Suppression of Dimer Correlations in the Two-Dimensional J1J_1-J2J_2 Heisenberg Model: an Exact Diagonalization Study

We present an exact diagonalization study of the ground state of the spin-half $J_1{-}J_2$ model. Dimer correlation functions and the susceptibility associated to the breaking of the translational invariance are calculated for the $4\times 4$ and the $6\times 6$ clusters. These results -- especially when compared to the one dimensional case, where the occurrence of a dimerized phase for large enough frustration is well established -- suggest either a homogeneous spin liquid or, possibly, a dimerized state with a rather small order parameter

CARS Temperature Measurements in a Hypersonic Propulsion Test Facility

Nonintrusive diagnostic measurements were performed in the supersonic reacting flow of the Hypersonic Propulsion Test Cell 2 at NASA-Langley. A Coherent Anti-stokes Raman Spectroscopy (CARS) system was assembled specifically for the test cell environment. System design considerations were: (1) test cell noise and vibration; (2) contamination from flow field or atmospheric borne dust; (3) unwanted laser or electrically induced combustion (inside or outside the duct); (4) efficient signal collection; (5) signal splitting to span the wide dynamic range present throughout the flow field; (6) movement of the sampling volume in the flow; and (7) modification of the scramjet model duct to permit optical access to the reacting flow with the CARS system. The flow in the duct was a nominal Mach 2 flow with static pressure near one atmosphere. A single perpendicular injector introduced hydrogen into the flow behind a rearward facing step. CARS data was obtained in three planes downstream of the injection region. At least 20 CARS data points were collected at each of the regularly spaced sampling locations in each data plane. Contour plots of scramjet combustor static temperature in a reacting flow region are presented

A Recursive Method of the Stochastic State Selection for Quantum Spin Systems

In this paper we propose the recursive stochastic state selection method, an extension of the recently developed stochastic state selection method in Monte Carlo calculations for quantum spin systems. In this recursive method we use intermediate states to define probability functions for stochastic state selections. Then we can diminish variances of samplings when we calculate expectation values of the powers of the Hamiltonian. In order to show the improvement we perform numerical calculations of the spin-1/2 anti-ferromagnetic Heisenberg model on the triangular lattice. Examining results on the ground state of the 21-site system we confide this method in its effectiveness. We also calculate the lowest and the excited energy eigenvalues as well as the static structure factor for the 36-site system. The maximum number of basis states kept in a computer memory for this system is about 3.6 x 10**7. Employing a translationally invariant initial trial state, we evaluate the lowest energy eigenvalue within 0.5 % of the statistical errors.Comment: 14 pages, 1 figur

Spontaneous plaquette dimerization in the J1−J2J_1-J_2 Heisenberg model

We investigate the non magnetic phase of the spin-half frustrated Heisenberg antiferromagnet on the square lattice using exact diagonalization (up to 36 sites) and quantum Monte Carlo techniques (up to 144 sites). The spin gap and the susceptibilities for the most important crystal symmetry breaking operators are computed. A genuine and somehow unexpected `plaquette RVB', with spontaneously broken translation symmetry and no broken rotation symmetry, comes out from our numerical simulations as the most plausible ground state for $J_2/J_1 \simeq 0.5$.Comment: 4 pages, 5 postscript figure

Resonating Valence Bond Wave Functions for Strongly Frustrated Spin Systems

The Resonating Valence Bond (RVB) theory for two-dimensional quantum antiferromagnets is shown to be the correct paradigm for large enough ``quantum frustration''. This scenario, proposed long time ago but never confirmed by microscopic calculations, is very strongly supported by a new type of variational wave function, which is extremely close to the exact ground state of the $J_1{-}J_2$ Heisenberg model for $0.4 \lesssim J_2/J_1\lesssim 0.5$. This wave function is proposed to represent the generic spin-half RVB ground state in spin liquids.Comment: 4 Pages, 5 figures, accepted for publication in PR

Coherent Behavior and Nonmagnetic Impurity Effects of the Spin Disordered State in NiGa2_2S4_4

Nonmagnetic impurity effects of the spin disordered state in the triangular antiferromagnet NiGa$_2$S$_4$ was studied through magnetic and thermal measurements for Ni$_{1-x}$Zn$_x$Ga$_2$S$_4$ (0.0\le x\le 0.3). Only 1 % substitution is enough to strongly suppress the coherence observed in the spin disordered state. However, the suppression is not complete and the robust feature of the T^2 dependent specific heat and its scaling behavior with the Weiss temperature indicate the existence of a coherent Nambu-Goldstone mode. Absence of either conventional magnetic order or bulk spin freezing suggests a novel symmetry breaking of the ground state.Comment: 4 pages, 4 figure

Coherent Anti-Stokes Raman Spectroscopic Thermometry in a Supersonic Combustor

An experiment has been conducted to acquire data for the validation of computational fluid dynamics codes used in the design of supersonic combustors. The flow in a supersonic combustor, consisting of a diverging duct with a single downstream-angled wail injector, is studied. Combustor entrance Mach number is 2 and enthalpy nominally corresponds to Mach 7 flight. The primary measurement technique is coherent anti-Stokes Raman spectroscopy, but surface pressures and temperatures have also been acquired. Modern design of experiment techniques have been used to maximize the quality of the data set (for the given level of effort) and to minimize systematic errors. Temperature maps are obtained at several planes in the flow for a case in which the combustor is piloted by injecting fuel upstream of the main injector and one case in which it is not piloted. Boundary conditions and uncertainties are characterized

Spin-1/2 frustrated antiferromagnet on a spatially anisotopic square lattice: contribution of exact diagonalizations

The phase diagram of a spin-1/2 $J-J'-J_2$ model is investigated by means of exact diagonalizations on finite samples. This model is a generalization of the $J_1-J_2$ model on the square lattice with two different nearest-neighbor couplings $J,J'$ and may be also viewed as an array of coupled Heisenberg chains. The results suggest that the resonnating valence bond state predicted by Nersesyan and Tsvelik [Phys. Rev. B {\bf 67}, 024422 (2003)] for $J_2=0.5J' \ll J$ is realized and extends beyond the limit of small interchain coupling along a curve nearly coincident with the line where the energy per spin is maximum. This line is likely bordered on both side by a columnar dimer long range order. This columnar order could extends for $J'\to J$ which correspond to the $J_1-J_2$ model.Comment: 14 pages, 21 figures, final versio

Superconductivity in Organic Compounds with Pseudo-Triangular Lattice

We study spin fluctuation (SF) mediated superconductivity (SC) in a half-filled square lattice Hubbard model with the transfer matrices -t between nearest neighbor sites and -t' between a half of next nearest neighbor sites neighboring along only one of the directions, considering application of this model to organic kappa-(BEDT-TTF)2X compounds. Varying the t'/t value from 0 to 1, one can interpolate between a square and an equilateral triangular lattice, the latter giving frustration to antiferromagnetically (AF) coupled spin systems. Within the fluctuation exchange (FLEX) approximation, we calculate chi(q,omega), Tc and the SC order parameter for various model parameter values and find that both AF and SC are suppressed as one approaches the frustration geometry or |(t'/t)-1| \to 0. The SC phase, however, extends beyond the AF phase boundary fairly close to t'/t=1 for realistic U/t values. The order parameter is of x2-y2-type for t'/t1.Comment: 4 pages, 5 eps figures, to appear in J. Phys. Soc. Jp

Spin-1/2 J1-J2 model on the body-centered cubic lattice

Using exact diagonalization (ED) and linear spin wave theory (LSWT) we study the influence of frustration and quantum fluctuations on the magnetic ordering in the ground state of the spin-1/2 J1-J2 Heisenberg antiferromagnet (J1-J2 model) on the body-centered cubic (bcc) lattice. Contrary to the J1-J2 model on the square lattice, we find for the bcc lattice that frustration and quantum fluctuations do not lead to a quantum disordered phase for strong frustration. The results of both approaches (ED, LSWT) suggest a first order transition at J2/J1 $\approx$ 0.7 from the two-sublattice Neel phase at low J2 to a collinear phase at large J2.Comment: 6.1 pages 7 figure