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Register a new userHow correlations change the magnetic structure factor of the kagome Hubbard model
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The kagome Hubbard model (KHM) is a paradigmatic example of a frustrated two-dimensional model. While its strongly correlated regime, described by a Heisenberg model, is of topical interest due to its enigmatic prospective spin-liquid ground state, the weakly and moderately correlated regimes remain largely unexplored. Motivated by the rapidly growing number of metallic kagome materials (e.g., Mn$_3$Sn, Fe$_3$Sn$_2$, FeSn, Co$_3$Sn$_2$S$_2$, Gd$_3$Ru$_4$Al$_{12}$), we study the respective regimes of the KHM by means of three complementary numerical methods: the dynamical mean-field theory (DMFT), the dynamical vertex approximation (D$Gamma$A), and determinant quantum Monte Carlo (DQMC). In contrast to the archetypal square-lattice, we find no tendencies towards magnetic ordering, as magnetic correlations remain short-range. Nevertheless, the magnetic correlations undergo a remarkable crossover as the system approaches the metal-to-insulator transition. The Mott transition itself does however not affect the magnetic correlations. Our equal-time and dynamical structure factors can be used as a reference for inelastic neutron scattering experiments on the growing family of metallic kagome materials.
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The repulsive Fermi Hubbard model on the square lattice has a rich phase diagram near half-filling (corresponding to the particle density per lattice site $n=1$): for $n=1$ the ground state is an antiferromagnetic insulator, at $0.6 < n lesssim 0.8$, it is a $d_{x^2-y^2}$-wave superfluid (at least for moderately strong interactions $U lesssim 4t$ in terms of the hopping $t$), and the region $1-n ll 1$ is most likely subject to phase separation. Much of this physics is preempted at finite temperatures and to an extent driven by strong magnetic fluctuations, their quantitative characteristics and how they change with the doping level being much less understood. Experiments on ultra-cold atoms have recently gained access to this interesting fluctuation regime, which is now under extensive investigation. In this work we employ a self-consistent skeleton diagrammatic approach to quantify the characteristic temperature scale $T_{M}(n)$ for the onset of magnetic fluctuations with a large correlation length and identify their nature. Our results suggest that the strongest fluctuations---and hence highest $T_{M}$ and easiest experimental access to this regime---are observed at $U/t approx 4-6$.
We introduce an efficient way to improve the accuracy of projected wave functions, widely used to study the two-dimensional Hubbard model. Taking the clue from the backflow contribution, whose relevance has been emphasized for various interacting systems on the continuum, we consider many-body correlations to construct a suitable approximation for the ground state at intermediate and strong couplings. In particular, we study the phase diagram of the frustrated $t{-}t^prime$ Hubbard model on the square lattice and show that, thanks to backflow correlations, an insulating and non-magnetic phase can be stabilized at strong coupling and sufficiently large frustrating ratio $t^prime/t$.
We present a microscopic study of a doped quantum spin liquid candidate, the hyperkagome Na$_3$Ir$_3$O$_8$ compound by using $^{23}$Na NMR. We determine the intrinsic behavior of the uniform textbf{q} $ = 0$ susceptibility via shift measurements and the dynamical response by probing the spin-lattice relaxation rate. Throughout the studied temperature range, the susceptibility is consistent with a semimetal behavior, though with electronic bands substantially modified by correlations. Remarkably, the antiferromagnetic fluctuations present in the insulating parent compound Na$_4$Ir$_3$O$_8$ survive in the studied compound. The spin dynamics are consistent with 120$^o$ excitations modes displaying short-range correlations.
We present a numerical study of the charge dynamical structure factor N(k,omega) of a one-dimensional (1D) ionic Hubbard model in the Mott insulator phase. We show that the low-energy spectrum of N(k,omega) is expressed in terms of the spin operators for the spin degrees of freedom. Numerical results of N(k,omega) for the spin degrees of freedom, obtained by the Lanczos diagonalization method, well reproduce the low-energy spectrum of N(k,omega) of the 1D ionic Hubbard model. In addition, we show that these spectral peaks probe the dispersion of the spin-singlet excitations of the system and are observed in the wide parameter region of the MI phase.
We analyze the dynamical nearest-neighbor and next-nearest-neighbor spin correlations in the 4-site and 8-site dynamical cluster approximation to the two-dimensional Hubbard model. Focusing on the robustness of these correlations at long imaginary times, we reveal enhanced ferromagnetic correlations on the lattice diagonal, consistent with the emergence of composite spin-1 moments at a temperature scale that essentially coincides with the pseudo-gap temperature $T^*$. We discuss these results in the context of the spin-freezing theory of unconventional superconductivity.
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