We have found the exact (factorized) ground state of a general class of ferrimagnets in the presence of a magnetic field which covers the frustrated, anisotropic and long range interactions for arbitrary dimensional space. In particular cases, our model represents the bond-alternating, ferromagnet-antiferromagnet and also homogeneous spin $s$ model. The factorized ground state is a product of single particle kets on a bipartite lattice composed of two different spins ($\rho, \sigma$). The spin waves analysis around the exact ground state show two branch of excitations which is the origin of two dynamics of the model. The signature of these dynamics is addressed as a peak and a broaden bump in the specific heat.Comment: 4 pages and 2 figures, some typos correcte

We introduce an inhomogeneous bosonic mixture composed of two kinds of hardcore and semihardcore boson with different nilpotency conditions and demonstrate that in contrast with the standard hardcore Bose Hubbard model, our bosonic mixture with nearest and next nearest neighbor interactions on a square lattice develops the checkerboard supersolid phase characterized by the simultaneous superfluid and checkerboard solid orders. Our bosonic mixture is created from a twoorbital Bose-Hubbard model including two kinds of bosons: a single orbital boson and a two-orbital boson. By mapping the bosonic mixture to an anisotropic inhomogeneous spin model in the presence of a magnetic field, we study the ground state phase diagram of the model by means of cluster mean field theory and linear spin wave theory and show that various phases such as solid, superfluid, supersolid and Mott insulator appear in the phase diagram of the mixture. Competition between the interactions and magnetic field causes the mixture to undergo different kinds of first and second order phase transitions. By studying the behavior of the spin wave excitations we find the reasons of all first and second order phase transitions. We also obtain the temperature phase diagram of the system using cluster mean field theory. We show that the checkerboard supersolid phase persists at finite temperature comparable with the interaction energies of bosons.

The (one-dimensional) Su-Schrieffer-Heeger Hamiltonian, augmented by spin-orbit coupling and longerrange hopping, is studied at half filling for an even number of sites. The ground-state phase diagram depends sensitively on the symmetry of the model. Charge-conjugation (particle-hole) symmetry is conserved if hopping is only allowed between the two sublattices of even and odd sites. In this case, we find a variety of topologically nontrivial phases, characterized by different numbers of edge states (or, equivalently, different quantized Zak phases). The transitions between these phases are clearly signalled by the entanglement entropy. Charge-conjugation symmetry is broken if hopping within the sublattices is admitted. We study specifically next-nearest-neighbor hopping with amplitudes t a and t b for the A and B sublattices, respectively. For t a = t b , parity is conserved, and also the quantized Zak phases remain unchanged in the gapped regions of the phase diagram. However, metallic patches appear due to the overlap between conduction and valence bands in some regions of parameter space. The case of alternating next-nearest-neighbor hopping, t a = −t b , is also remarkable, as it breaks both charge-conjugation C and parity P but conserves the product CP. Both the Zak phase and the entanglement spectrum still provide relevant information, in particular about the broken parity. Thus the Zak phase for small values of t a measures the disparity between bond strengths on A and B sublattices, in close analogy to the proportionality between the Zak phase and the polarization in the case of the related Aubry-André model.

Abstract. We study the surface conductivity of a three dimensional topological insulator doped with magnetic impurities. The spin-momentum locking of surface electrons makes their scattering from magnetic impurities anisotropic and the standard relaxation time approximation is not applicable. Using the semiclassical Boltzmann approach together with a generalized relaxation time scheme, we obtain closed forms for the relaxation times and analytic expressions for the surface conductivities of the system as functions of the bulk magnetization and the orientation of the aligned surface magnetic impurities. We show that the surface conductivity is anisotropic, and strongly depends both on the direction of the spins of magnetic impurities and on the magnitude of the bulk magnetization. In particular, we find that the surface conductivity has its minimum value when the spin of surface impurities are aligned perpendicular to the surface of TI, and therefore the backscattering probability is enhanced due to the magnetic torque exerted by impurities on the surface electrons.PACS numbers: 72.15.Lh