We consider extended Hubbard models with repulsive interactions on a honeycomb lattice, and the transitions from the semimetal to Mott insulating phases at half-filling. Because of the frustrated nature of the second-neighbor interactions, topological Mott phases displaying the quantum Hall and the quantum spin Hall effects are found for spinless and spin fermion models, respectively. The mean-field phase diagram is presented and the fluctuations are treated within the random phase approximation. Renormalization group analysis shows that these states can be favored over the topologically trivial Mott insulating states.We consider extended Hubbard models with repulsive interactions on a honeycomb lattice, and the transitions from the semimetal to Mott insulating phases at half-filling. Because of the frustrated nature of the second-neighbor interactions, topological Mott phases displaying the quantum Hall and the quantum spin Hall effects are found for spinless and spin fermion models, respectively. The mean-field phase diagram is presented and the fluctuations are treated within the random phase approximation. Renormalization group analysis shows that these states can be favored over the topologically trivial Mott insulating states.

arXiv:0710.0030Physical Review LettersApr 15, 2008659 citations

Detection of chiral spin fluctuations driven by frustration in Mott insulators

Kuan H. Hsu, Chunjing Jia, Emily Z. Zhang +4 more

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.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.

arXiv:2502.07108Physical review. B./Physical review. BMay 12, 20254 citations

{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.