Auxiliary-field Quantum Monte Carlo Methods in Nuclei

Abstract

Auxiliary-field quantum Monte Carlo methods enable the calculation of thermal and ground state properties of correlated quantum many-body systems in model spaces that are many orders of magnitude larger than those that can be treated by conventional diagonalization methods. We review recent developments and applications of these methods in nuclei using the framework of the configuration-interaction shell model. * yoram.alhassid@yale.edu 1 arXiv:1607.01870v1 [nucl-th]

The pseudogap regime in the unitary Fermi gas

“…These approaches are inspired by AFMC methods developed for nuclei [103,104] in which the number of protons and neutrons are fixed; for reviews see Refs. [105][106][107]. An advantage of the canonical ensemble formulation is that it allows the computation of a pairing gap from the staggering of the energy in particle number, Eq.…”

Statistical theory of deformation distributions in nuclear spectra

“…In the isotopes that are deformed in their ground state 150,152,154 Sm, the prolate state density dominates at low excitation energies but the spherical state density exceeds it at above a certain excitation energy that becomes higher for the heavier isotopes. 6 In the well-deformed nuclei 152,154 Sm the probability of the prolate shape is close to 1 up to excitations of E x ∼ 5 MeV, while in the transitional nucleus 150 Sm it is only ∼ 0.8 up to E x ∼ 3 MeV. In the spherical nucleus 148 Sm, the spherical state density dominates at all excitation energies although the prolate shape region makes a significant contribution.…”

“…Integrating the shape-projected state density over all shapes β, γ in the intrinsic frame should yield the total state density and can thus be compared with the total 6 We note that the exact excitation energy for which the crossing of the spherical and prolate densities occur depends on the value of β 0 used to differentiate between the spherical and deformed regions in Fig. 7.…”

“…The auxiliary-field Monte Carlo (AFMC) method, also known in nuclear physics as shell-model Monte Carlo (SMMC) [2][3][4][5][6], is a powerful technique for microscopic calculations of nuclear level densities within the configuration-interaction (CI) shell model approach [7,8]. The method has been applied to nuclei as heavy as the lanthanides [9,10].…”

Pairing Correlations across the Superfluid Phase Transition in the Unitary Fermi Gas

“…Finite-temperature AFMC.-The AFMC method (for a recent review, see Ref. [44]) is based on the Hubbard-Stratonovich (HS) transformation [45,46], which expresses the thermal propagator e −βĤ (β = 1/k B T is the inverse temperature T with Boltzmann constant k B ) as a path integral over external auxiliary fields.…”