At high frequency, a periodically driven quantum spin-1/2 system can emulate a chiral spin liquid (CSL) described by an effective static local chiral Hamiltonian. In contrast, at low frequency these settings realize “Swap” models exhibiting anomalous CSL phases, in which one-way spin transport occurs at the edge although the bulk time-evolution operator over one period is trivial. In this work, we explicitly construct a family of Floquet quantum spin-1/2 models on the square lattice implementing Swap models to investigate the stability of the anomalous CSL under frequency detuning and the transition to the high-frequency regime. We used the average-energy spectrum on finite-size tori and cylinders to unfold the Floquet quasienergy spectrum over the whole frequency range and obtain the geometrical Berry phases. This enabled us to identify three regimes upon increasing detuning: (i) a finite-size regime (with no folding of the Floquet spectrum), (ii) an intermediate (narrow) regime with folding and very few resonances, and (iii) a regime with an increased density of resonances suggesting heating. At small detuning, edge modes are revealed by spectroscopic tools and from the Streda response of the system, giving access to the anomalous winding number. The analysis of all the data suggests that the anomalous CSL is not continuously connected to the high-frequency CSL. We also discuss the possible occurrence of a long-lived prethermal anomalous CSL.

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• Quantum spin liquid
• Topological phases of matter
• Floquet systems
• Hamiltonian systems
• Quantum many-body systems
• Exact diagonalization