Spin picture of the one-dimensional Hubbard model: Two-fluid structure and phase dynamics

TL;DR

This paper introduces a novel variational approach using spin coherent states to analyze the quantum dynamics of the one-dimensional Hubbard model, revealing different regimes and phase behaviors.

Contribution

It develops a new scheme combining the time-dependent variational principle with spin coherent states to study the Hubbard model's dynamics.

Findings

Low-density regime maps to coupled nonlinear Schrödinger equations.

Near half-filling, the model resembles coupled Josephson junction arrays.

Standard one-band ground state phase space is recovered.

Abstract

We propose a scheme for investigating the quantum dynamics of interacting electron models by means of time-dependent variational principle and spin coherent states of space lattice operators. We apply such a scheme to the one-dimensional hubbard model, and solve the resulting equations in different regimes. In particular, we find that at low densities the dynamics is mapped into two coupled nonlinear Schroedinger equations, whereas near half-filling the model is described by two coupled Josephson junction arrays. Focusing then to the case in which only the phases of the spin variables are dynamically active, we examine a number of different solutions corresponding to the excitations of few macroscopic modes. Based on fixed point equation of the simpler among them, we show that the standard one-band ground state phase space is found.