220 research outputs found
Loop updates for quantum Monte Carlo simulations in the canonical ensemble
We present a new non-local updating scheme for quantum Monte Carlo
simulations, which conserves particle number and other symmetries. It allows
exact symmetry projection and direct evaluation of the equal-time Green's
function and other observables in the canonical ensemble. The method is applied
to bosonic atoms in optical lattices, neutron pairs in atomic nuclei and
electron pairs in ultrasmall superconducting grains.Comment: 4 pages, 3 figures, submitted to Physical Review Letter
Diagrammatic Monte Carlo study of the Fermi polaron in two dimensions
We study the properties of the two-dimensional Fermi polaron model in which
an impurity attractively interacts with a Fermi sea of particles in the
zero-range limit. We use a diagrammatic Monte Carlo (DiagMC) method which
allows us to sample a Feynman diagrammatic series to very high order. The
convergence properties of the series and the role of multiple particle-hole
excitations are discussed. We study the polaron and molecule energy as a
function of the coupling strength, revealing a transition from a polaron to a
molecule in the ground state. We find a value for the critical interaction
strength which complies with the experimentally measured one and predictions
from variational methods. For all considered interaction strengths, the polaron
factor from the full diagrammatic series almost coincides with the
one-particle-hole result. We also formally link the DiagMC and the variational
approaches for the polaron problem at hand.Comment: 7 pages, 5 figure
Quasiparticle properties of an impurity in a Fermi gas
We report on a study of a spin-down impurity strongly coupled to a spin-up
Fermi sea (a so-called Fermi polaron) with the diagrammatic Monte-Carlo
(DiagMC) technique. Conditions of zero temperature and three dimensions are
considered for an ultracold atomic gas with resonant interactions in the
zero-range limit. A Feynman diagrammatic series is developed for the one-body
and two-body propagators providing information about the polaron and molecule
channel respectively. The DiagMC technique allows us to reach diagram orders
that are high enough for extrapolation to infinite order. The robustness of the
extracted results is examined by checking various resummation techniques and by
running the simulations with various choices for the propagators and vertex
functions. It turns out that dressing the lines in the diagrams as much as
possible is not always the optimal choice. We also identify classes of dominant
diagrams for the one-body and two-body self-energy in the region of strong
interaction. These dominant diagrams turn out to be the leading processes of
the strong-coupling limit. The quasiparticle energies and -factor are
obtained as a function of the interaction strength. We find that the DiagMC
results for the molecule and polaron properties are very similar to those
obtained with a variational ansatz. Surprisingly, this variational ansatz gives
very good predictions for the quasiparticle residue even when this residue is
significantly smaller than one.Comment: 11 pages, 15 figure
Consequences of the Pauli exclusion principle for the Bose-Einstein condensation of atoms and excitons
The bosonic atoms used in present day experiments on Bose-Einstein
condensation are made up of fermionic electrons and nucleons. In this Letter we
demonstrate how the Pauli exclusion principle for these constituents puts an
upper limit on the Bose-Einstein-condensed fraction. Detailed numerical results
are presented for hydrogen atoms in a cubic volume and for excitons in
semiconductors and semiconductor bilayer systems. The resulting condensate
depletion scales differently from what one expects for bosons with a repulsive
hard-core interaction. At high densities, Pauli exclusion results in
significantly more condensate depletion. These results also shed a new light on
the low condensed fraction in liquid helium II.Comment: 4 pages, 2 figures, revised version, now includes a direct comparison
with hard-sphere QMC results, submitted to Phys. Rev. Let
Engineering Local optimality in Quantum Monte Carlo algorithms
Quantum Monte Carlo algorithms based on a world-line representation such as
the worm algorithm and the directed loop algorithm are among the most powerful
numerical techniques for the simulation of non-frustrated spin models and of
bosonic models. Both algorithms work in the grand-canonical ensemble and have a
non-zero winding number. However, they retain a lot of intrinsic degrees of
freedom which can be used to optimize the algorithm. We let us guide by the
rigorous statements on the globally optimal form of Markov chain Monte Carlo
simulations in order to devise a locally optimal formulation of the worm
algorithm while incorporating ideas from the directed loop algorithm. We
provide numerical examples for the soft-core Bose-Hubbard model and various
spin-S models.Comment: replaced with published versio
Microscopic calculation of symmetry projected nuclear level densities
We present a quantum Monte Carlo method with exact projection on parity and angular momentum that is free of a sign problem for seniority-conserving nuclear interactions. This technique allows the microscopic calculation of angular momentum and parity-projected nuclear level densities. We present results for the Fe-55, Fe-56, and Fe-57 isotopes. Signatures of the pairing phase transition are observed in the angular momentum distribution of the nuclear level density
Polynomial complexity despite the fermionic sign
It is commonly believed that in quantum Monte Carlo approaches to fermionic
many- body problems, the infamous sign problem generically implies
prohibitively large computational times for obtaining thermodynamic-limit
quantities. We point out that for convergent Feynman diagrammatic series
evaluated with the Monte Carlo algorithm of [Rossi, arXiv:1612.05184], the
computational time increases only polynomially with the inverse error on
thermodynamic-limit quantities
Phase diagram of Bose-Fermi mixtures in one-dimensional optical lattices
The ground state phase diagram of the one-dimensional Bose-Fermi Hubbard
model is studied in the canonical ensemble using a quantum Monte Carlo method.
We focus on the case where both species have half filling in order to maximize
the pairing correlations between the bosons and the fermions. In case of equal
hopping we distinguish between phase separation, a Luttinger liquid phase and a
phase characterized by strong singlet pairing between the species. True
long-range density waves exist with unequal hopping amplitudes.Comment: 5 pages, 5 figures, replaced with published versio
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