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:1402.4015 · Physical Review B

Diagrammatic Monte Carlo study of the Fermi polaron in two dimensions

Jonas Vlietinck, J. Ryckebusch, Kris Van Houcke

Published Feb 19, 2014• 50 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physrevb.89.085119

Related papers

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

Quasiparticle properties of an impurity in a Fermi gas

Jonas Vlietinck, J. Ryckebusch, Kris Van Houcke

We report 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 less than 1.

arXiv:1302.3505•Physical Review B•Mar 25, 2013•73 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

Ab initio Lattice Results for Fermi Polarons in Two Dimensions

Shahin Bour, Dean Lee, H.‐W. Hammer +1 more

We investigate the attractive Fermi polaron problem in two dimensions using nonperturbative Monte Carlo simulations. We introduce a new Monte Carlo algorithm called the impurity lattice Monte Carlo method. This algorithm samples the path integral in a computationally efficient manner and has only small sign oscillations for systems with a single impurity. As a benchmark of the method, we calculate the universal polaron energy in three dimensions in the scale-invariant unitarity limit and find agreement with published results. We then present the first fully nonperturbative calculations of the polaron energy in two dimensions and density correlations between the impurity and majority particles in the limit of zero-range interactions. We find evidence for a smooth crossover transition from fermionic quasiparticle to molecular state as a function of the interaction strength.

arXiv:1412.8175•Physical Review Letters•Oct 27, 2015•32 citations

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

Kris Van Houcke, Félix Werner, Riccardo Rossi

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.

arXiv:1911.01345•Physical review. B./Physical review. B•Jan 29, 2020•26 citations

Polarons and dimerons in the two-dimensional attractive Hubbard model

Gerard Pascual, Jordi Boronat, Kris Van Houcke

A two-dimensional (2D) spin-up ideal Fermi gas interacting attractively with a spin-down impurity in the continuum undergoes, at zero temperature, a first-order phase transition from a polaron to a dimeron state. Here, we study a similar system on a square lattice, by considering the attractive 2D Fermi-Hubbard model with a single spin-down and a finite filling fraction of spin-up fermions. We study polaron and dimeron quasiparticle properties via variational ansatz up to one particle-hole excitation. Moreover, we develop a determinant diagrammatic Monte Carlo algorithm for this problem based on expansion in bare on-site coupling U . This algorithm turns out to be sign-problem-free at any filling of spin-up fermions, allowing one to sample very high diagram order (larger than 200 in our study) and to do simulations for large U / t (we go up to U / t = − 20 with t the hopping strength). Both methods give qualitatively consistent results. With variational ansatz we go to even larger on-site attraction. At very low spin-up filling fraction, we observe the polaron-to-dimeron transition, in agreement with the continuum case. Upon increasing the filling fraction, however, the transition shifts to higher values of | U | / t and the transition disappears beyond a filling fraction of about 20 % . In this region, the polaron state always gives a lower energy and has a finite quasiparticle residue. Our findings are directly relevant to cold atom experiments with 2D optical lattices: A small and finite density of spin-down impurities in the ground state will form a superfluid at strong coupling at low spin-up filling fraction. Above some critical spin-up filling fraction, the system is expected to remain a normal Fermi liquid, even in the strong-coupling limit.

arXiv:2411.19725•Physical Review Research•Sep 11, 2025•2 citations
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 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 report 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 ZZZ 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 less than 1.
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.
We investigate the attractive Fermi polaron problem in two dimensions using nonperturbative Monte Carlo simulations. We introduce a new Monte Carlo algorithm called the impurity lattice Monte Carlo method. This algorithm samples the path integral in a computationally efficient manner and has only small sign oscillations for systems with a single impurity. As a benchmark of the method, we calculate the universal polaron energy in three dimensions in the scale-invariant unitarity limit and find agreement with published results. We then present the first fully nonperturbative calculations of the polaron energy in two dimensions and density correlations between the impurity and majority particles in the limit of zero-range interactions. We find evidence for a smooth crossover transition from fermionic quasiparticle to molecular state as a function of the interaction strength.
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.
A two-dimensional (2D) spin-up ideal Fermi gas interacting attractively with a spin-down impurity in the continuum undergoes, at zero temperature, a first-order phase transition from a polaron to a dimeron state. Here, we study a similar system on a square lattice, by considering the attractive 2D Fermi-Hubbard model with a single spin-down and a finite filling fraction of spin-up fermions. We study polaron and dimeron quasiparticle properties via variational ansatz up to one particle-hole excitation. Moreover, we develop a determinant diagrammatic Monte Carlo algorithm for this problem based on expansion in bare on-site coupling U . This algorithm turns out to be sign-problem-free at any filling of spin-up fermions, allowing one to sample very high diagram order (larger than 200 in our study) and to do simulations for large U / t (we go up to U / t = − 20 with t the hopping strength). Both methods give qualitatively consistent results. With variational ansatz we go to even larger on-site attraction. At very low spin-up filling fraction, we observe the polaron-to-dimeron transition, in agreement with the continuum case. Upon increasing the filling fraction, however, the transition shifts to higher values of | U | / t and the transition disappears beyond a filling fraction of about 20 % . In this region, the polaron state always gives a lower energy and has a finite quasiparticle residue. Our findings are directly relevant to cold atom experiments with 2D optical lattices: A small and finite density of spin-down impurities in the ground state will form a superfluid at strong coupling at low spin-up filling fraction. Above some critical spin-up filling fraction, the system is expected to remain a normal Fermi liquid, even in the strong-coupling limit.