scholarly journals A model study on superfluidity of a unitary Fermi gas of atoms interacting with a finite-ranged potential

2021 ◽  
Author(s):  
Subhanka Mal ◽  
Bimalendu Deb
Keyword(s):  
Quantum Monte Carlo ◽  
Chemical Potential ◽  
Scattering Length ◽  
Mean Field Theory ◽  
Mean Field ◽  
Fermi Gas ◽  
Range Limit ◽  
Contact Potential ◽  
Zero Range ◽  
Unitary Fermi Gas

Abstract We calculate Bardeen-Cooper-Schrieffer (BCS) state of a unitary Fermi gas of atoms interacting with the finite-ranged Jost-Kohn potential which has been recently shown to account for the resonant interactions [2019 {\rm J. Phys. B: At. Mol. Opt. Phys.} {\bf 52}, 165004]. Using exact scattering solution of the potential, we derive two-body ${\mathbf T}$-matrix element which is employed to construct the BCS Hamiltonian in momentum space. We present results on the energy- and range-dependence of the pairing gap and superfluid density and the range-dependence of the chemical potential for a wide variation of the scattering length including the \textcolor{red}{unitary} regime. In the zero range limit our calculated gap at the Fermi energy is found to be nearly equal to that calculated \textcolor{red}{in mean-field theory with contact potential}. The mean gap averaged over the full width at half maximum of the gap function in the zero range and unitary limits is found to be $0.42 E_F$ which is quite close to the recent result of the quantum Monte Carlo simulation [2018 {\rm Phys. Rev.A} {\bf 97}, 013601]. The chemical potential in the zero range limit also agrees well with that for the contact potential.

scholarly journals Ferromagnetism in the upper branch of the Feshbach resonance and the hard-sphere Fermi gas

2010 ◽  
Vol 108 (1) ◽  
pp. 51-54 ◽  
Author(s):  
Soon-Yong Chang ◽  
Mohit Randeria ◽  
Nandini Trivedi
Keyword(s):  
Quantum Monte Carlo ◽  
Hard Sphere ◽  
Feshbach Resonance ◽  
Scattering Length ◽  
Mean Field ◽  
Fermi Gas ◽  
Fundamental Interest ◽  
Pair Correlations ◽  
Total Energies ◽  
Quantum Monte Carlo Simulations

We address the question of ferromagnetism in repulsive Fermi gas, a problem of fundamental interest, using quantum Monte Carlo simulations that include backflow corrections. We investigate a two-component Fermi gas on the upper branch of a Feshbach resonance and contrast it with the hard-sphere gas. We find that, in both cases, the Fermi liquid becomes unstable to ferromagnetism at a kFa smaller than the mean field result, where kF is the Fermi wavevector and a is the scattering length. Even though the total energies E(kFa) are similar in the two cases, their pair correlations and kinetic energies are completely different, reflecting the underlying potentials. We discuss the extent to which our calculations shed light on recent experiments.

scholarly journals REALISTIC MODELING OF STRONGLY CORRELATED ELECTRON SYSTEMS: AN INTRODUCTION TO THE LDA+DMFT APPROACH

2001 ◽  
Vol 15 (19n20) ◽  
pp. 2611-2625 ◽  
Author(s):  
K. HELD ◽  
I. A. NEKRASOV ◽  
N. BLÜMER ◽  
V. I. ANISIMOV ◽  
D. VOLLHARDT
Keyword(s):  
Quantum Monte Carlo ◽  
Local Density ◽  
Mean Field Theory ◽  
Mean Field ◽  
Structure Theory ◽  
Strongly Correlated Electron ◽  
Correlated Electron Systems ◽  
Correlated Electron ◽  
Basic Ideas ◽  
Set Up

The LDA+DMFT approach merges conventional band structure theory in the local density approximation (LDA) with a state-of-the-art many-body technique, the dynamical mean-field theory (DMFT). This new computational scheme has recently become a powerful tool for ab initio investigations of real materials with strong electronic correlations. In this paper an introduction to the basic ideas and the set-up of the LDA+DMFT approach is given. Results for the photoemission spectra of the transition metal oxide La 1-x Sr x TiO 3, obtained by solving the DMFT equations by quantum Monte Carlo (QMC) simulations, are presented and are found to be in very good agreement with experiment. The numerically exact DMFT(QMC) solution is compared with results obtained by two approximative solutions, i.e. the iterative perturbation theory and the non-crossing approximation.

scholarly journals Effect of weak disorder on the BCS–BEC crossover in a two-dimensional Fermi gas

2017 ◽  
Vol 31 (09) ◽  
pp. 1750066
Author(s):  
Ayan Khan ◽  
B. Tanatar
Keyword(s):  
Field Theory ◽  
Mean Field Theory ◽  
Mean Field ◽  
Fermi Gas ◽  
Ultracold Fermi Gas ◽  
Condensate Fraction ◽  
Two Dimensional ◽  
Weak Disorder ◽  
Unique Nature

In this paper, we study the two-dimensional (2D) ultracold Fermi gas with weak impurity in the framework of mean-field theory where the impurity is introduced through Gaussian fluctuations. We have investigated the role of the impurity by studying the experimentally accessible quantities such as condensate fraction and equation of state of the ultracold systems. Our analysis reveals that at the crossover, the disorder enhances superfluidity, which we attribute to the unique nature of the unitary region and to the dimensional effect.

MOTT TRANSITION IN THE HALF-FILLED HUBBARD MODEL ON THE HONEYCOMB LATTICE WITHIN COHERENT POTENTIAL APPROXIMATION

2013 ◽  
Vol 27 (07) ◽  
pp. 1350046 ◽  
Author(s):  
DUC ANH LE
Keyword(s):  
Hubbard Model ◽  
Quantum Monte Carlo ◽  
Mean Field Theory ◽  
Mean Field ◽  
Coulomb Repulsion ◽  
Mott Transition ◽  
Coherent Potential Approximation ◽  
Honeycomb Lattice ◽  
Potential Approximation ◽  
Good Agreement

Using the coherent potential approximation, we study zero-temperature Mott transition in the half-filled Hubbard model on the honeycomb lattice. Although a pseudogap is already present for the non-interacting case, the gap will not occur until the onsite Coulomb repulsion exceeds a critical value U ≈ 3.6t, where t is the hopping integral. When increasing U/t, the density of states at the Fermi energy first goes up gradually from zero and after reaching a maximum it goes down to zero again. Our calculated critical interaction UC/t is in very good agreement with the ones obtained by quantum Monte Carlo simulation and cluster dynamical mean-field theory.

scholarly journals Low-Density Neutron Matter and the Unitary Limit

2021 ◽  
Vol 9 ◽  
Author(s):  
Isaac Vidaña
Keyword(s):  
Quantum Monte Carlo ◽  
Cold Atoms ◽  
Scattering Length ◽  
Fermi Gas ◽  
Neutron Matter ◽  
Bcs Theory ◽  
Unitary Limit ◽  
Strong Coupling Regime ◽  
Low Density ◽  
Contact Parameter

We review the properties of neutron matter in the low-density regime. In particular, we revise its ground state energy and the superfluid neutron pairing gap and analyze their evolution from the weak to the strong coupling regime. The calculations of the energy and the pairing gap are performed, respectively, within the Brueckner–Hartree–Fock (BHF) approach of nuclear matter and the Bardeen–Cooper–Schrieffer (BCS) theory using the chiral nucleon-nucleon interaction of Entem and Machleidt at N3LO and the Argonne V18 phenomenological potential. Results for the energy are also shown for a simple Gaussian potential with a strength and range adjusted to reproduce the 1S0 neutron-neutron scattering length and effective range. Our results are compared with those of quantum Monte Carlo (QMC) calculations for neutron matter and cold atoms. The Tan contact parameter in neutron matter is also calculated, finding a reasonable agreement with experimental data from ultra-cold atoms only at very low densities. We find that low-density neutron matter exhibits a behavior close to that of a Fermi gas at the unitary limit, although, this limit is actually never reached. We also review the properties (energy, effective mass, and quasiparticle residue) of a spin-down neutron impurity immersed in a low-density free Fermi gas of spin-up neutrons already studied by the author in a recent work where it was shown that these properties are very close to those of an attractive Fermi polaron in the unitary limit.

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