arXiv subjects

K. E. Schmidt

Publications and source records attributed to K. E. Schmidt.

28 records · Page 2Linked to original sources

arXiv2008

Pfaffian pairing and backflow wave functions for electronic structure quantum Monte Carlo methods

We investigate pfaffian trial wave functions with singlet and triplet pair orbitals by quantum Monte Carlo methods. We present mathematical identities and the key algebraic properties necessary for efficient evaluation of pfaffians. Following upon our previous study \cite{pfaffianprl}, we explore the possibilities of expanding the wave function in linear combinations of pfaffians. We observe that molecular systems require much larger expansions than atomic systems and linear combinations of a few pfaffians lead to rather small gains in correlation energy. We also test the wave function based on fully-antisymmetrized product of independent pair orbitals. Despite its seemingly large variational potential, we do not observe additional gains in correlation energy. We find that pfaffians lead to substantial improvements in fermion nodes when compared to Hartree-Fock wave functions and exhibit the minimal number of two nodal domains in agreement with recent results on fermion nodes topology. We analyze the nodal structure differences of Hartree-Fock, pfaffian and essentially exact large-scale configuration interaction wave functions. Finally, we combine the recently proposed form of backflow correlations \cite{drummond_bf,rios_bf} with both determinantal and pfaffian based wave functions.

cond-mat.other↗

arXiv2007

Auxiliary Field Diffusion Monte Carlo calculation of nuclei with A<40 with tensor interactions

We calculate the ground-state energy of 4He, 8He, 16O, and 40Ca using the auxiliary field diffusion Monte Carlo method in the fixed phase approximation and the Argonne v6' interaction which includes a tensor force. Comparison of our light nuclei results to those of Green's function Monte Carlo calculations shows the accuracy of our method for both open and closed shell nuclei. We also apply it to 16O and 40Ca to show that quantum Monte Carlo methods are now applicable to larger nuclei.

nucl-th↗

arXiv2006

QMC calculations of symmetric nuclear matter

We present an accurate numerical study of the equation of state of nuclear matter based on realistic nucleon--nucleon interactions by means of Auxiliary Field Diffusion Monte Carlo (AFDMC) calculations. The AFDMC method samples the spin and isospin degrees of freedom allowing for quantum simulations of large nucleonic systems and represents an important step forward towards a quantitative understanding of problems in nuclear structure and astrophysics.

nucl-th↗

arXiv2006

Pfaffian pairing wave functions in electronic structure quantum Monte Carlo

We investigate the accuracy of trial wave function for quantum Monte Carlo based on pfaffian functional form with singlet and triplet pairing. Using a set of first row atoms and molecules we find that these wave functions provide very consistent and systematic behavior in recovering the correlation energies on the level of 95%. In order to get beyond this limit we explore the possibilities of multi-pfaffian pairing wave functions. We show that a small number of pfaffians recovers another large fraction of the missing correlation energy comparable to the larger-scale configuration interaction wave functions. We also find that pfaffians lead to substantial improvements in fermion nodes when compared to Hartree-Fock wave functions.

cond-mat.other↗

arXiv2004

Quantum Monte Carlo Studies of Superfluid Fermi Gases

We report results of quantum Monte Carlo calculations of the ground state of dilute Fermi gases with attractive short range two-body interactions. The strength of the interaction is varied to study different pairing regimes which are characterized by the product of the s-wave scattering length and the Fermi wave vector, $ak_F$. We report results for the ground state energy, the pairing gap $Δ$ and the quasiparticle spectrum. In the weak coupling regime, $1/ak_F < -1$, we obtain BCS superfluid and the energy gap $Δ$ is much smaller than the Fermi gas energy $E_{FG}$. When $ a > 0$, the interaction is strong enough to form bound molecules with energy $E_{mol}$. For $1/ak_F \gtrsim 0.5$ we find that weakly interacting composite bosons are formed in the superfluid gas with $Δ$ and gas energy per particle approaching $|E_{mol}|/2$. In this region we seem to have Bose-Einstein condensation (BEC) of molecules. The behavior of the energy and the gap in the BCS to BEC transition region, $-0.5 < 1/ak_F < 0.5$ is discussed.

physics.atom-ph↗

arXiv2004

Auxiliary Field Diffusion Monte Carlo calculation of ground state properties of neutron drops

The Auxiliary Field Diffusion Monte Carlo method has been applied to simulate droplets of 7 and 8 neutrons. Results for realistic nucleon-nucleon interactions, which include tensor, spin--orbit and three--body forces, plus a standard one--body confining potential, have been compared with analogous calculations obtained with Green's Function Monte Carlo methods. We have studied the dependence of the binding energy, the one--body density and the spin--orbit splittings of $^7n$ on the depth of the confining potential. The results obtained show an overall agreement between the two quantum Monte Carlo methods, although there persist differences in the evaluation of spin--orbit forces, as previously indicated by bulk neutron matter calculations. Energy density functional models, largely used in astrophysical applications, seem to provide results significantly different from those of quantum simulations. Given its scaling behavior in the number of nucleons, the Auxiliary Field Diffusion Monte Carlo method seems to be one of the best candidate to perform {\sl ab initio} calculations on neutron rich nuclei.

nucl-th↗

arXiv2004

Neutron Matter: A Superfluid Gas

We review recent progress in the theory of neutron matter with particular emphasis on its superfluid properties. Results of quantum Monte Carlo calculations of simple and realistic models of uniform superfluid neutron gas are discussed along with those of neutrons interacting in a potential well chosen to approximate neutron-rich oxygen isotopes. The properties of dilute superfluid Fermi gases that may be produced in atom traps, and their relations with neutron matter, are illustrated. The density dependence of the effective interaction between neutrons, used to describe neutron-rich systems with the mean field approximations, is also discussed.

nucl-th↗

arXiv2003

Superfluid Fermi Gases with Large Scattering Length

We report quantum Monte Carlo calculations of superfluid Fermi gases with short-range two-body attractive interactions with infinite scattering length. The energy of such gases is estimated to be $(0.44 \pm 0.01)$ times that of the noninteracting gas, and their pairing gap is approximately twice the energy per particle.

physics.atom-ph↗

arXiv2003

Neutron matter at zero temperature with auxiliary field diffusion Monte Carlo

The recently developed auxiliary field diffusion Monte Carlo method is applied to compute the equation of state and the compressibility of neutron matter. By combining diffusion Monte Carlo for the spatial degrees of freedom and auxiliary field Monte Carlo to separate the spin-isospin operators, quantum Monte Carlo can be used to simulate the ground state of many nucleon systems $(A\alt 100)$. We use a path constraint to control the fermion sign problem. We have made simulations for realistic interactions, which include tensor and spin--orbit two--body potentials as well as three-nucleon forces. The Argonne $v_8'$ and $v_6'$ two nucleon potentials plus the Urbana or Illinois three-nucleon potentials have been used in our calculations. We compare with fermion hypernetted chain results. We report results of a Periodic Box--FHNC calculation, which is also used to estimate the finite size corrections to our quantum Monte Carlo simulations. Our AFDMC results for $v_6$ models of pure neutron matter are in reasonably good agreement with equivalent Correlated Basis Function (CBF) calculations, providing energies per particle which are slightly lower than the CBF ones. However, the inclusion of the spin--orbit force leads to quite different results particularly at relatively high densities. The resulting equation of state from AFDMC calculations is harder than the one from previous Fermi hypernetted chain studies commonly used to determine the neutron star structure.

nucl-th↗

arXiv2001

Spin susceptibility of neutron matter at zero temperature

The Auxiliary Field Diffusion Monte Carlo method is applied to compute the spin susceptibility and the compressibility of neutron matter at zero temperature. Results are given for realistic interactions which include both a two-body potential of the Argonne type and the Urbana IX three-body potential. Simulations have been carried out for about 60 neutrons. We find an overall reduction of the spin susceptibilty by about a factor 3 with respect to the Pauli susceptibility for a wide range of densities. Results for the compressibility of neutron matter are also presented and compared with other available estimates obtained for semirealistic nucleon-nucleon interactions by using other techniques.

nucl-th↗