Strongly Correlated Bosons on a Dynamical Lattice

TL;DR

This paper introduces a new bosonic model on a dynamical lattice that exhibits a Peierls transition and topological phases, providing insights into strongly correlated bosons and potential experimental realizations.

Contribution

The study extends the Bose-Hubbard model to include bond degrees of freedom, revealing a bosonic analog of the Peierls transition and topological insulators in a dynamical lattice.

Findings

Discovery of a bosonic Peierls transition.

Identification of topological solitons and bond order waves.

Numerical phase diagram characterization.

Abstract

We study a one-dimensional system of strongly correlated bosons on a dynamical lattice. To this end, we extend the standard Bose-Hubbard Hamiltonian to include extra degrees of freedom on the bonds of the lattice. We show that this minimal model exhibits phenomena reminiscent of fermion-phonon models. In particular, we discover a bosonic analog of the Peierls transition, where the translational symmetry of the underlying lattice is spontaneously broken. This provides a dynamical mechanism to obtain a topological insulator in the presence of interactions, analogous to the Su-Schrieffer-Heeger model for electrons. We characterize the phase diagram numerically, showing different types of bond order waves and topological solitons. Finally, we study the possibility of implementing the model using atomic systems.