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

TL;DR

This work demonstrates a pathway to realize and control chiral spin liquids on a kagome lattice by coupling to a gyrotropic cavity vacuum, using a unitary asymptotically decoupled frame to reveal an emergent gauge field that induces a chiral spin interaction without external driving. Weak electron photon coupling yields a CSL with nonzero chiral order and a topologically protected entanglement spectrum, while strong coupling polarizes spins and destroys chirality. The authors connect photon transport, via waveguide transmittance and average photon number, to the emergent topological order and provide a phase diagram for experimental exploration using real materials like Herbertsmithite and cold-atom implementations. This cavity-tunable approach opens a practical route to engineer and probe topological quantum phases and may enable doped CSLs and related exotic states with implications for quantum information processing.

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. Featured by long-range entanglement, topological order, and exotic fractional excitations, the CSL has inspired extensive exploration for practical realizations. In this work, we demonstrate that CSLs can emerge in a kagome lattice driven by vacuum quantum fluctuations over the non-interacting 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.

Figures (5)

• Figure 1: The schematic diagram of the setup. The kagome lattice is placed inside a gyrotropic cavity. The gyrotropic cavity is coupled to a waveguide, which is used for transport measurements.
• Figure 2: \ref{['kagome']} Kagome lattice potential from \ref{['Vlattice']}. The dark dots are the low-energy regions, which form the kagome lattice. \ref{['vector_potential']} The effective gauge vector potential $\mathbf{A}_{\rm eff}$, the darker color being the stronger strength. \ref{['flux']} The gauge field flux $\nabla \cross \mathbf{A}_{\rm eff}$, which is a scalar in 2d.
• Figure 3: Order parameters for the kagome lattice inside the gyrotropic cavity. \ref{['chiB']} is the chiral order parameter. DMRG simulation indicates a non-zero chiral order parameter for weak electron-photon interaction and a zero chiral order parameter for strong electron-photon interaction. $\beta = \frac{m \xi^2 V_0}{2}$ is the dimensionless parameter describing the strength of the effective gauge field. \ref{['Gzz']} is the spin $zz$ correlation when $\beta=0.5$. DMRG simulation indicates no or weak correlation for weak electron-photon interaction and a strong correlation for strong electron-photon interaction. Combining with the nonzero chiral order in the weak-coupling regime, this confirms the presence of a CSL phase, while strong coupling leads to a spin-polarized state. All the simulations above are done with $t=1$ and $U^'=5$. \ref{['ES']} displays the entanglement spectrum with a cylinder geometry at small $\mathcal{B}$. The $k_y$ corresponds to the eigenvalue of translation in the wrapped direction $y$. The spectrum reveals a characteristic degeneracy pattern $1,1,2,3,5,\dots$ in the low-energy sector colored in red. This sequence reflects the underlying edge state described by a chiral bosonic CFT associated with the topological phase.
• Figure 4: \ref{['TB']} shows the transmittance for a waveguide coupled to the gyrotropic cavity with a kagome lattice inside. The transmittance approaches a constant with strong electron-photon interaction. All the simulations above are done with $t=1$, $U^'=5$, $\omega_k = 1$ and $g=0.1$. \ref{['kappa']} shows the CS level fitting from the low-energy description of CSL. The results confirm the level-2 CS theory.
• Figure 5: A phase diagram computed using typical herbertsmithite experimental parameters. The saturation and brightness of the color represent the average magnetization and chirality separately. For small $U'$, the blue region is a band metallic phase with vanishing chirality and total magnetization. With small cavity frequency and large $U'$, the effective Zeeman term dominates and the state is polarized. As one increases the cavity frequency in the large $U'$ region, the system enters into the CSL phase with finite chirality. For super large cavity frequency, the photonic modes are effectively gapped, and the system becomes a clean kagome lattice, which potentially supports other QSLs.