The dimensionless universal coefficient ξ defines the ratio of the unitary fermions energy density to that for the ideal non-interacting ones in the non-relativistic limit with T = 0. The classical Thomson problem is taken as a nonperturbative quantum many-body arm to address the ground state energy including the low energy nonlinear quantum fluctuation/correlation effects. With the relativistic Dirac continuum field theory formalism, the concise expression for the energy density functional of the strongly interacting limit fermions at both finite temperature and density is obtained. Analytically, the universal factor is calculated to be ξ = 4/9. The energy gap is Δ = (5/18) k f 2 /(2 m ).The dimensionless universal coefficient ξ defines the ratio of the unitary fermions energy density to that for the ideal non-interacting ones in the non-relativistic limit with T = 0. The classical Thomson problem is taken as a nonperturbative quantum many-body arm to address the ground state energy including the low energy nonlinear quantum fluctuation/correlation effects. With the relativistic Dirac continuum field theory formalism, the concise expression for the energy density functional of the strongly interacting limit fermions at both finite temperature and density is obtained. Analytically, the universal factor is calculated to be ξ = 4/9. The energy gap is Δ = (5/18) k f 2 /(2 m ).

arXiv:nucl-th/0602065Chinese Physics LettersJun 28, 200723 citations

Density Functional Theory of the Lattice Fermion Model

Román López-Sandoval, G. M. Pastor

Springer eBooksJan 1, 20010 citations

Equilibrium Partition Function of Non-Relativistic CFTs in Harmonic Trap

Eunwoo Lee

We investigate the equilibrium partition function of non-relativistic conformal field theories in harmonic quantization. We first analyze the hydrodynamic regime and show that, at leading order, the partition function exhibits a universal structure determined by the equation of state: the logarithm of the partition function develops simple poles in $ω^2-Ω_a^2$ , where $ω$ is the harmonic trapping frequency and $Ω_a$ are angular velocities acting as chemical potentials for angular momentum. The corresponding residue is determined by a single-variable function of $μ/T$ , with $μ$ the particle-number chemical potential and $T$ the temperature. We then study the large-angular-momentum limit $Ω_a\toω$ . In this regime centrifugal effects nearly cancel the trapping potential, and the logarithm of the partition function again exhibits simple poles in $ω^2-Ω_a^2$ , but with a less universal residue depending separately on $μ/T$ and $ω/T$ . As explicit examples we analyze superfluid systems realizable in cold-atom experiments, in particular fermions at unitarity confined in a harmonic trap.We investigate the equilibrium partition function of non-relativistic conformal field theories in harmonic quantization. We first analyze the hydrodynamic regime and show that, at leading order, the partition function exhibits a universal structure determined by the equation of state: the logarithm of the partition function develops simple poles in $ω^2-Ω_a^2$, where $ω$ is the harmonic trapping frequency and $Ω_a$ are angular velocities acting as chemical potentials for angular momentum. The corresponding residue is determined by a single-variable function of $μ/T$, with $μ$ the particle-number chemical potential and $T$ the temperature. We then study the large-angular-momentum limit $Ω_a\toω$. In this regime centrifugal effects nearly cancel the trapping potential, and the logarithm of the partition function again exhibits simple poles in $ω^2-Ω_a^2$, but with a less universal residue depending separately on $μ/T$ and $ω/T$. As explicit examples we analyze superfluid systems realizable in cold-atom experiments, in particular fermions at unitarity confined in a harmonic trap.

arXiv:2603.09856Mar 10, 20260 citations

Density-functional theory for resonantly interacting fermions with effective range and neutron matter

Denis Lacroix A

A density-functional theory is proposed for strongly interacting fermions with arbitrary large negative scattering length. The functional has only two parameters that are directly fixed to reproduce the universal properties of unitary gas: the so-called Bertsch parameter ${\ensuremath{\xi}}_{0}$ and a parameter ${\ensuremath{\eta}}_{e}$ related to the possible influence of the effective range ${r}_{e}$ at infinite scattering length $a$ . Using most recent quantum Monte Carlo (QMC) estimates of these two parameters, it is shown that the functional properly reproduces the experimental measurements of interacting Fermi systems not only at unitarity but also away from this limit over a wide range of ${(a{k}_{F})}^{\ensuremath{-}1}$ values. The functional is applied to obtain an expression of Tan's contact parameter including the effect of ${r}_{e}$ . Application is finally made to neutron matter. It is shown that most recent QMC results are well reproduced.A density-functional theory is proposed for strongly interacting fermions with arbitrary large negative scattering length. The functional has only two parameters that are directly fixed to reproduce the universal properties of unitary gas: the so-called Bertsch parameter ${\ensuremath{\xi}}_{0}$ and a parameter ${\ensuremath{\eta}}_{e}$ related to the possible influence of the effective range ${r}_{e}$ at infinite scattering length $a$. Using most recent quantum Monte Carlo (QMC) estimates of these two parameters, it is shown that the functional properly reproduces the experimental measurements of interacting Fermi systems not only at unitarity but also away from this limit over a wide range of ${(a{k}_{F})}^{\ensuremath{-}1}$ values. The functional is applied to obtain an expression of Tan's contact parameter including the effect of ${r}_{e}$. Application is finally made to neutron matter. It is shown that most recent QMC results are well reproduced.

arXiv:1608.08411Physical Review AOct 7, 201626 citations

Density functional theory for fermionic atom gases

Matthias Troyer, Ping Nang Ma, Sebastiano Pilati +1 more

Bulletin of the American Physical SocietyMar 22, 20110 citations

ω^2-Ω_a^2

, where

ω

is the harmonic trapping frequency and

Ω_a

are angular velocities acting as chemical potentials for angular momentum. The corresponding residue is determined by a single-variable function of

μ/T

, with

μ

the particle-number chemical potential and

T

the temperature. We then study the large-angular-momentum limit

Ω_a\toω

. In this regime centrifugal effects nearly cancel the trapping potential, and the logarithm of the partition function again exhibits simple poles in

ω^2-Ω_a^2

, but with a less universal residue depending separately on

μ/T

and

ω/T

. As explicit examples we analyze superfluid systems realizable in cold-atom experiments, in particular fermions at unitarity confined in a harmonic trap.

{r}_{e}

at infinite scattering length

a

. Using most recent quantum Monte Carlo (QMC) estimates of these two parameters, it is shown that the functional properly reproduces the experimental measurements of interacting Fermi systems not only at unitarity but also away from this limit over a wide range of ${(a{k}_{F})}^{\ensuremath{-}1}$ values. The functional is applied to obtain an expression of Tan's contact parameter including the effect of

{r}_{e}

. Application is finally made to neutron matter. It is shown that most recent QMC results are well reproduced.