Dynamics of the Two-Site Hubbard Model

TL;DR

This paper derives the dynamical evolution of a two-site Hubbard model under a magnetic field, revealing complex behaviors in fermion number and magnetization, with applications to organic charge-transfer salts.

Contribution

It provides a detailed analysis of the time evolution of the two-site Hubbard model with external magnetic field for general initial states, highlighting non-periodic fermion number dynamics.

Findings

Fermion number can be non-periodic while magnetization remains periodic.

Complex dynamical behavior depends on initial conditions.

Results applicable to organic charge-transfer salts.

Abstract

The dynamical evolution of a two-site Hubbard model is derived in the presence of an uniform external magnetic field for a general initial state. The time evolution of the half-filled (two-particle) case has a complex behaviour. Under certain initial conditions, the average number of fermions in one-particle state, in the half-filled case, is not necessarily periodic, even though the magnetization remains periodic. The results obtained may be applied to study the magnetization and the transition dipole moment of the organic charge-transfer salts in the in-phase mode.