Dispersion relation and spectral function of an impurity in a one-dimensional quantum liquid

Austen Lamacraft 2009. Physical Review B

# Abstract

We consider the motion of an impurity particle in a general one-dimensional quantum fluid at zero temperature. The dispersion relation $$\Omega(P)$$ of the impurity is strongly affected by interactions with the fluid as the momentum approaches $$\pm \pi \hbar n$$, $$\pm 3\pi \hbar n$$, …, where $$n$$ is the density. This behavior is caused by singular $$\pm 2\pi \hbar n$$ scattering processes and can be understood by analogy to the Kondo effect, both at strong and weak couplings, with the possibility of a quantum phase transition where $$\Omega(\pm \pi \hbar n)$$ jumps to zero with increasing coupling. The low energy singularities in the impurity spectral function can be understood on the same footing.