Title: Topological orders of strongly interacting particles,
Abstract: We investigate the self-organization of strongly interacting particles
confined in 1D and 2D. We consider hardcore bosons in spinless Hubbard lattice
models with short range interactions. We show that, many-body orders with
topological characteristics emerge, at different energy bands separated by
large gaps. These topological orders manifest in the way the particles organize
in real space to form states with different energy. Each of these states
contains topological defects/condensations whose Euler characteristic can be
used as a topological number to categorize states belonging to the same energy
band. We provide analytical formulas for this topological number and the full
energy spectrum of the system for both sparsely and densely filled systems.
Furthermore, we discuss the connection with the Gauss-Bonnet theorem of
differential geometry, by using the curvature generated in real space by the
particle structures. Our result is a demonstration of how topological orders
can arise in strongly interacting many-body systems with simple underlying
rules, without considering the spin, long-range microscopic interactions, or
external fields.