Detuning the Floquet anomalous chiral spin liquid

TL;DR

This paper investigates the stability and transition of Floquet anomalous chiral spin liquids in quantum spin-1/2 systems under frequency detuning, revealing regimes with different spectral properties and edge behaviors.

Contribution

It constructs a family of Floquet models to study how anomalous CSL phases evolve with frequency detuning, highlighting the transition from anomalous to high-frequency regimes.

Findings

Identifies three regimes of spectral behavior with increasing detuning.

Edge modes and anomalous winding number are observed at small detuning.

Suggests the anomalous CSL is not continuously connected to the high-frequency CSL.

Abstract

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 {\it 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 torus and cylinders to unfold the Floquet quasi-energy 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.