Constrained-Path Quantum Monte-Carlo Approach for Non-Yrast States Within the Shell Model

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.Comment: 11 pages, 4 figure

A constrained-path quantum Monte-Carlo approach for the nuclear shell model

International audienceA new QMC approach for the shell model yielding nearly exact spectroscopy of nuclei is presented. The originality of the formalism lies in the use of a variational symmetry-restored wave function to ‘steer’ the Brownian motion, and to control the sign/phase problem that generally makes the traditional QMC samplings totally ineffective by causing a prohibitive growth of the statistical errors. Tests of convergence and proof-of-principle results are reported

Exotic spin, charge and pairing correlations of the two-dimensional doped Hubbard model: a symmetry entangled mean-field approach

Intertwining of spin, charge and pairing correlations in the repulsive two-dimensional Hubbard model is shown through unrestricted variational calculations, with projected wavefunctions free of symmetry breaking. A crossover from incommensurate antiferromagnetism to stripe order naturally emerges in the hole-doped region when increasing the on-site coupling. Although effective pairing interactions are identified, they are strongly fragmented in several modes including d-wave pairing and more exotic channels related to an underlying stripe. We demonstrate that the entanglement of a mean-field wavefunction by symmetry restoration can largely account for interaction effects.Comment: Minor corrections, one reference adde

Intertwined orders from symmetry projected wavefunctions of repulsively interacting Fermi gases in optical lattices

Unconventional strongly correlated phases of the repulsive Fermi-Hubbard model, which could be emulated by ultracold vapors loaded in optical lattices, are investigated by means of energy minimizations with quantum number projection before variation and without any assumed order parameter. In a tube-like geometry of optical plaquettes to realize the four-leg ladder Hubbard Hamiltonian, we highlight the intertwining of spin-, charge-, and pair-density waves embedded in a uniform d-wave superfluid background. As the lattice filling increases, this phase emerges from homogenous states exhibiting spiral magnetism and evolves towards a doped antiferromagnet. A concomitant enhancement of long-ranged d-wave pairing correlations is also found. Numerical tests of the approach for two-dimensional clusters are carried out, too.Comment: 26 pages, 15 figures ; replaced with the published manuscript ; substantial changes from previous versio

Symétries nucléaires à faible isospin

With the development of radioactive beams, an area of intense research in nuclear physics concerns the structure of exotic systems with roughly equal numbers of protons and neutrons. These nuclei might in fact develop a proton-neutron superfluidity whose importance compared to pairing correlations between like nucleons is currently investigated. The work presented in this thesis suggests to look at such a competition in an algebraic framework based on a Wigner SU(4) symmetry that combines the pseudo-spin and isospin degrees of freedom. After a detailed review of group theory in quantum mechanics, the validity of the pseudo-SU(4) classification is shown via a direct analysis of realistic shell model states. Its consequences on binding energies and β decay are also studied. Moreover, a simplified boson realisation with zero orbital angular momentum is used to find some physical features of N=Z nuclei such as the condensation of α-like structures or the destruction of isoscalar superfluid correlations by the spin-orbit potential. Finally, another bosonization scheme that includes quadrupole degrees of freedom (IBM-4 model) is tested for the first time by diagonalization of a full Hamiltonian deduced from a realistic shell model interaction. The quality of the results, especially for odd-odd nuclei, allows one to consider this boson approximation as an alternative to standard fermionic approaches for the collective structure of the exotic line N∼Z=28-50.Avec le développement des faisceaux radioactifs, un intérêt particulier est actuellement porté aux noyaux exotiques riches en protons. Ces structures offrent en effet la possibilité de développer une superfluidité proton-neutron dont l'importance vis à vis des corrélations d'appariement entre nucléons identiques fait l'objet de nombreuses études théoriques. Le travail présenté propose précisément d'aborder ce problème dans le cadre d'une approche algébrique basée sur une symétrie SU(4) de Wigner combinant les degrés de liberté de pseudo-spin et d'isospin. Après avoir repris en détail les implémentations de la théorie des groupes en mécanique quantique, la pertinence de la classification pseudo-SU(4) est directement montrée au niveau des états réalistes du modèle en couches. Ses conséquences au niveau des masses et des transitions de décroissance β sont également analysées. Sa réalisation partielle en bosons de moment orbital nul est de plus utilisée pour mettre en évidence un certain nombre de phénomènes physiques spécifiques à la ligne N = Z comme la condensation en structures de type α ou la destruction par le potentiel spin-orbite des corrélations superfluides isoscalaires. Enfin, un autre schéma de bosonisation incluant des degrés de liberté quadrupolaires (modèle IBM-4) est testé pour la première fois en diagonalisant un hamiltonien complet déduit d'une interaction réaliste du modèle en couches. La qualité des résultats obtenus, plus particulièrement pour les noyaux impair-impair, permet raisonnablement d'envisager l'utilisation de cette approximation en bosons comme alternative aux approches fermioniques standard pour élucider la structure collective de la ligne exotique N ∼ Z = 28-50

Three fermions in a box at the unitary limit: universality in a lattice model

We consider three fermions with two spin components interacting on a lattice model with an infinite scattering length. Low lying eigenenergies in a cubic box with periodic boundary conditions, and for a zero total momentum, are calculated numerically for decreasing values of the lattice period. The results are compared to the predictions of the zero range Bethe-Peierls model in continuous space, where the interaction is replaced by contact conditions. The numerical computation, combined with analytical arguments, shows the absence of negative energy solution, and a rapid convergence of the lattice model towards the Bethe-Peierls model for a vanishing lattice period. This establishes for this system the universality of the zero interaction range limit.Comment: 6 page

Exact pairing correlations in one-dimensionally trapped fermions with stochastic mean-field wave-functions

Accepted for publication in Physical Review Letters.The canonical thermodynamic properties of a one-dimensional system of interacting spin-1/2 fermions with an attractive zero-range pseudo-potential are investigated within an exact approach. The density operator is evaluated as the statistical average of dyadics formed from a stochastic mean-field propagation of independent Slater determinants. For an harmonically trapped Fermi gas and for fermions confined in a 1D-like torus, we observe the transition to a quasi-BCS state with Cooper-like momentum correlations and an algebraic long-range order. For few trapped fermions in a rotating torus, a dominant superfluid component with quantized circulation can be isolated

Generalized Gibbs ensembles for time dependent processes

An information theory description of finite systems explicitly evolving in time is presented for classical as well as quantum mechanics. We impose a variational principle on the Shannon entropy at a given time while the constraints are set at a former time. The resulting density matrix deviates from the Boltzmann kernel and contains explicit time odd components which can be interpreted as collective flows. Applications include quantum brownian motion, linear response theory, out of equilibrium situations for which the relevant information is collected within different time scales before entropy saturation, and the dynamics of the expansion

Sign-free stochastic mean-field approach to strongly correlated phases of ultracold fermions

We propose a new projector quantum Monte-Carlo method to investigate the ground state of ultracold fermionic atoms modeled by a lattice Hamiltonian with on-site interaction. The many-body state is reconstructed from Slater determinants that randomly evolve in imaginary-time according to a stochastic mean-field motion. The dynamics prohibits the crossing of the exact nodal surface and no sign problem occurs in the Monte-Carlo estimate of observables. The method is applied to calculate ground-state energies and correlation functions of the repulsive two-dimensional Hubbard model. Numerical results for the unitary Fermi gas validate simulations with nodal constraints.Comment: Accepted for publication in New Journal of Physic