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We develop a strong coupling approach towards quantum magnetism in Mott insulators for Wannier obstructed bands. Despite the lack of Wannier orbitals, electrons can still singly occupy a set of exponentially-localized but nonorthogonal orbitals to minimize the repulsive interaction energy. We develop a systematic method to establish an effective spin model from the electron Hamiltonian using a diagrammatic approach. The nonorthogonality of the Mott basis gives rise to multiple new channels of spin-exchange (or permutation) interactions beyond Hartree-Fock and superexchange terms. We apply this approach to a Kagome lattice model of interacting electrons in Wannier obstructed bands (including both Chern bands and fragile topological bands). Due to the orbital nonorthogonality, as parameterized by the nearest neighbor orbital overlap $g$, this model exhibits stable ferromagnetism up to a finite bandwidth $Wsim U g$, where $U$ is the interaction strength. This provides an explanation for the experimentally observed robust ferromagnetism in Wannier obstructed bands. The effective spin model constructed through our approach also opens up the possibility for frustrated quantum magnetism around the ferromagnet-antiferromagnet crossover in Wannier obstructed bands.
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Mott insulators sometimes show dramatic changes in their electronic states after photoirradiation, as indicated by photoinduced Mott-insulator-to-metal transition. In the photoexcited states of Mott insulators, electron wavefunctions are more delocalized than in the ground state, and long-range Coulomb interactions play important roles in charge dynamics. However, their effects are difficult to discriminate experimentally. Here, we show that in a one-dimensional Mott insulator, bis(ethylenedithio)tetrathiafulvalene-difluorotetracyanoquinodimethane (ET-F2TCNQ), long-range Coulomb interactions stabilize not only excitons, doublon-holon bound states, but also biexcitons. By measuring terahertz-electric-field-induced reflectivity changes, we demonstrate that odd- and even-parity excitons are split off from a doublon-holon continuum. Further, spectral changes of reflectivity induced by a resonant excitation of the odd-parity exciton reveals that an exciton-biexciton transition appears just below the exciton-transition peak. Theoretical simulations show that long-range Coulomb interactions over four sites are necessary to stabilize the biexciton. Such information is indispensable for understanding the non-equilibrium dynamics of photoexcited Mott insulators.
We study the electronic properties of GaV4S8 (GVS) and GaTaSe8 (GTS), two distant members within the large family of chalcogenides AM4X8, with A={Ga, Ge}, M={V, Nb, Ta, Mo} and X={S, Se}. While all these compounds are Mott insulators, their ground state show many types of magnetic order, with GVS being ferromagnetic and GTS non-magnetic. Based on their bandstructures, calculated with Density Functional Theory methods, we compute an effective tight binding Hamiltonian in a localised Wannier basis set, for each one of the two compounds. The localised orbitals provide a very accurate representation of the bandstructure, with hopping amplitudes that rapidly decrease with distance. We estimate the super-exchange interactions and show that the Coulomb repulsion with the Hunds coupling may account the for the different ground states observed in GVS and GTS. Our localised Wannier basis provides a starting point for realistic Dynamical Mean Field Theory studies of strong correlation effects in this family compounds.
We study the high harmonic generation (HHG) in Mott insulators using Floquet dynamical mean-field theory (DMFT). We show that the main origin of the HHG in Mott insulators is the doublon-holon recombination, and that the character of the HHG spectrum differs depending on the field strength. In the weaker-field regime, the HHG spectrum shows a single plateau as in the HHG from gases, and its cut-off energy $epsilon_{rm cut}$ scales linearly with the field strength $E_0$ as $epsilon_{rm cut}=Delta_{rm gap} + alpha E_0$, where $Delta_{rm gap}$ is the Mott gap. On the other hand, in the stronger-field regime, multiple plateaus emerge and the $m$-th cut-off scales as $epsilon_{rm cut,m}=U + m E_0$. We show that this difference originates from the different dynamics of the doublons and holons in the weak- and strong-field regimes. We also comment on the similarities and differences between HHG from Mott insulators and from semiconductors. This proceedings paper complements our recent work, Phys. Rev. Lett. 121, 057405 (2018), with additional results and analyses.
We study interaction-induced Mott insulators, and their topological properties in a 1D non-Hermitian strongly-correlated spinful fermionic superlattice system with either nonreciprocal hopping or complex-valued interaction. For the nonreciprocal hopping case, the low-energy neutral excitation spectrum is sensitive to boundary conditions, which is a manifestation of the non-Hermitian skin effect. However, unlike the single-particle case, particle density of strongly correlated system does not suffer from the non-Hermitian skin effect due to the Pauli exclusion principle and repulsive interactions. Moreover, the anomalous boundary effect occurs due to the interplay of nonreciprocal hopping, superlattice potential, and strong correlations, where some in-gap modes, for both the neutral and charge excitation spectra, show no edge excitations defined via only the right eigenvectors. We show that these edge excitations of the in-gap states can be correctly characterized by only biorthogonal eigenvectors. Furthermore, the topological Mott phase, with gapless particle excitations around boundaries, exists even for the purely imaginary-valued interaction, where the continuous quantum Zeno effect leads to the effective on-site repulsion between two-component fermions.
We study Bose-Hubbard models on tight-binding, non-Bravais lattices, with a filling of one boson per unit cell -- and thus fractional site filling. At integer filling of a unit cell neither symmetry breaking nor topological order is required, and in principle a trivial and featureless (i.e., symmetry-unbroken) insulator is allowed. We demonstrate by explicit construction of a family of wavefunctions that such a featureless Mott insulating state exists at 1/3 filling on the kagome lattice, and construct Hamiltonians for which these wavefunctions are exact ground states. We briefly comment on the experimental relevance of our results to cold atoms in optical lattices. Such wavefunctions also yield 1/3 magnetization plateau states for spin models in an applied field. The featureless Mott states we discuss can be generalized to any lattice for which symmetric exponentially localized Wannier orbitals can be found at the requisite filling, and their wavefunction is given by the permanent over all Wannier orbitals.
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