Recent Advances in the Microscopic Calculations of Level Densities by the Shell Model Monte Carlo Method

Alhassid, Y.; Bonett-Matiz, M.; Liu, S.; Mukherjee, Asok K.; Nakada, H.

doi:10.1051/epjconf/20136900010

Cited by 3 publications

(3 citation statements)

References 27 publications

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“…Our computation of the dynamical correlation functions here relies on a new algorithm which improved the computational scaling in the calculation of imaginarytime correlation functions [40] from O(N 3 s ) in standard algorithms [41][42][43][44][45][46] to O(N s N 2 p ). The algorithm lets fluctuations related to creation/destruction operators or density/spin operators propagate in imaginary time, coupled to the stochastic evolution of the underlying AFQMC random walk or path-integral [40].…”

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confidence: 99%

Visualizing the BEC-BCS crossover in a two-dimensional Fermi gas: Pairing gaps and dynamical response functions from ab initio computations

et al. 2017

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Experiments with ultracold atoms provide a highly controllable laboratory setting with many unique opportunities for precision exploration of quantum many-body phenomena. The nature of such systems, with strong interaction and quantum entanglement, makes reliable theoretical calculations challenging. Especially difficult are excitation and dynamical properties, which are often the most directly relevant to experiment. We carry out exact numerical calculations, by Monte Carlo sampling of imaginary-time propagation of Slater determinants, to compute the pairing gap in the two-dimensional Fermi gas from first principles. Applying state-of-art analytic continuation techniques, we obtain the spectral function, and the density and spin structure factors providing unique tools to visualize the BEC-BCS crossover. These quantities will allow for a direct comparison with experiments.It is truly unusual when, starting from a microscopic Hamiltonian, theory can achieve an exact description of a strongly correlated fermionic system which, at the same time, can be realized in a laboratory with great precision and control. Experiments with ultracold atoms [1,2] have provided a possibility to realize such a scenario. The accuracy that can be reached in experiments with Fermi atomic gases and optical lattices is exceptional, thus offering a unique setting to explore highly correlated quantum fermion systems. In this paper, we demonstrate that, from the theoretical side, advances in computational methods now make it feasible to obtain numerically exact results for not only equilibrium properties, but also excited states. We compute the pairing gap, spectral functions and dynamical response functions in the two-dimensional Fermi gas across the range of interactions, which will allow direct comparisons with spectroscopy or scattering experiments. The dynamical properties provide a powerful tool to probe the behavior of the system and to visualize the crossover from a gas of molecules to a BCS superfluid.We study the Fermi gas with a zero-range attractive interaction, which has generated a great deal of research activity [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15]. The interest of the system is very wide, ranging from condensed matter physics [6,16] to nuclear physics, with possible important applications also in the study of neutron stars [17,18]. This system describes experiments with a collection of atoms, for example 6 Li, which are cooled to degeneracy in an equal mixture of two hyperfine ground states, labeled | ↑ and | ↓ . Feshbach resonances allow the tuning of the interactions by varying an external magnetic field, making the system a unique laboratory to explore many-body physics [19,20]. Starting from a weakly interacting BCS regime, where the attraction between particles induces a pairing similar to the one observed in ordinary superconductors, a crossover is observed as the interaction strength is increased, leading to a BEC regime where the Cooper pairs are tightly bound such that the system behaves as a gas of...

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confidence: 99%

Visualizing the BEC-BCS crossover in a two-dimensional Fermi gas: Pairing gaps and dynamical response functions from ab initio computations

et al. 2017

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“…Using the stochastic linear combination (24) as an approximation to the ground state | Ψ 0 we get immediately:…”

Section: Computation Of Observablesmentioning

confidence: 99%

“…There are many examples of important applications along these lines [9][10][11][12][13][14][15][16][17], with the frontier of interesting sign-problem-free situations still being actively expanded. A key class of applications with direct experimental and theoretical importance are in systems involving ultracold Fermi atoms [18][19][20][21][22][23][24][25] and more recently, in cold atom systems with spin-orbit coupling [26,27]. It was also shown that the use of a BCS trial wave function in the unitary Fermi gas can both reduce projection time (to reach the ground state) and dramatically improve the statistical accuracy of the computed ground-state energy [18].…”

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confidence: 99%

Calculating ground-state properties of correlated fermionic systems with BCS trial wave functions in Slater determinant path-integral approaches

2019

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We introduce an efficient and numerically stable technique to make use of a BCS trial wave function in the computation of correlation functions of strongly correlated quantum fermion systems. The technique is applicable to any projection approach involving paths of independent-fermion propagators, for example in mean-field or auxiliary-field quantum Monte Carlo (AFQMC) calculations. Within AFQMC, in the absence of the sign problem, the methodology allows the use of a BCS reference state which can greatly reduce the required imaginary time of projection, and improves Monte Carlo sampling efficiency and statistical accuracy for systems where pairing correlations are important. When the sign problem is present, the approach provides a powerful generalization of the constrained-path AFQMC technique which usually uses Slater determinant trial wave functions. As a demonstration of the capability of the methodology, we present benchmark results for the attractive Hubbard model, both spin-balanced (no sign problem) and with a finite spin polarization (with sign problem). arXiv:1905.05012v1 [cond-mat.str-el]

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Spin cutoff factor and level density for Ni59 from an analysis of compound nuclear reactions

Voinov,

Alanazi,

Akhtar

et al. 2023

Phys. Rev. C

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Recent Advances in the Microscopic Calculations of Level Densities by the Shell Model Monte Carlo Method

Cited by 3 publications

References 27 publications

Visualizing the BEC-BCS crossover in a two-dimensional Fermi gas: Pairing gaps and dynamical response functions from ab initio computations

Visualizing the BEC-BCS crossover in a two-dimensional Fermi gas: Pairing gaps and dynamical response functions from ab initio computations

Calculating ground-state properties of correlated fermionic systems with BCS trial wave functions in Slater determinant path-integral approaches

Spin cutoff factor and level density for Ni59 from an analysis of compound nuclear reactions

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