Abstract:
We discuss the phase structure of chiral Yukawa models in the mean-field approximation. In particular, we examine under which conditions a ferrimagnetic phase appears, by calculating the slopes of possible second order phase transition lines near a critical point. Our results contrast with some statements which appeared in the literature recently.

Abstract:
The phase transitions in the Blume-Emery-Griffiths (BEG) model and antiferromagnetic Potts model on the diamond lattice are investigated using the cluster-variation method in the pair approximation. The ferrimagnetic phases are found to be different from those on the simple-cubic lattice. The phase diagrams of the BEG model are also calculated. In the vicinity of the parameter line where the BEG model reduces to the three-state antiferromagnetic Potts model, new types of phase diagram are obtained. The results are different from those of the mean-field theory, which is a good approximation only for large coordination number of the lattice.

Abstract:
We address the possibility of spiral ferrimagnetic phases in the mean-field phase diagram of the two-dimensional (2D) Hubbard model. For intermediate values of the interaction $U$ ($6 \lesssim U/t \lesssim 11$) and doping $n$, a spiral ferrimagnetic phase is the most stable phase in the $(n,U)$ phase diagram. Higher values of $U$ lead to a non-spiral ferrimagnetic phase. If phase separation is allowed and the chemical potential $\mu$ replaces the doping $n$ as the independent variable, the $(\mu,U)$ phase diagram displays, in a considerable region, a spiral (for $6 \lesssim U/t \lesssim 11$) and non-spiral (for higher values of $U$) ferrimagnetic phase with fixed particle density, $n=0.5$, reflecting the opening of an energy gap in the mean-field quasi-particle bands.

Abstract:
Recent experiments in ultracold atoms and photonic analogs have reported the implementation of artificial gauge fields in lattice systems, facilitating the realization of topological phases. Motivated by such advances, we investigate the Haldane honeycomb lattice tight-binding model, for bosons with local interactions at the average filling of one boson per site. We analyze the ground state phase diagram and uncover three distinct phases: a uniform superfluid (SF), a chiral superfluid (CSF) and a plaquette Mott insulator with local current loops (PMI). Nearest-neighbor and next-nearest neighbor currents distinguish CSF from SF, and the phase transition between them is first order. We apply bosonic dynamical mean field theory and exact diagonalization to obtain the phase diagram, complementing numerics with calculations of excitation spectra in strong and weak coupling perturbation theory. The characteristic density fluctuations, current correlation functions, and excitation spectra are measurable in ultracold atom experiments.

Abstract:
The ground state properties of the high spin Heisenberg chains with alternating single site anisotropy are investigated by means of the numerical exact daigonaization and DMRG method. It is found that the ferrimagnetic state appears between the Haldane phase and period doubled N\'eel phase for the integer spin chains. On the other hand, the transition from the Tomonaga-Luttinger liquid state into the ferrimagnetic state takes place for the half-odd-integer spin chains. In the ferrimagnetic phase, the spontaneous magnetization varies continuously with the modulation amplitude of the single site anisotropy. Eventually, the magnetization is locked to fractional values of the saturated magnetization. These fractional values satisfy the Oshikawa-Yamanaka-Affleck condition. The local spin profile is calculated to reveal the physical nature of each state. In contrast to the case of frustration induced ferrimagnetism, no incommensurate magnetic superstructure is found.

Abstract:
Gapped quantum spin chains with symmetry PSU(N)=SU(N)/Z(N) are known to possess N distinct symmetry protected topological phases. Besides the trivial phase, there are N-1 Haldane phases which are distinguished by the occurrence of massless boundary spins. Motivated by the potential realization in alkaline-earth atomic Fermi gases, we explicitly construct previously unknown Hamiltonians for two classes of chiral AKLT states and we discuss their physical properties. We also point out a deep connection between symmetry protection in gapped and gapless 1D quantum spin systems and its implications for a potential multicritical nature of topological phase transitions.

Abstract:
We investigate the ground state properties of an S=1/2 distorted diamond chain described by the Hamiltonian ${\cal H}=J_1\sum_\ell\bigl\{\bigl(\vecS_{3\ell-1}\cdot\vecS_{3\ell} +\vecS_{3\ell}\cdot\vecS_{3\ell+1}\bigr)+J_2\vecS_{3\ell-2}\cdot\vecS_{3\ell-1} +J_3\bigl(\vecS_{3\ell-2}\cdot\vecS_{3\ell}+\vecS_{3\ell}\cdot\vecS_{3\ ell+2}\bigr)-H S_{\ell}^z\bigr\}$ ($J_1,~J_2,~J_3\geq0$), which models well a trimerized S=1/2 spin chain system Cu$_3$Cl$_6$(H$_2$O)$_2$$\cdot$2H$_8$C$_4$SO$_2$. Using an exact diagonalization method by means of the Lancz\"os technique, we determine the ground state phase diagram in the H=0 case, composed of the dimerized, spin fluid, and ferrimagnetic phases. Performing a degenerate perturbation calculation, we analyze the phase boundary line between the latter two phases in the $J_2,~J_3\llJ_1$ limit, the result of which is in good agreement with the numerical result. We calculate, by the use of the density matrix renormalization group method, the ground state magnetization curve for the case (a) where $J_1=1.0$, $J_2=0.8$, and $J_3=0.5$, and the case (b) where $J_1=1.0$, $J_2=0.8$, and $J_3=0.3$. We find that in the case (b) the 2/3-plateau appears in addition to the 1/3-plateau which also appears in the case (a). The translational symmetry of the Hamiltonian $\cal H$ is spontaneously broken in the 2/3-plateau state as well as in the dimerized state.

Abstract:
A possible spin-reorientation transition in field-induced magnetic ordering phases of the S=1 Haldane system with large easy-plane anisotropy is proposed, using an effective Lagrangian formalism as well as the density matrix renormalization group method. Such a spin-reorientation transition is predicted in the case where the applied magnetic field is inclined from the easy axis of the anisotropy. We point out that this transition has a close connection with a variation of the order parameter even at zero temperature, although it is different from a quantum analog of the so-called spin-flop transition proposed for the system having a strong easy axis anisotropy. In connection with a novel phase observed recently in the Haldane system at high fields, we discuss possible implications for the field-induced magnetic ordering.

Abstract:
The Haldane Insulator is a gapped phase characterized by an exotic non-local order parameter. The parameter regimes at which it might exist, and how it competes with alternate types of order, such as supersolid order, are still incompletely understood. Using the Stochastic Green Function (SGF) quantum Monte Carlo (QMC) and the Density Matrix Renormalization Group (DMRG), we study numerically the ground state phase diagram of the one-dimensional bosonic Hubbard model (BHM) with contact and near neighbor repulsive interactions. We show that, depending on the ratio of the near neighbor to contact interactions, this model exhibits charge density waves (CDW), superfluid (SF), supersolid (SS) and the recently identified Haldane insulating (HI) phases. We show that the HI exists only at the tip of the unit filling CDW lobe and that there is a stable SS phase over a very wide range of parameters.

Abstract:
We investigate possible phase transitions among the different quantum anomalous Hall (QAH) phases in a zigzag graphene ribbon under the influence of the exchange field. The effective tight-binding Hamiltonian for graphene is made up of the hopping term, the Kane-Mele and Rashba spin-orbit couplings as well as the Haldane orbital term. We find that the variation of the exchange field results in bulk gap-closing phenomena and phase transitions occur in the graphene system. If the Haldane orbital coupling is absent, the phase transition between the chiral (anti-chiral) edge state $\nu=+2$ ($\nu=-2$) and the pseudo-quantum spin Hall state ($\nu=0$) takes place. Surprisingly, when the Haldane orbital coupling is taken into account, an intermediate QSH phase with two additional edge modes appears in between phases $\nu=+2$ and $\nu=-2$. This intermediate phase is therefore either the hyper-chiral edge state of high Chern number $\nu=+4$ or anti-hyper-chiral edge state of $\nu=-4$ when the direction of exchange field is reversed. We present the band structures, edge state wave functions and current distributions of the different QAH phases in the system. We also report the critical exchange field values for the QAH phase transitions.