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

A comparison between T-matrix and Quantum Monte Carlo results

Andrea Guidini, Elisa Fratini, Gianluca Bertaina, P. Pieri, Abdus Salam

Published Jan 1, 2015• 0 citations
OpenAlex

Abstract

We discuss how approximate theories for Bose-Fermi mixtures recover in the molecular limit the expected expression for Fermi-Fermi mixtures of molecules and unpaired fermions. In particu- lar, we compare the energy of the system resulting from a T-matrix diagrammatic approach with that obtained with Variational and Fixed-Node Diffusion Quantum Monte Carlo methods.

Related papers

Bose-Fermi mixtures in the molecular limit

Andrea Guidini, Gianluca Bertaina, Elisa Fratini +1 more

We consider a Bose-Fermi mixture in the molecular limit of the attractive interaction between fermions and bosons. For a boson density smaller than or equal to the fermion density, we show analytically how a T-matrix approach for the constituent bosons and fermions recovers the expected physical limit of a Fermi-Fermi mixture of molecules and atoms. In this limit, we derive simple expressions for the self-energies, the momentum distribution function, and the chemical potentials. By extending these equations to a trapped system, we determine how to tailor the experimental parameters of a Bose-Fermi mixture in order to enhance the indirect Pauli exclusion effect on the boson momentum distribution function. For the homogeneous system, we present finally a diffusion Monte Carlo simulation which confirms the occurrence of such a peculiar effect.

arXiv:1401.0686•Physical Review A•Feb 28, 2014•12 citations

Quantum Monte Carlo simulations of interacting electrons

Ryszard Olchawa

A brief introduction to the Monte Carlo methods and the most common types of Quantum Monte Carlo, Variational Monte Carlo and Diffusion Monte Carlo are presented. The fermion sign problem in Diffusion Monte Carlo is outlined and a way of bypassing the fixed-node approximation is discussed.

Journal of Physics Conference Series•Feb 28, 2006•1 citation

Comparative study of many-body t-matrix theories for a Fermi gas through the BCS-BEC crossover

Michele Pini, P. Pieri, Giancarlo Strinati Calvanese

In the latest several years, diagrammatic theories based on the t-matrix approximation with different \ndegrees of self-consistency have been developed to describe a Fermi gas through the BCS-BEC crossover. A comprehensive comparison between the results obtained by the different \napproaches for both thermodynamical and dynamical quantities is, however, still lacking. In the present \nwork, we consider all the possible ways of implementing self-consistency in the t-matrix approximation and \ncompare the outcomes of the different approaches between each other (and with the available experimental \nand Quantum Monte Carlo data) through the whole BCS-BEC crossover. In this way, we expect to provide \na guideline on the virtues and the drawbacks of each scheme that can help future research in this field.

•Jan 1, 2018•0 citations

Quantum Monte Carlo Study of a Resonant Bose-Fermi Mixture

Gianluca Bertaina, Elisa Fratini, S. Giorgini +1 more

We study a resonant Bose-Fermi mixture at zero temperature by using the fixed-node diffusion Monte Carlo method. We explore the system from weak to strong boson-fermion interaction, for different concentrations of the bosons relative to the fermion component. We focus on the case where the boson density n(B) is smaller than the fermion density n(F), for which a first-order quantum phase transition is found from a state with condensed bosons immersed in a Fermi sea, to a Fermi-Fermi mixture of composite fermions and unpaired fermions. We obtain the equation of state and the phase diagram, and we find that the region of phase separation shrinks to zero for vanishing n(B).

arXiv:1211.6011•Physical Review Letters•Mar 14, 2013•51 citations

Cluster expansion for ideal Fermi systems in the `fixed-node approximation'

Vladimir S. Filinov

Over the last ten years the `fixed-node approximation', well known in the literature, has been widely used for a numerical treatment of thermodynamic properties of strongly correlated Fermi systems. Results of the direct path integral Monte Carlo simulation performed here show that the `fixed-node approximation' describes the thermodynamic properties of the strongly coupling fermions rather well at `weak and moderate' degeneracy. To analyse the reasons for the increasing difference between the `fixed-node approximation' and the results of direct path integral Monte Carlo simulations for highly degenerate fermions, the correctness of the `fixed-node approximation' for ideal Fermi systems has been analysed by analytical methods. A rigorous proof has been given of the fact that the exact Fermi function with index 3 / 2 describing the logarithm of the grand partition function of ideal fermions cannot be reproduced in the `fixed-node approximation', which means that the `fixed-node approximation' does not give the correct ideal Fermi gas limit.

Journal of Physics A Mathematical and General•Feb 19, 2001•20 citations

Bose-Fermi mixtures with pairing

Andrea Guidini, Gianluca Bertaina, Davide Emilio Galli +1 more

I will review recent work by us on the properties of Bose-Fermi mixtures with a tunable pairing interaction between bosons and fermions. A many-body diagrammatic approach, able to describe the condensed phase of a Bose-Fermi mixture from weak to strong boson-fermion couplings, will be presented [1]. This approach will be validated by comparing it with previous [2] and new dedicated fixed-node diffusion Monte Carlo calculations. By using both methods, a universal behavior of the condensate fraction and bosonic momentum distribution with respect to the boson concentration is found in an extended range of boson-fermion couplings and concentrations. For vanishing boson density, the bosonic condensate fraction reduces to the quasiparticle weight Z of the Fermi polaron studied in the context of polarized Fermi gases, unifying in this way two apparently unrelated quantities. Finally, I will discuss an interesting effect occurring in the molecular limit of the boson- fermion coupling, where the condensation is completely suppressed [3]. This phenomenon is an indirect effect on bosons of the Pauli exclusion principle acting on fermions, and is the counterpart in BoseFermi mixtures of the so called “Sarma phase” discussed for polarized Fermi gases. [1] A. Guidini, G. Bertaina, D. Galli, and P. Pieri, arXiv:1412.2542. [2] G. Bertaina, E. Fratini, S. Giorgini, and P. Pieri, Phys. Rev. Lett. 110, 115303 (2013). [3] A. Guidini, G. Bertaina, E. Fratini, and P. Pieri, Phys. Rev. A 89, 023634 (2014).

•Jan 1, 2015•0 citations
We discuss how approximate theories for Bose-Fermi mixtures recover in the molecular limit the expected expression for Fermi-Fermi mixtures of molecules and unpaired fermions. In particu- lar, we compare the energy of the system resulting from a T-matrix diagrammatic approach with that obtained with Variational and Fixed-Node Diffusion Quantum Monte Carlo methods.
We consider a Bose-Fermi mixture in the molecular limit of the attractive interaction between fermions and bosons. For a boson density smaller than or equal to the fermion density, we show analytically how a T-matrix approach for the constituent bosons and fermions recovers the expected physical limit of a Fermi-Fermi mixture of molecules and atoms. In this limit, we derive simple expressions for the self-energies, the momentum distribution function, and the chemical potentials. By extending these equations to a trapped system, we determine how to tailor the experimental parameters of a Bose-Fermi mixture in order to enhance the indirect Pauli exclusion effect on the boson momentum distribution function. For the homogeneous system, we present finally a diffusion Monte Carlo simulation which confirms the occurrence of such a peculiar effect.
In the latest several years, diagrammatic theories based on the t-matrix approximation with different \ndegrees of self-consistency have been developed to describe a Fermi gas through the BCS-BEC crossover. A comprehensive comparison between the results obtained by the different \napproaches for both thermodynamical and dynamical quantities is, however, still lacking. In the present \nwork, we consider all the possible ways of implementing self-consistency in the t-matrix approximation and \ncompare the outcomes of the different approaches between each other (and with the available experimental \nand Quantum Monte Carlo data) through the whole BCS-BEC crossover. In this way, we expect to provide \na guideline on the virtues and the drawbacks of each scheme that can help future research in this field.
We study a resonant Bose-Fermi mixture at zero temperature by using the fixed-node diffusion Monte Carlo method. We explore the system from weak to strong boson-fermion interaction, for different concentrations of the bosons relative to the fermion component. We focus on the case where the boson density n(B) is smaller than the fermion density n(F), for which a first-order quantum phase transition is found from a state with condensed bosons immersed in a Fermi sea, to a Fermi-Fermi mixture of composite fermions and unpaired fermions. We obtain the equation of state and the phase diagram, and we find that the region of phase separation shrinks to zero for vanishing n(B).
Over the last ten years the `fixed-node approximation', well known in the literature, has been widely used for a numerical treatment of thermodynamic properties of strongly correlated Fermi systems. Results of the direct path integral Monte Carlo simulation performed here show that the `fixed-node approximation' describes the thermodynamic properties of the strongly coupling fermions rather well at `weak and moderate' degeneracy. To analyse the reasons for the increasing difference between the `fixed-node approximation' and the results of direct path integral Monte Carlo simulations for highly degenerate fermions, the correctness of the `fixed-node approximation' for ideal Fermi systems has been analysed by analytical methods. A rigorous proof has been given of the fact that the exact Fermi function with index 3 / 2 describing the logarithm of the grand partition function of ideal fermions cannot be reproduced in the `fixed-node approximation', which means that the `fixed-node approximation' does not give the correct ideal Fermi gas limit.
I will review recent work by us on the properties of Bose-Fermi mixtures with a tunable pairing interaction between bosons and fermions. A many-body diagrammatic approach, able to describe the condensed phase of a Bose-Fermi mixture from weak to strong boson-fermion couplings, will be presented [1]. This approach will be validated by comparing it with previous [2] and new dedicated fixed-node diffusion Monte Carlo calculations. By using both methods, a universal behavior of the condensate fraction and bosonic momentum distribution with respect to the boson concentration is found in an extended range of boson-fermion couplings and concentrations. For vanishing boson density, the bosonic condensate fraction reduces to the quasiparticle weight Z of the Fermi polaron studied in the context of polarized Fermi gases, unifying in this way two apparently unrelated quantities. Finally, I will discuss an interesting effect occurring in the molecular limit of the boson- fermion coupling, where the condensation is completely suppressed [3]. This phenomenon is an indirect effect on bosons of the Pauli exclusion principle acting on fermions, and is the counterpart in BoseFermi mixtures of the so called “Sarma phase” discussed for polarized Fermi gases. [1] A. Guidini, G. Bertaina, D. Galli, and P. Pieri, arXiv:1412.2542. [2] G. Bertaina, E. Fratini, S. Giorgini, and P. Pieri, Phys. Rev. Lett. 110, 115303 (2013). [3] A. Guidini, G. Bertaina, E. Fratini, and P. Pieri, Phys. Rev. A 89, 023634 (2014).