# The analytical description of a doped Mott insulator

## TL;DR

This paper analytically investigates a doped Mott insulator using Green's function methods, revealing intrinsic spin-charge separation and explaining spectral properties consistent with cuprate superconductor observations.

## Contribution

It provides an analytical solution for a doped Mott insulator, highlighting the intrinsic spin-charge separation and spectral features arising from strong Coulomb interactions.

## Key findings

- Spectral weight proportional to hole doping concentration.
- Electron excitation spectrum comprises spin and charge fluctuation contributions.
- Results align with experimental spectroscopy of cuprate superconductors.

## Abstract

With the hierarchical Green's function approach, we study a doped Mott insulator described with the Hubbard model by analytically solving the equations of motion of an one-particle Green's function and related multiple-point correlation functions, and find that the separation of the spin and charge degrees of freedom of the electrons is an intrinsic character of the doped Mott insulator. For enough of large on-site repulsive Coulomb interaction, we show that the spectral weight of the one-particle Green's function is proportional to the hole doping concentration that is mainly produced by the charge fluctuation of electrons, while the excitation spectrum of the electrons is composed of two parts: one is contributed by the spin fluctuation of the electrons which is proportional to the hole doping concentration, and another one is coming from the coupling between the charge and spin fluctuations of the electrons that takes the maximum at undoping. All of these low energy/temperature physical properties originate from the strong on-site Coulomb interaction. The present results are consistent with the spectroscopy observations of the cuprate superconductors, and the numerical calculations in normal state above pseudogap regime.