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Register a new userThe Union Jack model: a quantum spin model with frustration on the square lattice
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A new quantum spin model with frustration, the `Union Jack model on the square lattice, is analyzed using spin-wave theory. For small values of the frustrating coupling $alpha$, the system is N{ e}el ordered as usual, while for large $alpha$ the frustration is found to induce a canted phase. The possibility of an intermediate spin-liquid phase is discussed.
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We study the quantum phase diagram and excitation spectrum of the frustrated $J_1$-$J_2$ spin-1/2 Heisenberg Hamiltonian. A hierarchical mean-field approach, at the heart of which lies the idea of identifying {it relevant} degrees of freedom, is developed. Thus, by performing educated, manifestly symmetry preserving mean-field approximations, we unveil fundamental properties of the system. We then compare various coverings of the square lattice with plaquettes, dimers and other degrees of freedom, and show that only the {it symmetric plaquette} covering, which reproduces the original Bravais lattice, leads to the known phase diagram. The intermediate quantum paramagnetic phase is shown to be a (singlet) {it plaquette crystal}, connected with the neighboring Neel phase by a continuous phase transition. We also introduce fluctuations around the hierarchical mean-field solutions, and demonstrate that in the paramagnetic phase the ground and first excited states are separated by a finite gap, which closes in the Neel and columnar phases. Our results suggest that the quantum phase transition between Neel and paramagnetic phases can be properly described within the Ginzburg-Landau-Wilson paradigm.
The magnetic properties and Mott transition of the Hubbard model on the square lattice with frustration are studied at half-filling and zero temperature by the variational cluster approximation. When the on-site repulsion $U$ is large, magnetically disordered state is realized in highly frustrated region between the Neel and collinear phases, and no imcommensurate magnetic states are found there. As for the Mott transition, in addition to the Mott gap and double occupancy, which clarify the nature of the transition, the structure of the self-energy in the spectral representation is studied in detail below and above the Mott transition point. The spectral structure of the self-energy is almost featureless in the metallic phase, but clear single dispersion, leading to the Mott gap, appears in the Mott insulator phase.
We consider the $(2+1)$-d $SU(2)$ quantum link model on the honeycomb lattice and show that it is equivalent to a quantum dimer model on the Kagome lattice. The model has crystalline confined phases with spontaneously broken translation invariance associated with pinwheel order, which is investigated with either a Metropolis or an efficient cluster algorithm. External half-integer non-Abelian charges (which transform non-trivially under the $mathbb{Z}(2)$ center of the $SU(2)$ gauge group) are confined to each other by fractionalized strings with a delocalized $mathbb{Z}(2)$ flux. The strands of the fractionalized flux strings are domain walls that separate distinct pinwheel phases. A second-order phase transition in the 3-d Ising universality class separates two confining phases; one with correlated pinwheel orientations, and the other with uncorrelated pinwheel orientations.
We employ the Hartree-Fock approximation to identify the magnetic ground state of the Hubbard model on a frustrated square lattice. We investigate the phase diagram as a function of the Coulomb repulsions strength $U$, and the ratio $t/t$ between the nearest and next nearest neighbor hoppings $t$ and $t$. At half-filling and for a sufficiently large $U$, an antiferromagnetic chiral spin density wave order with nonzero spin chirality emerges as the ground state in a wide regime of the phase diagram near $t/t=1/sqrt{2}$, where the Fermi surface is well-nested for both $(pi,pi)$ and $(pi,0)/(0,pi)$ wave vectors. This triple-${bf Q}$ chiral phase is sandwiched by a single-${bf Q}$ N{e}el phase and a double-${bf Q}$ coplanar spin-vortex crystal phase, at smaller and larger $t/t$, respectively. The energy spectrum in the chiral spin density wave phase consists of four pairs of degenerate bands. These give rise to two pairs of Dirac cones with the same chirality at the point $({pi over 2},{piover 2})$ of the Brillouin zone. We demonstrate that the application of a diagonal strain induces a $d_{xy}$-wave next nearest neighbor hopping which, in turn, opens gaps in the two Dirac cones with opposite masses. As a result, four pairs of well-separated topologically-nontrivial bands emerge, and each pair of those contributes with a Chern number $pm1$. At half-filling, this leads to a zero total Chern number and renders the topologically-notrivial properties observable only in the ac response regime. Instead, we show that at $3/4$ filling, the triple-${bf Q}$ chiral phase yields a Chern insulator exhibiting the quantum anomalous Hall effect.
We study thermodynamic properties as well as the dynamical spin and quadrupolar structure factors of the O(3)-symmetric spin-1 Heisenberg model with bilinear-biquadratic exchange interactions on the triangular lattice. Based on a sign-problem-free quantum Monte Carlo approach, we access both the ferromagnetic and the ferroquadrupolar ordered, spin nematic phase as well as the SU(3)-symmetric point which separates these phases. Signatures of Goldstone soft-modes in the dynamical spin and the quadrupolar structure factors are identified, and the properties of the low-energy excitations are compared to the thermodynamic behavior observed at finite temperatures as well as to Schwinger-boson flavor-wave theory.
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