Floquet systems with continuous dynamical symmetries: characterization, time-dependent Noether charge, and solvability

TL;DR

This paper explores quantum Floquet systems with continuous dynamical symmetry, revealing how such symmetry constrains Hamiltonians, enables solving Floquet states via finite-dimensional eigenproblems, and introduces a time-dependent conserved charge, with applications to models like the Rabi and Heisenberg spin models.

Contribution

It provides a systematic framework for characterizing Floquet systems with continuous dynamical symmetry and deriving their Floquet states and conserved quantities.

Findings

Floquet states can be obtained by solving a finite-dimensional eigenvalue problem.

Continuous dynamical symmetry leads to a time-dependent conserved charge.

The approach explains the absence of hybridization in quasienergy diagrams.

Abstract

We study quantum Floquet (periodically-driven) systems having continuous dynamical symmetry (CDS) consisting of a time translation and a unitary transformation on the Hilbert space. Unlike the discrete ones, the CDS strongly constrains the possible Hamiltonians $H(t)$ and allows us to obtain all the Floquet states by solving a finite-dimensional eigenvalue problem. Besides, Noether's theorem leads to a time-dependent conservation charge, whose expectation value is time-independent throughout evolution. We exemplify these consequences of CDS in the seminal Rabi model, an effective model of a nitrogen-vacancy center in diamonds without strain terms, and Heisenberg spin models in rotating fields. Our results provide a systematic way of solving for Floquet states and explain how they avoid hybridization in quasienergy diagrams.