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arXiv:2411.08121 · Physical Review Letters

Cavity-Vacuum-Induced Chiral Spin Liquids in Kagome Lattices: Tuning and Probing Topological Quantum Phases via Cavity Quantum Electrodynamics

Chenan Wei, Liu Yang, Qing-Dong Jiang

Published Nov 17, 2025• 6 citations
arXivHTMLPDF

Abstract

Topological phases in frustrated quantum magnetic systems have captivated researchers for decades, with the chiral spin liquid (CSL) standing out as one of the most compelling examples. Featuring long-range entanglement, topological order, and exotic fractional excitations, the CSL has inspired extensive exploration for practical realizations. In this Letter, we demonstrate that CSLs can emerge in a kagome lattice driven by vacuum quantum fluctuations over the noninteracting vacuum within a single-mode gyrotropic cavity. The gyrotropic cavity imprints quantum fluctuations with time-reversal symmetry breaking and stabilizes a robust CSL phase without external laser excitation. Moreover, we identify experimentally accessible observables-such as average photon number and transport properties-that reveal connections between photon dynamics and the emergent chiral order. Our findings establish a novel pathway for creating, controlling, and probing topological and symmetry-breaking quantum phases in strongly correlated systems.

DOI
10.1103/8qx2-xxh2

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Topological phases in frustrated quantum magnetic systems have captivated researchers for decades, with the chiral spin liquid (CSL) standing out as one of the most compelling examples. Featuring long-range entanglement, topological order, and exotic fractional excitations, the CSL has inspired extensive exploration for practical realizations. In this Letter, we demonstrate that CSLs can emerge in a kagome lattice driven by vacuum quantum fluctuations over the noninteracting vacuum within a single-mode gyrotropic cavity. The gyrotropic cavity imprints quantum fluctuations with time-reversal symmetry breaking and stabilizes a robust CSL phase without external laser excitation. Moreover, we identify experimentally accessible observables-such as average photon number and transport properties-that reveal connections between photon dynamics and the emergent chiral order. Our findings establish a novel pathway for creating, controlling, and probing topological and symmetry-breaking quantum phases in strongly correlated systems.
The fractional quantum Hall effect (FQHE) realized in two-dimensional electron systems under a magnetic field is one of the most remarkable discoveries in condensed matter physics. Interestingly, it has been proposed that FQHE can also emerge in time-reversal invariant spin systems, known as the chiral spin liquid (CSL) characterized by the topological order and the emerging of the fractionalized quasiparticles. A CSL can naturally lead to the exotic superconductivity originating from the condense of anyonic quasiparticles. Although CSL was highly sought after for more than twenty years, it had never been found in a spin isotropic Heisenberg model or related materials. By developing a density-matrix renormalization group based method for adiabatically inserting flux, we discover a FQHE in a spin-½ isotropic kagome Heisenberg model. We identify this FQHE state as the long-sought CSL with a uniform chiral order spontaneously breaking time reversal symmetry, which is uniquely characterized by the half-integer quantized topological Chern number protected by a robust excitation gap. The CSL is found to be at the neighbor of the previously identified Z2 spin liquid, which may lead to an exotic quantum phase transition between two gapped topological spin liquids.
The breaking of chiral and time-reversal symmetries provides a pathway to exotic quantum phenomena and topological phases. Recent work has extensively explored the resulting emergence of chiral charge orders and chiral spin liquids (CSLs) on the kagome lattice. Such CSLs are closely tied to bosonic fractional quantum Hall states with anyonic quasiparticles; however, their connection to nearby ordered states has remained a mystery. Here, we use spin-wave theory, parton Gutzwiller wave functions, and exact diagonalization to show that two distinct magnetic orders with uniform scalar chirality---the XYZ umbrella state and the octahedral spin crystal--emerge as competing orders in close proximity to the CSL. In this letter, we highlight the intimate link between a topologically ordered liquid and broken symmetry states with nontrivial real-space topology.
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Kalmeyer-Laughlin (KL) chiral spin liquid (CSL) is a type of quantum spin liquid without time-reversal symmetry, and it is considered as the parent state of an exotic type of superconductor--anyon superconductor. Such an exotic state has been sought for more than twenty years; however, it remains unclear whether it can exist in a realistic system where time-reversal symmetry is breaking (T breaking) spontaneously. By using the density matrix renormalization group, we show that KL CSL exists in a frustrated anisotropic kagome Heisenberg model, which has spontaneous T breaking. We find that our model has two topological degenerate ground states, which exhibit nonvanishing scalar chirality order and are protected by finite excitation gap. Furthermore, we identify this state as KL CSL by the characteristic edge conformal field theory from the entanglement spectrum and the quasiparticles braiding statistics extracted from the modular matrix. We also study how this CSL phase evolves as the system approaches the nearest-neighbor kagome Heisenberg model.
Abstract The search for quantum spin liquids in frustrated quantum magnets recently has enjoyed a surge of interest, with various candidate materials under intense scrutiny. However, an experimental confirmation of a gapped topological spin liquid remains an open question. Here, we show that circularly polarized light can provide a knob to drive frustrated Mott insulators into a chiral spin liquid, realizing an elusive quantum spin liquid with topological order. We find that the dynamics of a driven Kagome Mott insulator is well-captured by an effective Floquet spin model, with heating strongly suppressed, inducing a scalar spin chirality S i · (S j × S k ) term which dynamically breaks time-reversal while preserving SU(2) spin symmetry. We fingerprint the transient phase diagram and find a stable photo-induced chiral spin liquid near the equilibrium state. The results presented suggest employing dynamical symmetry breaking to engineer quantum spin liquids and access elusive phase transitions that are not readily accessible in equilibrium.
Quantum spin liquids, exotic phases of matter with topological order, have been a major focus in physics for the past several decades. Such phases feature long-range quantum entanglement that can potentially be exploited to realize robust quantum computation. We used a 219-atom programmable quantum simulator to probe quantum spin liquid states. In our approach, arrays of atoms were placed on the links of a kagome lattice, and evolution under Rydberg blockade created frustrated quantum states with no local order. The onset of a quantum spin liquid phase of the paradigmatic toric code type was detected by using topological string operators that provide direct signatures of topological order and quantum correlations. Our observations enable the controlled experimental exploration of topological matter and protected quantum information processing.