Dynamics of the Hubbard model: a general approach by time dependent variational principle

TL;DR

This paper develops a semi-classical approach using the time-dependent variational principle to analyze the quantum dynamics of the Hubbard model, revealing complex phase behaviors and new model Hamiltonians.

Contribution

It introduces a novel semi-classical framework with time-dependent phases for the Hubbard model, including derivation of new Hamiltonians and analysis of phase dynamics.

Findings

Vortex-like ground state phase dynamics for U>0 away from half filling

Oscillatory ground state dynamics at the Fermi surface for any U at half-filling

Exact solution of low-energy dynamics by separating fast and slow variables

Abstract

We describe the quantum dynamics of the Hubbard model at semi-classical level, by implementing the Time-Dependent Variational Principle (TDVP) procedure on appropriate macroscopic wavefunctions constructed in terms of su(2)-coherent states. Within the TDVP procedure, such states turn out to include a time-dependent quantum phase, part of which can be recognized as Berry's phase. We derive two new semi-classical model Hamiltonians for describing the dynamics in the paramagnetic, superconducting, antiferromagnetic and charge density wave phases and solve the corresponding canonical equations of motion in various cases. Noticeably, a vortex-like ground state phase dynamics is found to take place for U>0 away from half filling. Moreover, it appears that an oscillatory-like ground state dynamics survives at the Fermi surface at half-filling for any U. The low-energy dynamics is also exactly solved by separating fast and slow variables. The role of the time-dependent phase is shown to be particularly interesting in the ordered phases.