Anomalous Chiral Spin Liquid Achieves Stability under Frequency Detuning, Enabling Swap Models

The pursuit of exotic quantum states of matter has led researchers to investigate periodically-driven systems, which can exhibit unusual properties resembling chiral spin liquids. Matthieu Mambrini, Nathan Goldman, and Didier Poilblanc, from institutions including CNRS and the Collège de France, now demonstrate how these systems respond to changes in the driving frequency, revealing a surprising transition between different quantum phases. Their work explicitly constructs models that mimic these spin liquids, allowing them to map out the system’s behaviour across a broad range of frequencies and identify distinct regimes, from stable states to those prone to energy absorption and instability. This research is significant because it establishes that the anomalous chiral spin liquid is fundamentally different from its high-frequency counterpart, and suggests the possibility of creating long-lived, prethermal states with unique properties, potentially paving the way for novel quantum technologies.

One-way spin transport occurs at the edge, although the bulk time-evolution operator over one period is trivial. This work explicitly constructs a family of Floquet quantum spin-1/2 models on the square lattice, implementing Swap Models to investigate the stability of the anomalous Chern-Simons liquid under frequency detuning and the transition to the high-frequency regime. The average-energy spectrum on finite-size tori and cylinders unfolds the Floquet quasi-energy spectrum over the whole frequency range, and obtains the geometrical Berry phases. This enables identification of three regimes upon increasing detuning: a finite-size regime with no folding of the Floquet spectrum, an intermediate and narrow regime with folding and very few resonances, and a regime with an infinite.

Floquet Systems, Topology, and Chiral Spin Liquids

The provided text is not a single cohesive research article but rather a large bibliography accompanied by brief explanatory descriptions of related concepts in condensed matter physics. It functions as a curated collection of references and thematic notes intended to guide researchers who are exploring advanced topics such as Floquet systems, topological phases, and chiral spin liquids. The explanatory portions serve to contextualize the cited works rather than to present new results or a unified theoretical framework.

A central theme throughout the references is Floquet physics, which studies quantum systems under time-periodic driving. Much of the cited work focuses on understanding how periodically driven systems can be described using effective, time-independent Hamiltonians, making their complex dynamics more tractable. Within this framework, researchers explore how periodic driving can induce novel topological phases, including Chern insulators and chiral spin liquids, that do not exist in equilibrium settings. These phases are characterized by non-trivial topological invariants and often support robust edge states, including anomalous edge modes unique to driven systems. Related topics such as prethermalization, many-body localization, and counterdiabatic driving are also highlighted, as they address how driven systems can avoid rapid heating and retain coherent, non-equilibrium behavior.

Another major focus of the bibliography is chiral spin liquids (CSLs), which are exotic quantum phases of matter lacking conventional magnetic order. CSLs exhibit chiral order and topological order, featuring long-range quantum entanglement and fractionalized excitations such as spinons. Some theoretical models predict that certain CSLs host non-Abelian anyons, making them promising candidates for topological quantum computation. The resonating valence bond (RVB) picture is frequently referenced as a conceptual framework for understanding these states, emphasizing fluctuating spin singlets rather than static order.

The text also emphasizes the importance of topological invariants and geometric phases, particularly Berry phases, as essential mathematical tools for characterizing topological properties of quantum systems. These concepts underpin much of the theoretical analysis in both equilibrium and driven topological matter. To study such complex systems, the references include extensive use of advanced numerical methods, especially tensor network approaches like Projected Entangled Pair States (PEPS) and infinite PEPS (iPEPS), which are well suited for simulating strongly correlated two-dimensional systems.

Based on the cited literature, several specific topics recur, including the dynamic Hall effect in driven materials, the Kitaev model and its connection to Majorana fermions, time crystals as non-equilibrium phases with emergent periodicity, synthetic gauge fields engineered through external driving, U(1) symmetries in spin liquids, and the Středa formula linking Chern numbers to Hall conductivity. The bibliography also features recurring contributions from prominent researchers in the field, reflecting key schools of thought and methodological approaches within this research area.

Overall, the text serves as a valuable reference resource for researchers interested in the intersection of periodically driven quantum systems, topological phases, and chiral spin liquids. While it does not function as a tutorial, review article, or presentation of new results, it provides a structured entry point into the existing literature and highlights the major conceptual and methodological pillars shaping current research in this area of condensed matter physics.

Driven Quantum Systems Emulate Anomalous Spin Liquids

Researchers have demonstrated that periodically driven quantum systems can mimic complex magnetic states, specifically chiral spin liquids. They investigated these systems, known as Swap Models, across a range of driving frequencies, revealing distinct behaviors at high and low frequencies. At high frequencies, the system emulates a conventional chiral spin liquid, while at lower frequencies, an unusual “anomalous” chiral spin liquid emerges, characterized by one-way spin transport along its edges despite an overall time-independent behavior. This work explicitly constructs these models and explores their stability as the driving frequency is altered., The team employed a technique involving the analysis of the system’s energy spectrum to map its behavior across the full range of frequencies.

This revealed three regimes: a finite-size regime, an intermediate regime with minimal energy disturbances, and a regime prone to energy gain suggesting instability. Importantly, spectroscopic measurements and analysis of the system’s response to magnetic fields confirmed the existence of edge modes in the anomalous chiral spin liquid at small frequency deviations, and allowed the determination of its anomalous winding number. The data indicates that the anomalous and high-frequency chiral spin liquids are fundamentally different states, not smoothly connected to each other., The authors acknowledge that their analysis relies on simulations of relatively small systems, which may limit the direct applicability of their findings to larger, more realistic materials. They suggest that further research should focus on understanding the potential for a long-lived “prethermal” anomalous chiral spin liquid state, which could persist for extended periods before succumbing to heating. Future investigations could also explore the behavior of these systems in three dimensions and with different interaction parameters, potentially paving the way for the design of novel quantum materials with tailored properties.