P-band in a rotating optical lattice

TL;DR

This paper studies how rotation affects the excited p-band in a tight-binding optical lattice, revealing a modified magnetic structure and deriving an effective Hamiltonian that matches first-principles calculations.

Contribution

It introduces a modified Peierls substitution for the p-band under rotation and derives an effective Hamiltonian validated by comparison with detailed calculations.

Findings

Rotation causes non-trivial splitting of the p-band.

The effective Hamiltonian accurately reproduces the magnetic band structure.

The approach enables investigation of many-particle phenomena in rotating p-bands.

Abstract

We investigate the effects of rotation on the excited bands of a tight binding lattice, focusing particulary on the first excited (p-) band. Both the on-site energies and the hopping between lattice sites are modified by the effective magnetic field created by rotation, causing a non-trivial splitting and magnetic fine structure of the p-band. We show that Peierls substitution can be modified to describe p-band under rotation, and use this method to derive an effective Hamiltonian. We compare the spectrum of the effective Hamiltonian with a first principles calculation of the magnetic band structure and find excellent agreement, confirming the validity of our approach. We also discuss the on-site interaction terms for bosons and argue that many-particle phenomena in a rotating p-band can be investigated starting from this effective Hamiltonian.