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We calculate the bipartite von Neumann and second Rényi entanglement entropies of the ground states of spin-1/2 dimerized Heisenberg antiferromagnets on a square lattice. Two distinct dimerization patterns are considered: columnar and staggered. In both cases, we concentrate on the valence bond solid (VBS) phase and describe such a phase with the bond-operator representation. Within this formalism, the original spin Hamiltonian is mapped into an effective interacting boson model for the triplet excitations. We study the effective Hamiltonian at the harmonic approximation and determine the spectrum of the elementary triplet excitations. We then follow an analytical procedure, which is based on a modified spin-wave theory for finite systems and was originally employed to calculate the entanglement entropies of magnetic ordered phases, and calculate the entanglement entropies of the VBS ground states. In particular, we consider one-dimensional (line) subsystems within the square lattice, a choice that allows us to consider line subsystems with sizes up to L = 1000. We combine such a procedure with the results of the bond-operator formalism at the harmonic level and show that, for both dimerized Heisenberg models, the entanglement entropies of the corresponding VBS ground states obey an area law as expected for gapped phases. For both columnar-dimer and staggered-dimer models, we also show that the entanglement entropies increase but they seem to not diverge as the dimerization decreases and the system approaches the Néel-VBS quantum phase transition. Finally, the entanglement spectra associated with the VBS ground states are presented. arXiv:1902.04355v2 [cond-mat.str-el]

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We study the flat-band ferromagnetic phase of a spinfull and time-reversal symmetric Haldane-Hubbard model on a honeycomb lattice within a bosonization formalism for flat-band Z2 topological insulators. Such a study extend our previous one [L. S. G. Leite and R. L. Doretto, Phys. Rev. B 104, 155129 (2021)] concerning the flat-band ferromagnetic phase of a correlated Chern insulator described by a Haldane-Hubbard model. We consider the topological Hubbard model at 1/4 filling of its corresponding noninteracting limit and in the nearly flat band limit of its lower free-electronic bands. We show that it is possible to define boson operators associated with two distinct spin-flip excitations, one that changes (mixed-lattice excitations) and a second one that preserves (samelattice excitations) the index related with the two triangular sublattices. Within the bosonization scheme, the fermionic model is mapped into an effective interacting boson model, whose quadratic term is considered at the harmonic approximation in order to determine the spin-wave excitation spectrum. For both mixed and same-lattice excitations, we find that the spin-wave spectrum is gapped and has two branches, with an energy gap between the lower and the upper bands at the K and K points of the first Brillouin zone. Such a behavior is distinct from the one of the corresponding correlated Chern insulator, whose spin-wave spectrum has a Goldstone mode at the center of the first Brillouin zone and Dirac points at K and K points. Moreover, we consider the effects on the spin-wave spectrum when an energy offset in the on-site repulsion energies associated with the two triangular sublattices is introduced and when the width of the lower free-electronic bands is increased. We also find some evidences that the spin-wave bands for the same-lattice excitations might be topologically nontrivial even in the completely flat band limit.