Ground-state phase diagram of the spin-1/2 square-lattice J1-J2 model with plaquette structure

Using the coupled cluster method for high orders of approximation and Lanczos exact diagonalization we study the ground-state phase diagram of a quantum spin-1/2 J1-J2 model on the square lattice with plaquette structure. We consider antiferromagnetic (J1>0) as well as ferromagnetic (J1<0) nearest-neighbor interactions together with frustrating antiferromagnetic next-nearest-neighbor interaction J2>0. The strength of inter-plaquette interaction lambda varies between lambda=1 (that corresponds to the uniform J1-J2 model) and lambda=0 (that corresponds to isolated frustrated 4-spin plaquettes). While on the classical level (s \to \infty) both versions of models (i.e., with ferro- and antiferromagnetic J1) exhibit the same ground-state behavior, the ground-state phase diagram differs basically for the quantum case s=1/2. For the antiferromagnetic case (J1 > 0) Neel antiferromagnetic long-range order at small J2/J1 and lambda \gtrsim 0.47 as well as collinear striped antiferromagnetic long-range order at large J2/J1 and lambda \gtrsim 0.30 appear which correspond to their classical counterparts. Both semi-classical magnetic phases are separated by a nonmagnetic quantum paramagnetic phase. The parameter region, where this nonmagnetic phase exists, increases with decreasing of lambda. For the ferromagnetic case (J1 < 0) we have the trivial ferromagnetic ground state at small J2/|J1|. By increasing of J2 this classical phase gives way for a semi-classical plaquette phase, where the plaquette block spins of length s=2 are antiferromagnetically long-range ordered. Further increasing of J2 then yields collinear striped antiferromagnetic long-range order for lambda \gtrsim 0.38, but a nonmagnetic quantum paramagnetic phase lambda \lesssim 0.38.Comment: 10 pages, 15 figure

Dynamical Supersymmetry Breaking in Intersecting Brane Models

In this paper we study dynamical supersymmetry breaking in absence of gravity with the matter content of the minimal supersymmetric standard model. The hidden sector of the theory is a strongly coupled gauge theory, realized in terms of microscopic variables which condensate to form mesons. The supersymmetry breaking scalar potential combines F, D terms with instanton generated interactions in the Higgs-mesons sector. We show that for a large region in parameter space the vacuum breaks in addition to supersymmetry also electroweak gauge symmetry. We furthermore present local D-brane configurations that realize these supersymmetry breaking patterns.Comment: 30 pages, 4 figures, pdflate

High-Order Coupled Cluster Calculations Via Parallel Processing: An Illustration For CaV4_4O9_9

The coupled cluster method (CCM) is a method of quantum many-body theory that may provide accurate results for the ground-state properties of lattice quantum spin systems even in the presence of strong frustration and for lattices of arbitrary spatial dimensionality. Here we present a significant extension of the method by introducing a new approach that allows an efficient parallelization of computer codes that carry out ``high-order'' CCM calculations. We find that we are able to extend such CCM calculations by an order of magnitude higher than ever before utilized in a high-order CCM calculation for an antiferromagnet. Furthermore, we use only a relatively modest number of processors, namely, eight. Such very high-order CCM calculations are possible {\it only} by using such a parallelized approach. An illustration of the new approach is presented for the ground-state properties of a highly frustrated two-dimensional magnetic material, CaV$_4$O$_9$. Our best results for the ground-state energy and sublattice magnetization for the pure nearest-neighbor model are given by $E_g/N=-0.5534$ and $M=0.19$, respectively, and we predict that there is no N\'eel ordering in the region $0.2 \le J_2/J_1 \le 0.7$. These results are shown to be in excellent agreement with the best results of other approximate methods.Comment: 4 page

Coupled Cluster Treatment of the Shastry-Sutherland Antiferromagnet

We consider the zero-temperature properties of the spin-half two-dimensional Shastry-Sutherland antiferromagnet by using a high-order coupled cluster method (CCM) treatment. We find that this model demonstrates various groundstate phases (N\'{e}el, magnetically disordered, orthogonal dimer), and we make predictions for the positions of the phase transition points. In particular, we find that orthogonal-dimer state becomes the groundstate at ${J}^{d}_2/J_1 \sim 1.477$. For the critical point $J_2^{c}/J_1$ where the semi-classical N\'eel order disappears we obtain a significantly lower value than $J_2^{d}/J_1$, namely, ${J}^{c}_2/J_1$ in the range $[1.14, 1.39]$. We therefore conclude that an intermediate phase exists between the \Neel and the dimer phases. An analysis of the energy of a competing spiral phase yields clear evidence that the spiral phase does not become the groundstate for any value of $J_2$. The intermediate phase is therefore magnetically disordered but may exhibit plaquette or columnar dimer ordering.Comment: 6 pages, 5 figure

Direct calculation of the spin stiffness on square, triangular and cubic lattices using the coupled cluster method

We present a method for the direct calculation of the spin stiffness by means of the coupled cluster method. For the spin-half Heisenberg antiferromagnet on the square, the triangular and the cubic lattices we calculate the stiffness in high orders of approximation. For the square and the cubic lattices our results are in very good agreement with the best results available in the literature. For the triangular lattice our result is more precise than any other result obtained so far by other approximate method.Comment: 5 pages, 2 figure

Quantum Phase Transitions in Spin Systems

We discuss the influence of strong quantum fluctuations on zero-temperature phase transitions in a two-dimensional spin-half Heisenberg system. Using a high-order coupled cluster treatment, we study competition of magnetic bonds with and without frustration. We find that the coupled cluster treatment is able to describe the zero-temperature transitions in a qualitatively correct way, even if frustration is present and other methods such as quantum Monte Carlo fail.Comment: 8 pages, 12 Postscipt figures; Accepted for publication in World Scientifi

The spin-half Heisenberg antiferromagnet on two Archimedian lattices: From the bounce lattice to the maple-leaf lattice and beyond

We investigate the ground state of the two-dimensional Heisenberg antiferromagnet on two Archimedean lattices, namely, the maple-leaf and bounce lattices as well as a generalized $J$-$J'$ model interpolating between both systems by varying $J'/J$ from $J'/J=0$ (bounce limit) to $J'/J=1$ (maple-leaf limit) and beyond. We use the coupled cluster method to high orders of approximation and also exact diagonalization of finite-sized lattices to discuss the ground-state magnetic long-range order based on data for the ground-state energy, the magnetic order parameter, the spin-spin correlation functions as well as the pitch angle between neighboring spins. Our results indicate that the "pure" bounce ($J'/J=0$) and maple-leaf ($J'/J=1$) Heisenberg antiferromagnets are magnetically ordered, however, with a sublattice magnetization drastically reduced by frustration and quantum fluctuations. We found that magnetic long-range order is present in a wide parameter range $0 \le J'/J \lesssim J'_c/J$ and that the magnetic order parameter varies only weakly with $J'/J$. At $J'_c \approx 1.45 J$ a direct first-order transition to a quantum orthogonal-dimer singlet ground state without magnetic long-range order takes place. The orthogonal-dimer state is the exact ground state in this large-$J'$ regime, and so our model has similarities to the Shastry-Sutherland model. Finally, we use the exact diagonalization to investigate the magnetization curve. We a find a 1/3 magnetization plateau for $J'/J \gtrsim 1.07$ and another one at 2/3 of saturation emerging only at large $J'/J \gtrsim 3$.Comment: 9 pages, 10 figure

Frustrated spin-12\frac{1}{2} Heisenberg magnet on a square-lattice bilayer: High-order study of the quantum critical behavior of the J1J_{1}--J2J_{2}--J1⊥J_{1}^{\perp} model

The zero-temperature phase diagram of the spin-$\frac{1}{2}$ $J_{1}$--$J_{2}$--$J_{1}^{\perp}$ model on an $AA$-stacked square-lattice bilayer is studied using the coupled cluster method implemented to very high orders. Both nearest-neighbor (NN) and frustrating next-nearest-neighbor Heisenberg exchange interactions, of strengths $J_{1}>0$ and $J_{2} \equiv \kappa J_{1}>0$, respectively, are included in each layer. The two layers are coupled via a NN interlayer Heisenberg exchange interaction with a strength $J_{1}^{\perp} \equiv \delta J_{1}$. The magnetic order parameter $M$ (viz., the sublattice magnetization) is calculated directly in the thermodynamic (infinite-lattice) limit for the two cases when both layers have antiferromagnetic ordering of either the N\'{e}el or the striped kind, and with the layers coupled so that NN spins between them are either parallel (when $\delta 0$) to one another. Calculations are performed at $n$th order in a well-defined sequence of approximations, which exactly preserve both the Goldstone linked cluster theorem and the Hellmann-Feynman theorem, with $n \leq 10$. The sole approximation made is to extrapolate such sequences of $n$th-order results for $M$ to the exact limit, $n \to \infty$. By thus locating the points where $M$ vanishes, we calculate the full phase boundaries of the two collinear AFM phases in the $\kappa$--$\delta$ half-plane with $\kappa > 0$. In particular, we provide the accurate estimate, ($\kappa \approx 0.547,\delta \approx -0.45$), for the position of the quantum triple point (QTP) in the region $\delta < 0$. We also show that there is no counterpart of such a QTP in the region $\delta > 0$, where the two quasiclassical phase boundaries show instead an ``avoided crossing'' behavior, such that the entire region that contains the nonclassical paramagnetic phases is singly connected

Nonlinear projective filtering in a data stream

We introduce a modified algorithm to perform nonlinear filtering of a time series by locally linear phase space projections. Unlike previous implementations, the algorithm can be used not only for a posteriori processing but includes the possibility to perform real time filtering in a data stream. The data base that represents the phase space structure generated by the data is updated dynamically. This also allows filtering of non-stationary signals and dynamic parameter adjustment. We discuss exemplary applications, including the real time extraction of the fetal electrocardiogram from abdominal recordings.Comment: 8 page

Density-functional investigation of rhombohedral stacks of graphene: topological surface states, nonlinear dielectric response, and bulk limit

A DFT-based investigation of rhombohedral (ABC)-type graphene stacks in finite static electric fields is presented. Electronic band structures and field-induced charge densities are compared with related literature data as well as with own results on (AB) stacks. It is found, that the undoped AB-bilayer has a tiny Fermi line consisting of one electron pocket around the K-point and one hole pocket on the line K-$\Gamma$. In contrast to (AB) stacks, the breaking of translational symmetry by the surface of finite (ABC) stacks produces a gap in the bulk-like states for slabs up to a yet unknown critical thickness $N^{\rm semimet} \gg 10$, while ideal (ABC) bulk ($\beta$-graphite) is a semi-metal. Unlike in (AB) stacks, the ground state of (ABC) stacks is shown to be topologically non-trivial in the absence of external electric field. Consequently, surface states crossing the Fermi level must unavoidably exist in the case of (ABC)-type stacking, which is not the case in (AB)-type stacks. These surface states in conjunction with the mentioned gap in the bulk-like states have two major implications. First, electronic transport parallel to the slab is confined to a surface region up to the critical layer number $N^{\rm semimet}$. Related implications are expected for stacking domain walls and grain boundaries. Second, the electronic properties of (ABC) stacks are highly tunable by an external electric field. In particular, the dielectric response is found to be strongly nonlinear and can e.g. be used to discriminate slabs with different layer numbers. Thus, (ABC) stacks rather than (AB) stacks with more than two layers should be of potential interest for applications relying on the tunability by an electric field.Comment: 36 pages, 17 figure