Abstract
The momentum, fermionic density, spin density, and interaction dependencies of the exponents that control the (k,ω)-plane singular features of the one-fermion spectral functions of a one-dimensional gas of spin-1/2 fermions with repulsive delta-function interaction both at zero and finite magnetic field are studied in detail. Our results refer to energy scales beyond the reach of the low-energy Tomonaga-Luttinger liquid and rely on the pseudofermion dynamical theory for integrable models. The one-fermion spectral weight distributions associated with the spectral functions studied in this paper may be observed in systems of spin-1/2 ultra-cold fermionic atoms in optical lattices.
Highlights
The one-dimensional (1D) continuous fermionic gas with repulsive delta-function interaction, which in this paper we call 1D repulsive fermion model, was one of the first quantum problems solved by the Bethe ansatz (BA) [1]
At zero magnetic field, h = 0, and zero spin density, m = 0, our study focuses on the one-fermion spectral function, Bγ (k, ω) =
In this paper we have studied the high-energy one-fermion spectral properties of the 1D repulsive fermion model, Eq (1), and the momentum and energy dependence of the exponents and energy spectra that control the line shape of the one-fermion spectral function, Eq (2), at zero magnetic field and of the up-spin and down-spin one-fermion spectral functions, Eq (4), at finite magnetic field near those functions singularities
Summary
The one-dimensional (1D) continuous fermionic gas with repulsive delta-function interaction, which in this paper we call 1D repulsive fermion model, was one of the first quantum problems solved by the Bethe ansatz (BA) [1]. Our main goal is deriving the (k, ω)-plane line shape near the singularities of the spectral functions in Eq (2) at zero spin density, m = 0, and in Eq (4) for m > 0 This includes the detailed study of the dependence of the exponents that control that line shape on the excitation momentum, repulsive interaction C, fermionic density n ∈ [0, ∞[, and spin-density m ∈ [0, n]. [40] for the related lattice 1D Hubbard model, which applies to other integrable systems as well [41,42,43], including the present 1D repulsive fermion model For the latter we use in our study an exact representation suitable to the PDT in terms of pseudofermions of that model BA solution in the subspace spanned by the ground state and one-fermion excited energy eigenstates.
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