Strongly Correlated Bosons on a Dynamical Lattice

Area of Science:

• Condensed Matter Physics
• Quantum Simulation
• Many-Body Physics

Background:

• Strongly correlated bosons on lattices are crucial for understanding quantum phenomena.
• Existing models often lack mechanisms for spontaneous symmetry breaking and topological phase transitions.
• Dynamical lattices offer new avenues for exploring exotic quantum states.

Purpose of the Study:

• To introduce and investigate a minimal model of one-dimensional strongly correlated bosons on a dynamical lattice.
• To explore phenomena analogous to fermion-phonon interactions and the Peierls transition in a bosonic system.
• To identify a dynamical mechanism for achieving topological insulating states in interacting bosonic systems.

Main Methods:

• Extension of the standard Bose-Hubbard Hamiltonian to include bond degrees of freedom.
• Numerical characterization of the model's phase diagram.
• Investigation of topological properties and soliton excitations.

Main Results:

• Discovery of a bosonic analog to the Peierls transition, breaking lattice translational symmetry.
• Identification of different types of bond order waves.
• Demonstration of topological solitons within the model.
• Characterization of a dynamical mechanism for topological insulation in interacting bosons.

Conclusions:

• The proposed minimal model successfully captures complex phenomena, including a bosonic Peierls transition and topological insulating phases.
• This work provides a novel, interaction-driven route to topological states in bosonic systems.
• The model is potentially implementable in current atomic experimental systems, paving the way for quantum simulations.