Symmetry Protected Dynamical Symmetry in the Generalized Hubbard Models

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.

arXiv comment5 pages, 3 figures

References in corpus (8)

• Many-Body Physics with Ultracold Gases
• Observation of many-body localization of interacting fermions in a quasi-random optical lattice
• Realization of the Hofstadter Hamiltonian with ultracold atoms in optical lattices
• Realizing the Harper Hamiltonian with Laser-Assisted Tunneling in Optical Lattices
• The cold atom Hubbard toolbox
• Fermionic transport in a homogeneous Hubbard model: Out-of-equilibrium dynamics with ultracold atoms
• Microscopy of the interacting Harper-Hofstadter model in the few-body limit
• Anomalous Expansion of Attractively Interacting Fermionic Atoms in an Optical Lattice

Cited by in corpus (10)

• Asymmetric Particle Transport and Light-Cone Dynamics Induced by Anyonic Statistics
• Manipulating synthetic gauge fluxes via multicolor dressing of Rydberg-atom arrays
• Multi-particle quantum walks and Fisher information in one-dimensional lattices
• Bloch oscillations of multi-magnon excitations in a Heisenberg XXZ chain
• Quantum many-body scars in spin-1 Kitaev chain with uniaxial single-ion anisotropy
• Flux induced re-entrant dynamics in the quantum walk of interacting bosons
• Dynamical symmetry in quantum dissipative models
• On the Equivalence between Spin and Charge Dynamics of the Fermi Hubbard Model
• Chirally-protected state manipulation by tuning one-dimensional statistics
• Fermionic-propagator and alternating-basis quantum Monte Carlo methods for correlated electrons on a lattice