Quantitative measure for the spin-charge separation in two dimensional Hubbard model

TL;DR

This paper introduces a new quantitative measure, $ta(t)$, for spin-charge separation in strongly correlated systems, applicable to non-equilibrium dynamics in the 2D Hubbard model, and explores its potential as an order parameter for Mott insulators.

Contribution

The paper proposes a novel measure for spin-charge separation based on fluctuations, applicable to various geometries, and links its long-term behavior to the Mott insulating phase.

Findings

The measure $ta(t)$ is consistent across chain, ladder, and 2D geometries.

A threshold time in $ta(t)$ indicates the breakdown of the Mott insulator.

The measure effectively captures non-equilibrium spin-charge dynamics.

Abstract

We introduce a qauantitative measure of spin-charge separation, $\zeta (t)$ which is based on the difference between the fluctuations with respect to background of the spin and charge profiles at any time t and is suitable for studying the non-equilibrium dynamics of excitations in strongly correlated systems. This quantity is not only a direct measure of the spin-charge separation in strongly correlated systems, but its long time behaviour can further serve as a possible order parameter for the interaction induced (Mott) insulating state. Within the nu- merically exact diagonzalization we calculate this quantity for the two dimensional Hubbard model away from Half filling. Our quantitative measure in chain, ladder and two-dimensional geometries gives the same order of magnitude for the quantity of spin-charge separation. Furthermore from the temporal behaviour of $\zeta (t)$ a threshold time can be identified that provides clues onto the breakdown of underlying Mott insulating phase.