Symmetry Protected Dynamical Symmetry in the Generalized Hubbard Models

Area of Science:

• Condensed matter physics
• Quantum mechanics
• Atomic physics

Background:

• Generalized Hubbard models are crucial for understanding interacting quantum systems.
• Symmetries in physical systems often lead to conserved quantities and simplified dynamics.
• Recent cold atom experiments explore complex dynamics in optical lattices.

Purpose of the Study:

• To present a theorem on the dynamics of generalized Hubbard models.
• To demonstrate how single-particle Hamiltonian symmetry can protect interaction-driven dynamical symmetries.
• To provide a unified framework for understanding diverse phenomena in cold atom experiments.

Main Methods:

• Formulation of a mathematical theorem concerning generalized Hubbard model dynamics.
• Demonstration of the theorem using three distinct symmetry examples: bipartite lattice, reflection, and translation symmetry.
• Connecting the theoretical framework to specific experimental observations in cold atom systems.

Main Results:

• The theorem establishes that single-particle Hamiltonian symmetry protects a form of dynamical symmetry.
• Dynamical symmetry implies symmetric time evolution of observables between repulsive and attractive Hubbard models.
• The theorem successfully explains phenomena in cold atom experiments, including expansion dynamics, chiral motion, and charge-density-wave melting.

Conclusions:

• The presented theorem offers a unified perspective on interaction-driven dynamical symmetries in quantum many-body systems.
• This work bridges theoretical insights from condensed matter physics with experimental findings in cold atom research.
• The findings have implications for designing and interpreting experiments involving quantum simulations with ultracold atoms.