Fractional corner charges in a 2D super-lattice Bose-Hubbard model

TL;DR

This paper investigates a 2D super-lattice Bose-Hubbard model, revealing higher order topological phases with fractional corner charges, characterized by a topological invariant, and supported by numerical and experimental feasibility analyses.

Contribution

It demonstrates the existence of higher order symmetry protected topological phases with fractional corner charges in a 2D Bose-Hubbard model, using DMRG and topological invariants.

Findings

Identification of two gapped topological phases with fractional corner charges.

Numerical evidence of quantized corner charge distribution.

Potential for experimental observation in ultracold atomic systems.

Abstract

We study a two dimensional super-lattice Bose-Hubbard model with alternating hoppings in the limit of strong on-site interactions. We evaluate the phase diagram of the model around half-filling using the density matrix renormalization group method and find two gapped phases separated by a gapless superfluid region. We demonstrate that the gapped states realize two distinct higher order symmetry protected topological phases, which are protected by a combination of charge conservation and $C_4$ lattice symmetry. The phases are distinguished in terms of a quantized fractional corner charge and a many-body topological invariant that is robust against arbitrary, symmetry preserving edge manipulations. We support our claims by numerically studying the full counting statistics of the corner charge, finding a sharp distribution peaked around the quantized values. These results are experimentally observable in ultracold atomic settings using state of the art quantum gas microscopy.