Schrieffer-Wolff Transformation for Periodically Driven Systems: Strongly Correlated Systems with Artificial Gauge Fields

TL;DR

This paper extends the Schrieffer-Wolff transformation to periodically driven systems using Floquet theory, analyzing strongly interacting Fermi-Hubbard models to identify different effective low-energy Hamiltonians and phase transitions.

Contribution

It introduces a generalized Schrieffer-Wolff transformation for Floquet systems and applies it to strongly correlated models with artificial gauge fields.

Findings

Identifies nonresonant regime with static gauge field effects.

Derives effective Hamiltonian with doublon processes in resonant regime.

Shows phase transition between ordered and Luttinger liquid phases.

Abstract

We generalize the Schrieffer-Wolff transformation to periodically driven systems using Floquet theory. The method is applied to the periodically driven, strongly interacting Fermi-Hubbard model, for which we identify two regimes resulting in different effective low-energy Hamiltonians. In the nonresonant regime, we realize an interacting spin model coupled to a static gauge field with a nonzero flux per plaquette. In the resonant regime, where the Hubbard interaction is a multiple of the driving frequency, we derive an effective Hamiltonian featuring doublon association and dissociation processes. The ground state of this Hamiltonian undergoes a phase transition between an ordered phase and a gapless Luttinger liquid phase. One can tune the system between different phases by changing the amplitude of the periodic drive.