Many-body chaos and topological order in flat-band optical lattices

Optical lattices are remarkable for their capacity to host rich physics. In this talk, I will discuss the flat-band optical lattices from the perspective of the potential realization of novel states of quantum matter, including the quantum chaotic Sachdev-Ye-Kitaev system and spin-liquids. 

The many-body chaotic property of the Sachdev-Ye-Kitaev model is a reliable framework for studying thermalization in quantum systems with strong interactions and promises to shed light on the black hole information paradox. In the first part of the talk, I will show that the low energy theory of flat band kagome optical lattice with geometric disorders realizes the Sachdev-Ye-Kitaev physics with different symmetry classes. These can be obtained upon tuning the magnetic flux, allowing one to verify many theoretical proposals by experiments with ultracold fermions in optical lattices.

In the second part of the talk, I will discuss a similar setup with bosonic ultracold atoms in a kagome optical lattice that may lead to a quantum spin liquid supporting a topological order. This state of matter has various exotic properties, including emergent excitations with fractional quantum numbers and fractional statistics and robust topology-dependent ground state degeneracies.

I will conclude by arguing that recent developments in this field may lead to the realization of the SYK model and quantum spin liquids in experiments with ultracold atoms.