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arXiv:2502.07108 · Physical review. B./Physical review. B

Detection of chiral spin fluctuations driven by frustration in Mott insulators

Kuan H. Hsu, Chunjing Jia, Emily Z. Zhang, Daniel Jost, Brian Moritz, R. Hackl, Thomas Devereaux

Published May 12, 2025• 4 citations
arXivHTMLPDF

Abstract

Topologically ordered states, such as chiral spin liquids, have been proposed as candidates that host fraction alized excitations. However, detecting chiral character or proximity to these nontrivial states remains a challenge. Resonant Raman scattering can be a powerful tool for detecting chiral fluctuations, as the ${A}_{2g}$ channel probes excitations with broken time-reversal symmetry and local chiral order. Here, we use exact diagonalization to characterize the resonant ${A}_{2g}$ channel, alongside two-magnon scattering in ${B}_{1g}$ and ${E}_{g}$ channels, for the Hubbard model on lattices with increasing levels of geometric spin frustration, where tuning the incident energy near the Mott gap reveals strong chiral spin excitation intensity. Increased spin frustration in the Mott insulator results in an overall softening of the Raman ${A}_{2g}$ response, indicating a tendency toward low energy chiral-chiral fluctuations in Mott insulators with magnetic frustration and proximity to chiral spin liquid states that can potentially be tuned by external perturbations.

DOI
10.1103/physrevb.111.205115

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Topologically ordered states, such as chiral spin liquids, have been proposed as candidates that host fraction alized excitations. However, detecting chiral character or proximity to these nontrivial states remains a challenge. Resonant Raman scattering can be a powerful tool for detecting chiral fluctuations, as the A2g{A}_{2g}A2g​ channel probes excitations with broken time-reversal symmetry and local chiral order. Here, we use exact diagonalization to characterize the resonant A2g{A}_{2g}A2g​ channel, alongside two-magnon scattering in B1g{B}_{1g}B1g​ and Eg{E}_{g}Eg​ channels, for the Hubbard model on lattices with increasing levels of geometric spin frustration, where tuning the incident energy near the Mott gap reveals strong chiral spin excitation intensity. Increased spin frustration in the Mott insulator results in an overall softening of the Raman A2g{A}_{2g}A2g​ response, indicating a tendency toward low energy chiral-chiral fluctuations in Mott insulators with magnetic frustration and proximity to chiral spin liquid states that can potentially be tuned by external perturbations.
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.
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 novel knob to drive frustrated Mott insulators into a chiral spin liquid (CSL), 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 Si⋅(Sj×Sk)S_i \cdot (S_j \times S_k)Si​⋅(Sj​×Sk​) term which dynamically breaks time-reversal while preserving SU(2) spin symmetry. We fingerprint the transient phase diagram and find a stable photo-induced CSL 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.
Optical probes have emerged as versatile tools for detecting exotic fractionalized phases in quantum materials. We calculate the low-energy Raman response arising from mobile, interacting Ising anyons in the chiral Kitaev spin liquid perturbed by symmetry allowed interactions---a phase relevant to $\ensuremath{\alpha}\ensuremath{-}{\mathrm{RuCl}}_{3}$ under a magnetic field. At zero temperature, the two-anyon continuum response shows a leading power-law scaling of the intensity near the onset of the signal: $I(\ensuremath{\omega})\ensuremath{\sim}{(\ensuremath{\omega}\ensuremath{-}{E}_{2\ensuremath{\sigma}}^{0})}^{\frac{1}{8}}$ for linear and parallel-circular polarization channels, where ${E}_{2\ensuremath{\sigma}}^{0}$ is the two-particle gap. Strong corrections due to short-range interactions arise at order 1/41/41/4. For cross-circularly polarized channels, the scaling is given by $I(\ensuremath{\omega})\ensuremath{\sim}{(\ensuremath{\omega}\ensuremath{-}{E}_{2\ensuremath{\sigma}}^{0})}^{|l\ifmmode\pm\else\textpm\fi{}1/8|}$, where the value of l=0,1,2l=0,1,2l=0,1,2 is determined by the number of minima in the single anyon dispersion. The exponents are directly related to the topological spin of Ising anyons ${\ensuremath{\theta}}_{\ensuremath{\sigma}}=\ensuremath{\pi}/8$, describing their exchange statistics. Our theory generalizes to spectral probes of anyonic quasiparticles with multiple band minima in other quantum liquids. Interaction between anyons may also induce bound states, resulting in sharp peaks that show strong polarization dependence.
Recently, the frustrated XY model for spins 1/2 on the honeycomb lattice has attracted a lot of attention in relation with the possibility to realize a chiral spin liquid state. This model is relevant to the physics of some quantum magnets. Using the flexibility of ultracold atom setups, we propose an alternative way to realize this model through the Mott regime of the bosonic Kane-Mele-Hubbard model. The phase diagram of this model is derived using bosonic dynamical mean-field theory. Focusing on the Mott phase, we investigate its magnetic properties as a function of frustration. We do find an emergent chiral spin state in the intermediate frustration regime. Using exact diagonalization we study more closely the physics of the effective frustrated XY model and the properties of the chiral spin state. This gapped phase displays a chiral order, breaking time-reversal and parity symmetry, but is not topologically ordered (the Chern number is zero).
We consider the question of whether resonant inelastic x-ray scattering (RIXS) can be used to detect many-body excitations that are coupled to the spin-chirality terms ${\mathbf{S}}_{i}\ifmmode\cdot\else\textperiodcentered\fi{}({\mathbf{S}}_{j}\ifmmode\times\else\texttimes\fi{}{\mathbf{S}}_{k})$ in a Mott insulator. We find that while the spin-chirality terms are in general absent in the usual experimental setups of RIXS, there are prospects of realizing such terms if one considers instead the scattering near a pre-edge. We then perform detailed analyses for the square and the kagome lattices, and brief analyses for the triangular and the honeycomb lattices, in which we show that the spin-chirality terms are indeed present in all the above lattices, but that they occur at a higher order in our expansion for the kagome and the honeycomb lattices. The merit of using RIXS in addition to Raman spectroscopy to detect excitations that are coupled to the spin-chirality terms is also briefly discussed in the context of the emergent gauge boson in the U(1)\text{U}(1)U(1) Dirac spin liquid.
We propose multi-layer moire structures in strong external magnetic fields as a novel platform for realizing highly-tunable, frustrated Hubbard physics with topological order. Identifying the layer degree of freedom as a pseudo spin, allows us to retain SU(2) symmetry while controlling ring-exchange processes and concurrently quenching the kinetic energy by large external magnetic fields. This way, a broad class of interacting Hubbard-Hofstadter states and their transitions can be studied. Remarkably, in the limit of strong interactions the system becomes Mott insulating and we find chiral pseudo spin liquid phases which are induced by the magnetic field. We find that this topologically ordered state remains exceptionally stable towards relevant perturbations. We discuss how layer pseudo-spin can be probed in near-term experiments. As the magnetic flux can be easily tuned in moire systems, our approach provides a promising route towards the experimental realization and control of topologically ordered phases of matter.