Constrained-path quantum Monte Carlo approach for non-yrast states within the shell model

Abstract

The present paper intends to present an extension of the constrained-path quantum Monte-Carlo approach allowing to reconstruct non-yrast states in order to reach the complete spectroscopy of nuclei within the interacting shell model. As in the yrast case studied in a previous work, the formalism involves a variational symmetry-restored wave function assuming two central roles. First, it guides the underlying Brownian motion to improve the efficiency of the sampling. Second, it constrains the stochastic paths according to the phaseless approximation to control sign or phase problems that usually plague fermionic QMC simulations. Proof-of-principle results in the sd valence space are reported. They prove the ability of the scheme to offer remarkably accurate binding energies for both even-and odd-mass nuclei irrespective of the considered interaction.

Phaseless quantum Monte-Carlo approach to strongly correlated superconductors with stochastic Hartree–Fock–Bogoliubov wavefunctions

“…Up to date, no numerical applications involving Slater determinants have taken into account an imaginary-time dependence of the gauges {g s }, and the choices g s = 0 or g s = Ô s Ψ T ,Ψ T have been proposed [42]. It should be finally noted that the Brownian motion (44,45) of HFB walkers allows to find the usual reconstruction scheme (23) …”

“…In view of the expression (46) of the factor Π, a phase problem arises with the sampling (23,44,45) as soon as some coefficients ω s < 0 are required. This situation is in fact systematic for all realistic Hamiltonian rewritten as a quadratic form of one-body operators [46,47].…”

“…The Hubbard model, which allows one to highlight the generic properties of a fermionic system on a lattice, is an example that meets such conditions both in the attractive and repulsive regimes, irrespective of the dimensionality of the lattice. The QMC reformulation with guided dynamics (23,44,45) then encounters no phase problem provided it is initiated with a HFB state which matrices U and V are real. Moreover, one should also be able to write the trial state |Ψ T as linear combination of such HFB vacua with real amplitudes.…”

“…Frustrated magnetic models have also been apprehended with a similar random walk within matrix-product states [43]. Finally, the approach has been generalized to rebuild, in the context of nuclear structure, the ground state [44] as well as excited states [45] in each symmetry sector of the Hamiltonian via wavefunctions projected onto the related quantum numbers. In the following, we extend the guided dynamics QMC scheme (23) to HFB-type walkers.…”

“…It should be finally noted that the Brownian motion (44,45) of HFB walkers allows to find the usual reconstruction scheme (23) By solely retaining in the rewriting (37) of the Hamiltonian operators Ôs that conserve the particle number, this structure is preserved by the dynamics (44), which immediately gives the evolution of the occupied states |φ n . The results obtained this way are identical to those presented in the original reference [30] in the limit of a continuous imaginary time.…”