Green's function for magnetically incoherent interacting electrons in one dimension

TL;DR

This paper calculates the low-energy Green's function for a strongly interacting, magnetically incoherent one-dimensional electron gas, revealing spin-charge separation features and anomalous exponents, using a path integral and bosonization approach.

Contribution

It introduces a novel calculation of the Green's function for magnetically incoherent electrons, highlighting features like exponential decay and interaction-dependent exponents.

Findings

Green's function shows spin-charge separation-like features.

Tunneling density of states follows a power-law with energy.

Results extend previous work by Cheianov and Zvonarev.

Abstract

Using a path integral approach and bosonization, we calculate the low energy asymptotics of the one particle Green's function for a ``magnetically incoherent'' one dimensional strongly interacting electron gas at temperatures much greater than the typical exchange energy but much lower than the Fermi energy. The Green's function exhibits features reminiscent of spin-charge separation, with exponential spatial decay and scaling behavior with interaction dependent anomalous exponents inconsistent with any unitary conformal field theory. We compute the tunneling density of states at low energies and find that it is a power law in energy with exponent $1/(4g)-1$, where $g$ is the Luttinger interaction parameter in the charge sector. The underlying physics is made transparent by the simplicity of the approach. Our results generalize those of Cheianov and Zvonarev [Phys. Rev. Lett. {\bf 92}, 176401 (2004)].