Symmetry Protected Dynamical Symmetry in the Generalized Hubbard Models

TL;DR

This paper proves a theorem showing how certain symmetries in the single particle Hamiltonian of generalized Hubbard models can protect a dynamical symmetry in the system's evolution, linking various experimental observations.

Contribution

It introduces a unified theorem demonstrating how Hamiltonian symmetries protect dynamical symmetries in Hubbard models, connecting multiple experimental phenomena.

Findings

Dynamical symmetry is protected by Hamiltonian symmetries.

The theorem applies to bipartite, reflection, and translation symmetries.

Experimental phenomena like atom expansion and charge-density-wave melting are explained.

Abstract

In this letter we present a theorem on the dynamics of the generalized Hubbard models. This theorem shows that the symmetry of the single particle Hamiltonian can protect a kind of dynamical symmetry driven by the interactions. Here the dynamical symmetry refers to that the time evolution of certain observables are symmetric between the repulsive and attractive Hubbard models. We demonstrate our theorem with three different examples in which the symmetry involves bipartite lattice symmetry, reflection symmetry and translation symmetry, respectively. Each of these examples relates to one recent cold atom experiment on the dynamics in the optical lattices where such a dynamical symmetry is manifested. These experiments include expansion dynamics of cold atoms, chirality of atomic motion within a synthetic magnetic field and melting of charge-density-wave order. Therefore, our theorem provides a unified view of these seemingly disparate phenomena.