Recursive Method for the Density of States in One Dimension

TL;DR

This paper introduces a recursive analytical method to compute the local density of states in one-dimensional fermionic systems, accounting for interactions and boundaries, with implications for experimental detection of spin-charge separation.

Contribution

It presents a new recursive approach for calculating the local density of states in 1D systems, including effects of interactions and boundaries, extending previous methods.

Findings

Derived a recursive method for local DOS in 1D fermionic systems.

Identified signatures of spin-charge separation in STM experiments.

Obtained closed-form expressions using hypergeometric functions for semi-infinite systems.

Abstract

We derive a powerful yet simple method for analyzing the local density of states in gapless one dimensional fermionic systems, including extensions such as momentum dependent interaction parameters and hard-wall boundaries. We study the crossover of the local DOS from individual density waves to the well-known asymptotic powerlaws and identify characteristic signs of spin charge separation in possible STM experiments. For semi-infinite systems a closed analytic expression is found in terms of hypergeometric functions.