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

Many-Body Composite Bosons from the Viewpoint of Functional Renormalization

Yuya Tanizaki

Published Jan 1, 2014• 0 citations
OpenAlex

Abstract

Fermionic functional renormalization group is applied to describe Bose-Einstein condensation of composite dimers in a two-component fermionic system with a short-range interaction. Since fermions are bounded in dimers, they do not affect long-range nature of the system. This requires us to invent a renormalization group procedure, which controls the dispersion relation of composite bosons without affecting that of fermionic excitations. In order to realize it without introducing auxiliary bosonic fields, we introduce a vertex infrared regulator so as to compute the critical temperature.

Related papers

Fermionic functional renormalization group approach to Bose-Einstein condensation of dimers

Yuya Tanizaki

The fermionic functional renormalization group (f-FRG) is applied to describe Bose–Einstein condensation (BEC) of dimers for a two-component fermionic system with attractive contact interaction. In order to describe the system of dimers without introducing auxiliary bosonic fields (bosonization), we propose a new exact evolution equation of the effective action in f-FRG with an infrared regulator for the fermion vertex. Then we analyze its basic properties in detail. We show explicitly that the critical temperature of the free Bose gas is obtained naturally by this method without bosonization. Methods to make systematic improvement from the deep BEC limit are briefly discussed.

arXiv:1311.4157•Progress of Theoretical and Experimental Physics•Feb 10, 2014•3 citations

Fermionic functional renormalization group with multiple regulators and the BCS-BEC crossover

Yuya Tanizaki

New formulation of fermionic functional renormalization group (f-FRG) with multiple regulators is proposed. It is applied to a two-component fermionic system with an attractive contact interaction in order to study the whole region of the Bardeen-Cooper-Schrieffer to Bose-Einstein condensation crossover. Combining a conventional formalism of FRG with a two-point infrared (IR) regulator and a new formalism with an IR regulator inside the four-fermion vertex, we control both one-particle fermion excitations and collective bosonic excitations. This justifies a simple approximation on the f-FRG method, so that the connection of the f-FRG formalism to the Nozi\`eres-Schmitt-Rink (NSR) theory is made clear. Aspects of f-FRG to go beyond the NSR theory are also discussed.

•Feb 3, 2014•0 citations

Multi-regulator functional renormalization group for many-fermion systems

Yuya Tanizaki, Tetsuo Hatsuda

We propose a method of multi-regulator functional renormalization group (MR-FRG) which is a novel formulation of functional renormalization group with multiple infrared (IR) regulators. It is applied to a two-component fermionic system with an attractive contact interaction to study crossover phenomena between the Bardeen–Cooper–Schrieffer (BCS) phase and the Bose–Einstein condensation (BEC) phase. To control both the fermionic one-particle excitations and the bosonic collective excitations, IR regulators are introduced, one for the fermionic two-point function and another for the four-fermion vertex. It is shown that the Nozières–Schmitt-Rink (NSR) theory, which is successful to capture qualitative features of the BCS–BEC crossover, can be derived from MR–FRG. Some aspects of MR-FRG to go beyond the NSR theory are also discussed.

arXiv:1402.0283•International Journal of Modern Physics E•Jan 1, 2017•0 citations

Superfluid Equation of State of Dilute Composite Bosons

X. Leyronas, R. Combescot

We present an exact theory of the BEC-BCS crossover in the Bose-Einstein-condensate (BEC) regime, which treats explicitly dimers as made of two fermions. We apply our framework, at zero temperature, to the calculation of the equation of state. We find that, when expanding the chemical potential in powers of the density n up to the Lee-Huang-Yang order, proportional to n(3/2), the result is identical to the one of elementary bosons in terms of the dimer-dimer scattering length a(M), the composite nature of the dimers appearing only in the next order term proportional to n(2).

arXiv:0706.3774•Physical Review Letters•Oct 23, 2007•31 citations

Functional renormalization for Bose-Einstein condensation

Stefan Floerchinger, CHRISTOF WETTERICH

We investigate Bose-Einstein condensation for interacting bosons at zero and nonzero temperature. Functional renormalization provides us with a consistent method to compute the effect of fluctuations beyond the Bogoliubov approximation. For three-dimensional dilute gases, we find an upper bound on the scattering length $a$ which is of the order of the microphysical scale---typically the range of the van der Waals interaction. In contrast to fermions near the unitary bound, no strong interactions occur for bosons with approximately pointlike interactions, thus explaining the high quantitative reliability of perturbation theory for most quantities. For zero temperature we compute the quantum phase diagram for bosonic quasiparticles with a general dispersion relation, corresponding to an inverse microphysical propagator with terms linear and quadratic in the frequency. We compute the temperature dependence of the condensate and particle density $n$, and find for the critical temperature ${T}_{c}$ a deviation from the free theory, $\ensuremath{\Delta}{T}_{c}/{T}_{c}=2.1a{n}^{1/3}$. For the sound velocity at zero temperature we find very good agreement with the Bogoliubov result, such that it may be used to determine the particle density accurately.

arXiv:0801.2910•Physical Review A•May 8, 2008•53 citations

Functional-renormalization-group approach to strongly coupled Bose-Fermi mixtures in two dimensions

Jonas von Milczewski, Félix Rose, Richard Schmidt

We study theoretically the phase diagram of strongly coupled two-dimensional Bose-Fermi mixtures interacting with attractive short-range potentials as a function of the particle densities. We focus on the limit where the size of the bound state between a boson and a fermion is small compared to the average interboson separation and develop a functional-renormalization-group approach that accounts for the bound-state physics arising from the extended Fr\"ohlich Hamiltonian. By including three-body correlations we are able to reproduce the polaron-to-molecule transition in two-dimensional Fermi gases in the extreme limit of vanishing boson density. We predict frequency- and momentum-resolved spectral functions and study the impact of three-body correlations on quasiparticle properties. At finite boson density, we find that when the bound-state energy exceeds the Fermi energy by a critical value, the fermions and bosons can form a fermionic composite with a well-defined Fermi surface. These composites constitute a Fermi sea of dressed Feshbach molecules in the case of ultracold atoms, while in the case of atomically thin semiconductors a trion liquid emerges. As the boson density is increased further, the effective energy gap of the composites decreases, leading to a transition into a strongly correlated phase where polarons are hybridized with molecular degrees of freedom. We highlight the universal connection between two-dimensional semiconductors and ultracold atoms, and we discuss perspectives for further exploring the rich structure of strongly coupled Bose-Fermi mixtures in these complementary systems.

arXiv:2104.14017•Physical Review A•Jan 24, 2022•23 citations
Fermionic functional renormalization group is applied to describe Bose-Einstein condensation of composite dimers in a two-component fermionic system with a short-range interaction. Since fermions are bounded in dimers, they do not affect long-range nature of the system. This requires us to invent a renormalization group procedure, which controls the dispersion relation of composite bosons without affecting that of fermionic excitations. In order to realize it without introducing auxiliary bosonic fields, we introduce a vertex infrared regulator so as to compute the critical temperature.
The fermionic functional renormalization group (f-FRG) is applied to describe Bose–Einstein condensation (BEC) of dimers for a two-component fermionic system with attractive contact interaction. In order to describe the system of dimers without introducing auxiliary bosonic fields (bosonization), we propose a new exact evolution equation of the effective action in f-FRG with an infrared regulator for the fermion vertex. Then we analyze its basic properties in detail. We show explicitly that the critical temperature of the free Bose gas is obtained naturally by this method without bosonization. Methods to make systematic improvement from the deep BEC limit are briefly discussed.
New formulation of fermionic functional renormalization group (f-FRG) with multiple regulators is proposed. It is applied to a two-component fermionic system with an attractive contact interaction in order to study the whole region of the Bardeen-Cooper-Schrieffer to Bose-Einstein condensation crossover. Combining a conventional formalism of FRG with a two-point infrared (IR) regulator and a new formalism with an IR regulator inside the four-fermion vertex, we control both one-particle fermion excitations and collective bosonic excitations. This justifies a simple approximation on the f-FRG method, so that the connection of the f-FRG formalism to the Nozi\`eres-Schmitt-Rink (NSR) theory is made clear. Aspects of f-FRG to go beyond the NSR theory are also discussed.
We propose a method of multi-regulator functional renormalization group (MR-FRG) which is a novel formulation of functional renormalization group with multiple infrared (IR) regulators. It is applied to a two-component fermionic system with an attractive contact interaction to study crossover phenomena between the Bardeen–Cooper–Schrieffer (BCS) phase and the Bose–Einstein condensation (BEC) phase. To control both the fermionic one-particle excitations and the bosonic collective excitations, IR regulators are introduced, one for the fermionic two-point function and another for the four-fermion vertex. It is shown that the Nozières–Schmitt-Rink (NSR) theory, which is successful to capture qualitative features of the BCS–BEC crossover, can be derived from MR–FRG. Some aspects of MR-FRG to go beyond the NSR theory are also discussed.
We present an exact theory of the BEC-BCS crossover in the Bose-Einstein-condensate (BEC) regime, which treats explicitly dimers as made of two fermions. We apply our framework, at zero temperature, to the calculation of the equation of state. We find that, when expanding the chemical potential in powers of the density n up to the Lee-Huang-Yang order, proportional to n(3/2), the result is identical to the one of elementary bosons in terms of the dimer-dimer scattering length a(M), the composite nature of the dimers appearing only in the next order term proportional to n(2).
We investigate Bose-Einstein condensation for interacting bosons at zero and nonzero temperature. Functional renormalization provides us with a consistent method to compute the effect of fluctuations beyond the Bogoliubov approximation. For three-dimensional dilute gases, we find an upper bound on the scattering length aaa which is of the order of the microphysical scale---typically the range of the van der Waals interaction. In contrast to fermions near the unitary bound, no strong interactions occur for bosons with approximately pointlike interactions, thus explaining the high quantitative reliability of perturbation theory for most quantities. For zero temperature we compute the quantum phase diagram for bosonic quasiparticles with a general dispersion relation, corresponding to an inverse microphysical propagator with terms linear and quadratic in the frequency. We compute the temperature dependence of the condensate and particle density nnn, and find for the critical temperature Tc{T}_{c}Tc​ a deviation from the free theory, $\ensuremath{\Delta}{T}_{c}/{T}_{c}=2.1a{n}^{1/3}$. For the sound velocity at zero temperature we find very good agreement with the Bogoliubov result, such that it may be used to determine the particle density accurately.
We study theoretically the phase diagram of strongly coupled two-dimensional Bose-Fermi mixtures interacting with attractive short-range potentials as a function of the particle densities. We focus on the limit where the size of the bound state between a boson and a fermion is small compared to the average interboson separation and develop a functional-renormalization-group approach that accounts for the bound-state physics arising from the extended Fr\"ohlich Hamiltonian. By including three-body correlations we are able to reproduce the polaron-to-molecule transition in two-dimensional Fermi gases in the extreme limit of vanishing boson density. We predict frequency- and momentum-resolved spectral functions and study the impact of three-body correlations on quasiparticle properties. At finite boson density, we find that when the bound-state energy exceeds the Fermi energy by a critical value, the fermions and bosons can form a fermionic composite with a well-defined Fermi surface. These composites constitute a Fermi sea of dressed Feshbach molecules in the case of ultracold atoms, while in the case of atomically thin semiconductors a trion liquid emerges. As the boson density is increased further, the effective energy gap of the composites decreases, leading to a transition into a strongly correlated phase where polarons are hybridized with molecular degrees of freedom. We highlight the universal connection between two-dimensional semiconductors and ultracold atoms, and we discuss perspectives for further exploring the rich structure of strongly coupled Bose-Fermi mixtures in these complementary systems.