Floquet Many-body Engineering: Topological and Many-body Physics in Phase Space Lattices

TL;DR

This paper proposes using periodically driven 1D harmonic systems with interactions to engineer 2D topological and many-body phases in phase space, revealing novel long-range interactions and persistent exchange effects.

Contribution

It introduces a method to realize 2D topological and many-body physics in phase space via Floquet engineering in driven harmonic systems, highlighting new interaction types.

Findings

Phase space lattice structures depend on driving parameters.

Contact interactions become Coulomb-like in phase space.

Floquet exchange interactions persist in the classical limit.

Abstract

Hamiltonians which are inaccessible in static systems can be engineered in periodically driven many-body systems, i.e., Floquet many-body systems. We propose to use interacting particles in a one-dimensional (1D) harmonic potential with periodic kicking to investigate two-dimensional (2D) topological and many-body physics. Depending on the driving parameters, the Floquet Hamiltonian of single kicked harmonic oscillator has various lattice structures in phase space. The noncommutative geometry of phase space gives rise to the topology of the system. We investigate the effective interactions of particles in phase space and find that the point-like contact interaction in quasi-1D real space becomes a long-rang Coulomb-like interaction in phase space, while the hardcore interaction in pure-1D real space becomes a confinement quark-like potential in phase space. We also find that the Floquet exchange interaction does not disappear even in the classical limit, and can be viewed as an effective long-range spin-spin interaction induced by collision. Our proposal may provide platforms to explore new physics and exotic phases by \textit{Floquet many-body engineering}.