteristic dome structure in doping. Furthermore, we show that the energy gain due to the presence of a finite BCS pairing above $U_{\rm Mott}$ shifts from the potential to the kinetic sector by increasing the value of the Coulomb repulsion.

Correlations in lowest-Landau-level vortex states

We show how the configuration-space form of the Bogoliubov ground state wave function of a bosonic condensate with a single vortex in a harmonic trap can be described in terms of bosonic Jastrow correlations. We then generalize this result to study the first effects of such correlations on a mean-field vortex lattice state and show that the included correlations lower the energy below that of the mean-field state. Although the reduction is relatively small, it is a precursor of the more general expected effect of correlations in describing the melting of the vortex lattice at large angular momentum per particle.

Further improvement in the variational many-body wave functions for light nuclei

An improved variational ansatz is proposed and implemented for variational many-body wave functions for light nuclei with nucleons interacting through Argonne (AV${}_{18}$) and Urbana IX (UIX) three-nucleon interactions. The new ansatz is based upon variationally distinguishing between the various components of the two-body Jastrow and operatorial correlations, which are operated upon by three-body and spin-orbit correlations. We obtain noticeable improvement in the quality of the wave function and lowering of the energies compared to earlier results. The new energies are \ensuremath{-}8.38(1), \ensuremath{-}28.07(1), and \ensuremath{-}29.90(1) MeV for ${}^{3}$H, ${}^{4}$He, and ${}^{6}$Li, respectively. Though, the present improved ansatz still fails to stabilize the ${}^{6}$Li nucleus against a breakup into an \ensuremath{\alpha} particle and a deuteron by 390 KeV; nonetheless, it is an improvement over previous studies.

Supersolidity in the Triangular Lattice Spin-1/2XXZModel: A Variational Perspective

We study the spin-1/2 XXZ model on the triangular lattice with a nearest neighbor antiferromagnetic Ising coupling J(z) > 0 and unfrustrated (J(perpendicular) < 0) or frustrated (J(perpendicular) >0) kinetic terms in a zero magnetic field. Incorporating long-range Jastrow correlations over a mean-field spin state, we obtain the variational phase diagram of this model on large lattices for arbitrary J(z) and either sign of J(perpendicular). For J(perpendicular) < 0, we find a square root(3) x square root(3) supersolid for J(z)/J(perpendicular)| approximately > 4.7, in excellent agreement with quantum Monte Carlo data. For J(perpendicular) > 0, a distinct square root(3) x square root(3) supersolid is found to emerge for J(z)/J(perpendicular) > or = 1. Both supersolids exhibit a spontaneous density deviation from half-filling. At J(z)/J(perpendicular) = infinity, the crystalline order parameters of these two supersolids are nearly identical, consistent with exact results.

Resonating valence bond wave function with molecular orbitals: Application to first-row molecules

We introduce a method for accurate quantum chemical calculations based on a simple variational wave function, defined by a single geminal that couples all the electrons into singlet pairs, combined with a real space correlation factor. The method uses a constrained variational optimization, based on an expansion of the geminal in terms of molecular orbitals. It is shown that the most relevant nondynamical correlations are correctly reproduced once an appropriate number n of molecular orbitals is considered. The value of n is determined by requiring that, in the atomization limit, the atoms are described by Hartree-Fock Slater determinants with Jastrow correlations. The energetics, as well as other physical and chemical properties, are then given by an efficient variational approach based on standard quantum Monte Carlo techniques. We test this method on a set of homonuclear (Be(2), B(2), C(2), N(2), O(2), and F(2)) and heteronuclear (LiF and CN) dimers for which strong nondynamical correlations and/or weak van der Waals interactions are present.

0νββ-decay nuclear matrix elements with self-consistent short-range correlations

A self-consistent calculation of nuclear matrix elements of the neutrinoless double-beta decays ($0\ensuremath{\nu}\ensuremath{\beta}\ensuremath{\beta}$) of $^{76}\mathrm{Ge}$, $^{82}\mathrm{Se}$, $^{96}\mathrm{Zr}$, $^{100}\mathrm{Mo}$, $^{116}\mathrm{Cd}$, $^{128}\mathrm{Te}$, $^{130}\mathrm{Te}$, and $^{136}\mathrm{Xe}$ is presented in the framework of the renormalized quasiparticle random phase approximation (RQRPA) and the standard QRPA. The pairing and residual interactions as well as the two-nucleon short-range correlations are for the first time derived from the same modern realistic nucleon-nucleon potentials, namely, from the charge-dependent Bonn potential (CD-Bonn) and the Argonne V18 potential. In a comparison with the traditional approach of using the Miller-Spencer Jastrow correlations, matrix elements for the $0\ensuremath{\nu}\ensuremath{\beta}\ensuremath{\beta}$ decay are obtained that are larger in magnitude. We analyze the differences among various two-nucleon correlations including those of the unitary correlation operator method (UCOM) and quantify the uncertainties in the calculated $0\ensuremath{\nu}\ensuremath{\beta}\ensuremath{\beta}$-decay matrix elements.

S-pairing in neutron matter: I. Correlated basis function theory

S-wave pairing in neutron matter is studied within an extension of correlated basis function (CBF) theory to include the strong, short range spatial correlations due to realistic nuclear forces and the pairing correlations of the Bardeen, Cooper and Schrieffer (BCS) approach. The correlation operator contains central as well as tensor components. The correlated BCS scheme of [S. Fantoni, Nucl. Phys. A 363 (1981) 381], developed for simple scalar correlations, is generalized to this more realistic case. The energy of the correlated pair condensed phase of neutron matter is evaluated at the two-body order of the cluster expansion, but considering the one-body density and the corresponding energy vertex corrections at the first order of the Power Series expansion. Based on these approximations, we have derived a system of Euler equations for the correlation factors and for the BCS amplitudes, resulting in correlated nonlinear gap equations, formally close to the standard BCS ones. These equations have been solved for the momentum independent part of several realistic potentials (Reid, Argonne v 14 and Argonne v 8 ′ ) to stress the role of the tensor correlations and of the many-body effects. Simple Jastrow correlations and/or the lack of the density corrections enhance the gap with respect to uncorrelated BCS, whereas it is reduced according to the strength of the tensor interaction and following the inclusion of many-body contributions.

State-dependent correlated wavefunctions for sd-shell nuclei

Correlated trial wavefunctions built as the product of a correlation factor times a model wavefunction are obtained for the 20Ne, 24Mg, 28Si, 32S, 36Ar and 40Ca nuclei. The correlation factor includes both central Jastrow and linear state dependent correlations. For 20Ne, 24Mg and 28Si we have considered two different approaches, one based on the SU(3) deformed model and the other on a multi-cluster model, while for 32S, 36Ar and 40Ca only the first model has been considered. A systematic analysis of the competition between the different correlation mechanisms included in the trial wavefunction on the ground state and binding energies of some members of its rotational band is carried out. One- and two-body radial densities have also been obtained. All the calculations have been performed by means of the variational Monte Carlo method.

Jastrow correlations and near degeneracy effects in neutral atoms and cations with 3 ⩽ Z ⩽ 36

The ground state of the cations Li + through Kr + has been studied by using explicitly correlated wave functions. The variational wave function has been previously used [E. Buendía, F.J. Gálvez, A. Sarsa, Chem. Phys. Lett. 428 (2006) 241] to study the corresponding neutral atoms. Near degeneracy has been also considered by means of a multi-configurational model wave function for a number of neutral atoms and cations. Starting from the total energy of the cations here obtained along with previously reported neutral atom energies (except for some cases here discussed), the ionization potential of these atoms has been calculated by including relativistic effects perturbatively. The calculation has been carried out by using the variational Monte Carlo method.

Projected multicluster model with Jastrow and linear state dependent correlations for12⩽A⩽16nuclei

Variational wave functions based on a Margenau-Brink cluster model with short-range and state-dependent correlations and angular momentum projection are obtained for some nuclei with $12\ensuremath{\leqslant}A\ensuremath{\leqslant}16$. The calculations have been carried out starting from the nucleon-nucleon interaction by using the variational Monte Carlo method. The configuration used consists of three alpha clusters located at the apexes of an equilateral triangle and an additional cluster, not necessarily of alpha type, forming a tetrahedron. This cluster is located at the top of its height. Short-range and state dependent correlations are included by means of a central Jastrow factor and a linear operatorial correlation factor, respectively. Angular momentum projection is performed by using the Peierls-Yoccoz operators. Optimal structures are obtained for all the nuclei studied. Some aspects of our methodology have been tested by comparing with previous calculations carried out without short-range correlations. The binding energy, the root mean square radius, and the one- and two-body densities are reported. The effects of correlations on both the energy and nucleon distributions are analyzed systematically.

Simple correlated wave functions for the ground and some excited states ofsdshell nuclei

Trial wave functions including angular momentum projection and deformation with central Jastrow and linear-type correlations are calculated to study the ground state rotational band of the ${}^{20}\mathrm{Ne},$ ${}^{24}\mathrm{Mg},$ ${}^{28}\mathrm{Si},$ ${}^{32}\mathrm{S},$ and ${}^{36}\mathrm{Ar}$ nuclei and the ground state of ${}^{40}\mathrm{Ca}.$ A systematic analysis of the competition among different correlation mechanisms on the binding energy and other properties such as the root mean square radius and the transition amplitudes of the rotational band is carried out. The one- and two-body radial densities and the momentum distribution are obtained. All the calculations have been performed by means of the variational Monte Carlo method.

Trial wave functions with long-range Coulomb correlations for two-dimensionalN-electron systems in high magnetic fields

A new class of analytic wave functions is derived for two dimensional N-electron $(2&lt;~N&lt;\ensuremath{\infty})$ systems in high magnetic fields. These functions are constructed through breaking (at the Hartree-Fock level) and subsequent restoration (via post-Hartree-Fock methods) of the circular symmetry. They are suitable for describing long-range Coulomb correlations, while the Laughlin and composite-fermion functions describe Jastrow correlations associated with a short-range repulsion. Underlying our approach is a collectively-rotating-electron-molecule picture, yielding for all N an oscillatory radial electron density that extends throughout the system.

Margenau–Brink alpha model with central Jastrow and linear state-dependent correlations for p-shell nuclei

Wave functions based on the alpha cluster model of Margenau–Brink without effective interactions have been obtained for p-shell nuclei. In this approach the constituent clusters are located at fixed centers which are taken as variational parameters. The trial wave functions have been built up with correct total angular momentum and include central Jastrow and linear state dependent correlations. The ground state and the 2 + and 4 + excited states of 8Be, 12C, and the ground state of 16O are studied. The role of the different correlation mechanisms incorporated by the trial wave function is analyzed and the results are compared with previous calculations. The energies of the different bound states have been calculated by using the Variational Monte Carlo method.

Correlated model forΛhypernuclei

We study the properties of hypernuclei containing one $\ensuremath{\Lambda}$ hyperon in the framework of the correlated basis function theory with Jastrow correlations. Fermi hypernetted chain integral equations are derived and used to evaluate energies and one-body densities of $\ensuremath{\Lambda}$ hypernuclei having a doubly closed shell nucleonic core in the $\mathrm{jj}$ coupling scheme, from carbon to lead. We also study hypernuclei having the least bound neutron substituted by the $\ensuremath{\Lambda}$ particle. The semirealistic Afnan and Tang nucleon-nucleon potential and Bodmer and Usmani $\ensuremath{\Lambda}$-nucleon potential are adopted. The effect of many-body forces are considered by means either of a three-body $\ensuremath{\Lambda}$-nucleon-nucleon potential of the Argonne type or of a density-dependent modification of the $\ensuremath{\Lambda}$-nucleon interaction, fitted to reproduce the $\ensuremath{\Lambda}$ binding energy in nuclear matter. While Jastrow correlations underestimate the attractive contribution of the three-body $\ensuremath{\Lambda}$ interaction, the density-dependent potential provides a good description of the $\ensuremath{\Lambda}$ binding energies over all the nuclear masses range, in spite of the relative simplicity of the model.

One-body density matrix, natural orbits, and quasihole states in16Oand40Ca

The one body density matrix, momentum distribution, natural orbits and quasi hole states of 16O and 40Ca are analyzed in the framework of the correlated basis function theory using state dependent correlations with central and tensor components. Fermi hypernetted chain integral equations and single operator chain approximation are employed to sum cluster diagrams at all orders. The optimal trial wave function is determined by means of the variational principle and the realistic Argonne v8' two-nucleon and Urbana IX three-nucleon interactions. The correlated momentum distributions are in good agreement with the available variational Monte Carlo results and show the well known enhancement at large momentum values with respect to the independent particle model. Diagonalization of the density matrix provides the natural orbits and their occupation numbers. Correlations deplete the occupation number of the first natural orbitals by more than 10%. The first following ones result instead occupied by a few percent. Jastrow correlations lower the spectroscopic factors of the valence states by a few percent (~1-3%) and an additional ~8-12% depletion is provided by tensor correlations. It is confirmed that short range correlations do not explain the spectroscopic factors extracted from (e,e'p) experiments. 2h-1p perturbative corrections in the correlated basis are expected to provide most of the remaining strength, as in nuclear matter.

Central Jastrow and linearstate-dependent correlations in nuclei

Linearized state-dependent and central Jastrow correlated trialwavefunctions are used to study the ground state of spin-isospinsaturated p-shell nuclei with V4-type forces.We extend the variational Monte Carlomethod to incorporate this kind of operatorial correlationbyintroducing only minor changes with respect to the case of centralcorrelations. Very good energies are obtained with this wavefunctionfor the nuclei studied.Finally, a discussion of the role of thedifferent correlation mechanisms included in this trial wavefunctionis performed in terms of both the momentum distribution and the one-and two-particle densities in position space.

Tensor correlations in nuclei and exclusive electron scattering

The effect of tensor nucleon-nucleon correlations upon exclusive and semi-exclusive electronuclear reactions is studied. Differential cross sections for the semi-exclusive ^{16}O(e,e'p) and exclusive ^{16}O(e,e'pn) processes are computed by explicitly evaluating the dynamical electromagnetic coupling to a tensor correlated nucleon pair. In both reaction channels the tensor correlations contribute in a very substantial way. Tensor correlations are found to generate more electronuclear strength than central Jastrow correlations do.

Condensate fraction and momentum distribution in the ground state of liquid 4He.

In an earlier paper we calculated the condensate fraction and momentum distribution of atoms in liquid $^{4}\mathrm{He}$, using a variational wave function which takes into account Jastrow and three-body correlations. In the present paper we point out an error in the expression used to compute the condensate fraction when three-body correlations were included. We report the corrected numerical results for both condensate fraction and momentum distributions for three densities. In addition, we calculate the condensate fraction and momentum distribution with and without the l=0 part of the three-body correlations in the wave function. Even though the l=0 part gives a small contribution to the ground-state energy, we find that the l=0 and l=1 terms have opposite and almost canceling effects on the condensate fraction and momentum distribution; each term separately alters the results obtained with pure Jastrow correlations by about 15--20 %, while when considered together they give only a small contribution.

A study of short-range correlation effects on nuclear spatial and momentum distribution

The relation between the nuclear spatial and momentum densities is studied by means of their integral representations in terms of uniform distributions. Examples of this approach are given for the harmonic oscillator model of4He and16O, with and without Jastrow correlations, and for the single-particle potential model of40Ca.

Triplet Correlation Effects in the Maxon-Roton Spectrum of Superfluid 4He

Using Brillouin-Wigner perturbation theory up to the second order, it was shown that triplet correlations play an important role in the spectrum of elementary excitations of liquid 4He as well as in the ground state. Their influence is increased with the increase in density. These effects for Lennard-Jones potential, with respect to Jastrow's correlations, are from 16 to 20% in maxon and 15 to 26% in roton part of the spectrum. It was also found that at the particle densities (in 1028 m-3) beyond 2.46 for MDD-2 and 2.8 for Lennard-Jones the energy of a maxon is greater than the double roton energy. The effects of different potentials were also studied. It was shown that Bruch-McGee's MDD-2 potential leads to the smallest value of the roton gap.