Proves that the ground state energy of dilute 1D spin-J Fermi gases with repulsive interactions asymptotes to the ground state energy of a corresponding spin chain.
The Huang-Yang formula for the low-density Fermi gas: upper bound
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abstract
We study the ground state energy of a gas of spin $1/2$ fermions with repulsive short-range interactions. We derive an upper bound that agrees, at low density $\rho$, with the Huang-Yang conjecture. The latter captures the first three terms in an asymptotic low-density expansion, and in particular the Huang-Yang correction term of order $\rho^{7/3}$. Our trial state is constructed using an adaptation of the bosonic Bogoliubov theory to the Fermi system, where the correlation structure of fermionic particles is incorporated by quasi-bosonic Bogoliubov transformations. In the latter, it is important to consider a modified zero-energy scattering equation that takes into account the presence of the Fermi sea, in the spirit of the Bethe-Goldstone equation.
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UNVERDICTED 2representative citing papers
Derives an upper bound on the ground state energy of a dilute 2D Fermi gas that captures the first three terms in the small ρa² asymptotic expansion.
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Ground State Energy of Dilute Fermi Gases in 1D
Proves that the ground state energy of dilute 1D spin-J Fermi gases with repulsive interactions asymptotes to the ground state energy of a corresponding spin chain.
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The Huang--Yang formula for a two-dimensional Fermi gas: upper bound
Derives an upper bound on the ground state energy of a dilute 2D Fermi gas that captures the first three terms in the small ρa² asymptotic expansion.