Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1911.01345 · Physical review. B./Physical review. B

High-precision numerical solution of the Fermi polaron problem and large-order behavior of its diagrammatic series

Kris Van Houcke, Félix Werner, Riccardo Rossi

Published Jan 29, 2020• 26 citations
arXivHTMLPDF

Abstract

The Fermi polaron is a quasiparticle that emerges when a mobile impurity is coupled to an ideal Fermi gas through a short-range interaction. Here, the authors introduce a simple Monte Carlo algorithm to compute its ground-state properties by evaluating the Feynman diagrammatic series. The fermionic sign does not cause any fundamental problem when going to high diagrammatic orders, and order $N$=30 is easily reached. Resummation of the divergent series through a conformal mapping yields the polaron energy with record accuracy.

DOI
10.1103/physrevb.101.045134

Related papers

Diagrammatic Monte Carlo study of the Fermi polaron in two dimensions

Jonas Vlietinck, J. Ryckebusch, Kris Van Houcke

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 $Z$ 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.

arXiv:1402.4015•Physical Review B•Feb 19, 2014•50 citations

Fermi-polaron problem: Diagrammatic Monte Carlo method for divergent sign-alternating series

Nikolay V. Prokof'ev, Boris V. Svistunov

We use the diagrammatic Monte Carlo approach to solve the problem of a single spin-down fermion resonantly interacting with a Fermi gas of spin-up particles. Our solution is important for understanding the phase diagram and properties of the crossover from the BCS regime to the Bose-Einstein condensate in the strongly imbalanced regime. On the technical side, we develop a generic sign-problem-tolerant method for exact numerical solution of polaron-type models. This is a characteristic example of how Monte Carlo methods can be used to simulate divergent sign-alternating diagrammatic series.

arXiv:0707.4259•Physical Review B•Jan 22, 2008•317 citations

Diagrammatic Monte Carlo study of polaron systems

Jonas Vlietinck

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 Z-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.

•Jan 1, 2015•0 citations

Bold diagrammatic Monte Carlo: A generic sign-problem tolerant technique for polaron models and possibly interacting many-body problems

Nikolay V. Prokof'ev, Boris V. Svistunov

We develop a Monte Carlo scheme for sampling series of Feynman diagrams for the proper self-energy, which are self-consistently expressed in terms of renormalized particle propagators. This approach is used to solve the problem of a single spin-down fermion resonantly interacting with the Fermi gas of spin-up particles. Though the original series based on bare propagators are sign alternating and divergent, one can still determine the answer behind them by using two strategies (separately or together): (i) using proper series resummation techniques and (ii) introducing renormalized propagators which are defined in terms of the simulated proper self-energy, i.e., making the entire scheme self-consistent. Our solution is important for understanding the phase diagram and properties of the Bardeen-Cooper-Schrieffer--Bose-Einstein Condensation crossover in the strongly imbalanced regime. On the technical side, we develop a generic sign-problem tolerant method for exact numerical solution of polaron-type models and, possibly, of the interacting many-body Hamiltonians.

Physical Review B•Mar 3, 2008•202 citations

Bold diagrammatic Monte Carlo: A generic technique for polaron (and many-body?) problems

Nikolay V. Prokof'ev, Boris V. Svistunov

We develop a Monte Carlo scheme for sampling series of Feynman diagrams for the proper self-energy which are self-consistently expressed in terms of renormalized particle propagators. This approach is used to solve the problem of a single spin-down fermion resonantly interacting with the Fermi gas of spin-up particles. Though the original series based on bare propagators are sign-alternating and divergent one can still determine the answer behind them by using two strategies (separately or together): (i) using proper series re-summation techniques, and (ii) introducing renormalized propagators which are defined in terms of the simulated proper self-energy, i.e. making the entire scheme self-consistent. Our solution is important for understanding the phase diagram and properties of the BCS-BEC crossover in the strongly imbalanced regime. On the technical side, we develop a generic sign-problem tolerant method for exact numerical solution of polaron-type models, and, possibly, of the interacting many-body Hamiltonians.

arXiv:0801.0911•Jan 7, 2008•2 citations

Diagrammatic Monte Carlo study of quasi-two-dimensional Fermi polarons

Peter Kroiß, Lode Pollet

We apply a diagrammatic Monte Carlo method to the problem of an impurity interacting resonantly with a homogeneous Fermi bath for a quasi-two-dimensional setup. Notwithstanding the series divergence, we can show numerically that the three particle-hole diagrammatic contributions are not contributing significantly to the final answer, thus demonstrating a nearly perfect destructive interference of contributions in subspaces with higher-order particle-hole lines. Consequently, for strong enough confinement in the third direction, the transition between the polaron and the molecule ground state is found to be in good agreement with the pure two-dimensional case and agrees very well with the one found by the wave-function approach in the two-particle-hole subspace.

arXiv:1407.3731•Physical Review B•Sep 16, 2014•33 citations
The Fermi polaron is a quasiparticle that emerges when a mobile impurity is coupled to an ideal Fermi gas through a short-range interaction. Here, the authors introduce a simple Monte Carlo algorithm to compute its ground-state properties by evaluating the Feynman diagrammatic series. The fermionic sign does not cause any fundamental problem when going to high diagrammatic orders, and order NNN=30 is easily reached. Resummation of the divergent series through a conformal mapping yields the polaron energy with record accuracy.
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 ZZZ 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.
We use the diagrammatic Monte Carlo approach to solve the problem of a single spin-down fermion resonantly interacting with a Fermi gas of spin-up particles. Our solution is important for understanding the phase diagram and properties of the crossover from the BCS regime to the Bose-Einstein condensate in the strongly imbalanced regime. On the technical side, we develop a generic sign-problem-tolerant method for exact numerical solution of polaron-type models. This is a characteristic example of how Monte Carlo methods can be used to simulate divergent sign-alternating diagrammatic series.
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 Z-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.
We develop a Monte Carlo scheme for sampling series of Feynman diagrams for the proper self-energy, which are self-consistently expressed in terms of renormalized particle propagators. This approach is used to solve the problem of a single spin-down fermion resonantly interacting with the Fermi gas of spin-up particles. Though the original series based on bare propagators are sign alternating and divergent, one can still determine the answer behind them by using two strategies (separately or together): (i) using proper series resummation techniques and (ii) introducing renormalized propagators which are defined in terms of the simulated proper self-energy, i.e., making the entire scheme self-consistent. Our solution is important for understanding the phase diagram and properties of the Bardeen-Cooper-Schrieffer--Bose-Einstein Condensation crossover in the strongly imbalanced regime. On the technical side, we develop a generic sign-problem tolerant method for exact numerical solution of polaron-type models and, possibly, of the interacting many-body Hamiltonians.
We develop a Monte Carlo scheme for sampling series of Feynman diagrams for the proper self-energy which are self-consistently expressed in terms of renormalized particle propagators. This approach is used to solve the problem of a single spin-down fermion resonantly interacting with the Fermi gas of spin-up particles. Though the original series based on bare propagators are sign-alternating and divergent one can still determine the answer behind them by using two strategies (separately or together): (i) using proper series re-summation techniques, and (ii) introducing renormalized propagators which are defined in terms of the simulated proper self-energy, i.e. making the entire scheme self-consistent. Our solution is important for understanding the phase diagram and properties of the BCS-BEC crossover in the strongly imbalanced regime. On the technical side, we develop a generic sign-problem tolerant method for exact numerical solution of polaron-type models, and, possibly, of the interacting many-body Hamiltonians.
We apply a diagrammatic Monte Carlo method to the problem of an impurity interacting resonantly with a homogeneous Fermi bath for a quasi-two-dimensional setup. Notwithstanding the series divergence, we can show numerically that the three particle-hole diagrammatic contributions are not contributing significantly to the final answer, thus demonstrating a nearly perfect destructive interference of contributions in subspaces with higher-order particle-hole lines. Consequently, for strong enough confinement in the third direction, the transition between the polaron and the molecule ground state is found to be in good agreement with the pure two-dimensional case and agrees very well with the one found by the wave-function approach in the two-particle-hole subspace.