Floquet dynamical chiral spin liquid at finite frequency

TL;DR

This paper demonstrates the stabilization of a dynamical chiral spin liquid phase at finite frequencies using Floquet engineering, revealing topological order and tensor network representations beyond high-frequency approximations.

Contribution

It extends the understanding of Floquet-driven chiral spin liquids to lower frequencies where high-frequency approximations fail, showing their stability and topological nature.

Findings

DCSL is stabilized at finite frequencies outside high-frequency limit.

Topological order persists in the dynamical phase, linked to Floquet spectrum features.

Tensor network methods faithfully represent the DCSL state.

Abstract

Chiral Spin Liquids (CSL) are quantum spin analogs of electronic Fractional Chern Insulators. Their realizations on ultracold-atom or Rydberg-atom platforms remain very challenging. Recently, a setup of time-periodic modulations of nearest-neighbor Heisenberg couplings applied on an initial genuine spin liquid state on the square lattice has been proposed to stabilize a (Abelian) $\mathbb{Z}_2$ CSL phase. In the high-frequency limit, it was shown that time evolution can be described in terms of a static effective chiral Hamiltonian. Here we revisit this proposal and consider drives at lower frequency in a regime where the high-frequency Magnus expansion fails. We show that a Dynamical CSL (DCSL) is nevertheless stabilized in a finite range of frequency. The topological nature of this dynamical phase, as well as its instability below a critical frequency, is connected to specific features of the Floquet pseudo-energy spectrum. We also show that the DCSL can be represented faithfully by a two-dimensional time-periodic tensor network and, as in the static case, topological order is associated to a tensor gauge symmetry ($\mathbb{Z}_2$ in that case).