Contact interactions can be used to describe a system of particles at unitarity, contribute to the leading part of nuclear interactions and are numerically non-trivial because they require a proper regularization and renormalization scheme. We explain how to tune the coefficient of a contact interaction between non-relativistic particles on a discretized space in 1, 2, and 3 spatial dimensions such that we can remove all discretization artifacts. By taking advantage of a latticized Lüscher zeta function, we can achieve a momentum-independent scattering amplitude at any finite lattice spacing.Contact interactions can be used to describe a system of particles at unitarity, contribute to the leading part of nuclear interactions and are numerically non-trivial because they require a proper regularization and renormalization scheme. We explain how to tune the coefficient of a contact interaction between non-relativistic particles on a discretized space in 1, 2, and 3 spatial dimensions such that we can remove all discretization artifacts. By taking advantage of a latticized Lüscher zeta function, we can achieve a momentum-independent scattering amplitude at any finite lattice spacing.

arXiv:1912.04425Dec 10, 20192 citations

Scattering amplitudes in non-Fermi-liquid systems

A. Koutouza, Frédéric Lesage, Hubert Saleur

By a mix of form factors and analyticity techniques, we determine some fundamental scattering amplitudes in non-Fermi-liquid systems. These include the reflection and transmission amplitudes for Laughlin quasiparticles at a point contact between two $g=\frac{1}{2}$ Luttinger liquids, and the $\stackrel{\ensuremath{\rightarrow}}{e}e,$ $\mathrm{lq}\stackrel{\ensuremath{\rightarrow}}{p}\mathrm{lqp}$ and $\stackrel{\ensuremath{\rightarrow}}{e}{e}_{\mathrm{edge}}$ at a point contact between a Fermi liquid and a $g=\frac{1}{3}$ Luttinger liquid (all liquids chiral or not). These results are obtained in closed form, and give rise to rather simple expressions for the probabilities of the most basic processes of non-Fermi-liquid physics at these special values of the couplings.By a mix of form factors and analyticity techniques, we determine some fundamental scattering amplitudes in non-Fermi-liquid systems. These include the reflection and transmission amplitudes for Laughlin quasiparticles at a point contact between two $g=\frac{1}{2}$ Luttinger liquids, and the $\stackrel{\ensuremath{\rightarrow}}{e}e,$ $\mathrm{lq}\stackrel{\ensuremath{\rightarrow}}{p}\mathrm{lqp}$ and $\stackrel{\ensuremath{\rightarrow}}{e}{e}_{\mathrm{edge}}$ at a point contact between a Fermi liquid and a $g=\frac{1}{3}$ Luttinger liquid (all liquids chiral or not). These results are obtained in closed form, and give rise to rather simple expressions for the probabilities of the most basic processes of non-Fermi-liquid physics at these special values of the couplings.

arXiv:cond-mat/0304058Physical review. B, Condensed matterSep 25, 20035 citations

g=\frac{1}{2}

Luttinger liquids, and the $\stackrel{\ensuremath{\rightarrow}}{e}e,$ $\mathrm{lq}\stackrel{\ensuremath{\rightarrow}}{p}\mathrm{lqp}$ and $\stackrel{\ensuremath{\rightarrow}}{e}{e}_{\mathrm{edge}}$ at a point contact between a Fermi liquid and a

g=\frac{1}{3}

Luttinger liquid (all liquids chiral or not). These results are obtained in closed form, and give rise to rather simple expressions for the probabilities of the most basic processes of non-Fermi-liquid physics at these special values of the couplings.