25 research outputs found
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
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
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
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
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
Resummation of diagrammatic series with zero convergence radius for strongly correlated fermions
We demonstrate that summing up series of Feynman diagrams can yield unbiased
accurate results for strongly-correlated fermions even when the convergence
radius vanishes. We consider the unitary Fermi gas, a model of non-relativistic
fermions in three-dimensional continuous space. Diagrams are built from
partially-dressed or fully-dressed propagators of single particles and pairs.
The series is resummed by a conformal-Borel transformation that incorporates
the large-order behavior and the analytic structure in the Borel plane, which
are found by the instanton approach. We report highly accurate numerical
results for the equation of state in the normal unpolarized regime, and
reconcile experimental data with the theoretically conjectured fourth virial
coefficient
Diagrammatic Monte Carlo study of the acoustic and the BEC polaron
We consider two large polaron systems that are described by a Fr\"{o}hlich
type of Hamiltonian, namely the Bose-Einstein condensate (BEC) polaron in the
continuum and the acoustic polaron in a solid. We present ground-state energies
of these two systems calculated with the Diagrammatic Monte Carlo (DiagMC)
method and with a Feynman all-coupling approach. The DiagMC method evaluates up
to very high order a diagrammatic series for the polaron Green's function. The
Feynman all-coupling approach is a variational method that has been used for a
wide range of polaronic problems. For the acoustic and BEC polaron both methods
provide remarkably similar non-renormalized ground-state energies that are
obtained after introducing a finite momentum cutoff. For the renormalized
ground-state energies of the BEC polaron, there are relatively large
discrepancies between the DiagMC and the Feynman predictions. These differences
can be attributed to the renormalization procedure for the contact interaction.Comment: 9 pages, 10 figure