Quantum Entanglement and Magnon Hall Effect on the Lieb Lattice Model

L.S. Lima

L.S. Lima

Jixun K. Ding, Emily Z. Zhang, Wen O. Wang +4 more

In light of recent experimental data indicating a substantial thermal Hall effect in square lattice antiferromagnetic Mott insulators, we investigate whether a simple Mott insulator can sustain a finite thermal Hall effect. We verify that the answer is "no" if one performs calculations within a spin-only low-energy effective spin model with noninteracting magnons. However, by performing determinant quantum Monte Carlo simulations, we show the single-band t-t^{'}-U Hubbard model coupled to an orbital magnetic field does support a finite thermal Hall effect when t^{'}≠0 and B≠0 in the Mott insulating phase. We argue that the (carrier agnostic) necessary conditions for observing a finite thermal Hall effect are time-reversal and particle-hole symmetry breaking. By considering magnon-magnon scattering using a semiclassical Boltzmann analysis, we illustrate a physical mechanism by which finite transverse thermal conductivity may arise, consistent with our symmetry argument and numerical results. Our results indicate that square and triangular lattices with SU(2) symmetry can support a finite thermal Hall effect and call for a critical reexamination of thermal Hall effect data in insulating magnets, as the magnon contribution should not be excluded a priori.

Lucie Maude Fournier, William Witczak‐Krempa

Nathan Goldman, Daniel F. Urban, Dario Bercioux

We investigate the properties of the Lieb lattice, that is, a face-centered square lattice, subjected to external gauge fields. We show that an Abelian gauge field leads to a peculiar quantum Hall effect, which is a consequence of the single Dirac cone and the flat band characterizing the energy spectrum. Then we explore the effects of an intrinsic spin-orbit term---a non-Abelian gauge field---and demonstrate the occurrence of the quantum spin Hall effect in this model. Besides, we obtain the relativistic Hamiltonian describing the Lieb lattice at low energy and derive the Landau levels in the presence of external Abelian and non-Abelian gauge fields. Finally, we describe concrete schemes for realizing these gauge fields with cold fermionic atoms trapped in an optical Lieb lattice. In particular, we provide a very efficient method to reproduce the intrinsic (Kane-Mele) spin-orbit term with assisted-tunneling schemes. Consequently, our model could be implemented in order to produce a variety of topological states with cold atoms.

Anonymous, Hugo U. R. Strand, Benjamin T. Zhou +1 more

We investigate the magnetic orders and excitations in a half-filled Hubbard model that continuously interpolates between the Lieb and kagome lattices. Using the self-consistent Hartree-Fock approximation combined with the Bethe-Salpeter equation in the random phase approximation, we map the U − t ′ phase diagram of the Lieb-kagome lattices and compute real-frequency transverse spin susceptibilities, i.e., the magnon spectra. Dynamical mean-field theory and exact diagonalization are used as complementary checks of static magnetic phases. In particular, besides gapless Goldstone magnons, the symmetry-broken ferrimagnetic and antiferromagnetic phases also exhibit gapped Higgs magnon bands, which originate from amplitude fluctuations in the order parameter characterizing spontaneous symmetry breaking.