Highly frustrated spin-lattice models of magnetism and their quantum phase transitions: A microscopic treatment via the coupled cluster method

We outline how the coupled cluster method of microscopic quantum many-body theory can be utilized in practice to give highly accurate results for the ground-state properties of a wide variety of highly frustrated and strongly correlated spin-lattice models of interest in quantum magnetism, including their quantum phase transitions. The method itself is described, and it is shown how it may be implemented in practice to high orders in a systematically improvable hierarchy of (so-called LSUB$m$) approximations, by the use of computer-algebraic techniques. The method works from the outset in the thermodynamic limit of an infinite lattice at all levels of approximation, and it is shown both how the "raw" LSUB$m$ results are themselves generally excellent in the sense that they converge rapidly, and how they may accurately be extrapolated to the exact limit, $m \rightarrow \infty$, of the truncation index $m$, which denotes the {\it only} approximation made. All of this is illustrated via a specific application to a two-dimensional, frustrated, spin-half $J^{XXZ}_{1}$--$J^{XXZ}_{2}$ model on a honeycomb lattice with nearest-neighbor and next-nearest-neighbor interactions with exchange couplings $J_{1}>0$ and $J_{2} \equiv \kappa J_{1} > 0$, respectively, where both interactions are of the same anisotropic $XXZ$ type. We show how the method can be used to determine the entire zero-temperature ground-state phase diagram of the model in the range $0 \leq \kappa \leq 1$ of the frustration parameter and $0 \leq \Delta \leq 1$ of the spin-space anisotropy parameter. In particular, we identify a candidate quantum spin-liquid region in the phase space

Spin-1/2 J1J_{1}-J2J_{2} Heisenberg model on a cross-striped square lattice

Using the coupled cluster method (CCM) we study the full (zero-temperature) ground-state (GS) phase diagram of a spin-half ($s=1/2$) $J_{1}$-$J_{2}$ Heisenberg model on a cross-striped square lattice. Each site of the square lattice has 4 nearest-neighbour exchange bonds of strength $J_{1}$ and 2 next-nearest-neighbour (diagonal) bonds of strength $J_{2}$. The $J_{2}$ bonds are arranged so that the basic square plaquettes in alternating columns have either both or no $J_{2}$ bonds included. The classical ($s \rightarrow \infty$) version of the model has 4 collinear phases when $J_{1}$ and $J_{2}$ can take either sign. Three phases are antiferromagnetic (AFM), showing so-called N\'{e}el, double N\'{e}el and double columnar striped order respectively, while the fourth is ferromagnetic. For the quantum $s=1/2$ model we use the 3 classical AFM phases as CCM reference states, on top of which the multispin-flip configurations arising from quantum fluctuations are incorporated in a systematic truncation hierarchy. Calculations of the corresponding GS energy, magnetic order parameter and the susceptibilities of the states to various forms of valence-bond crystalline (VBC) order are thus carried out numerically to high orders of approximation and then extrapolated to the (exact) physical limit. We find that the $s=1/2$ model has 5 phases, which correspond to the four classical phases plus a new quantum phase with plaquette VBC order. The positions of the 5 quantum critical points are determined with high accuracy. While all 4 phase transitions in the classical model are first order, we find strong evidence that 3 of the 5 quantum phase transitions in the $s=1/2$ model are of continuous deconfined type

A frustrated spin-1/2 Heisenberg antiferromagnet on a chevron-square lattice

The coupled cluster method (CCM) is used to study the zero-temperature properties of a frustrated spin-half ($s={1}{2}$) $J_{1}$--$J_{2}$ Heisenberg antiferromagnet (HAF) on a 2D chevron-square lattice. Each site on an underlying square lattice has 4 nearest-neighbor exchange bonds of strength $J_{1}>0$ and 2 next-nearest-neighbor (diagonal) bonds of strength $J_{2} \equiv x J_{1}>0$, with each square plaquette having only one diagonal bond. The diagonal bonds form a chevron pattern, and the model thus interpolates smoothly between 2D HAFs on the square ($x=0$) and triangular ($x=1$) lattices, and also extrapolates to disconnected 1D HAF chains ($x \to \infty$). The classical ($s \to \infty$) version of the model has N\'{e}el order for $0 < x < x_{{\rm cl}}$ and a form of spiral order for $x_{{\rm cl}} < x < \infty$, where $x_{{\rm cl}} = {1}{2}$. For the $s={1}{2}$ model we use both these classical states, as well as other collinear states not realized as classical ground-state (GS) phases, as CCM reference states, on top of which the multispin-flip configurations resulting from quantum fluctuations are incorporated in a systematic truncation scheme, which we carry out to high orders and extrapolate to the physical limit. We calculate the GS energy, GS magnetic order parameter, and the susceptibilities of the states to various forms of valence-bond crystalline (VBC) order, including plaquette and two different dimer forms. We find that the $s={1}{2}$ model has two quantum critical points, at $x_{c_{1}} \approx 0.72(1)$ and $x_{c_{2}} \approx 1.5(1)$, with N\'{e}el order for $0 < x < x_{c_{1}}$, a form of spiral order for $x_{c_{1}} < x < x_{c_{2}}$ that includes the correct three-sublattice $120^{\circ}$ spin ordering for the triangular-lattice HAF at $x=1$, and parallel-dimer VBC order for $x_{c_{2}} < x < \infty$

Kink-antikink interactions in the double sine-Gordon equation and the problem of resonance frequencies

We studied the kink-antikink collision process for the "double sine-Gordon" (DSG) equation in 1+1 dimensions at different values of the potential parameter $R>0$. For small values of $R$ we discuss the problem of resonance frequencies. We give qualitative explanation of the frequency shift in comparison with the frequency of the discrete level in the potential well of isolated kink. We show that in this region of the parameter $R$ the effective long-range interaction between kink and antikink takes place.Comment: 9 pages, LaTeX, 4 figures (eps

Reinventing spacetime on a dynamical hypersurface

In braneworld models, Space-Time-Matter and other Kaluza-Klein theories, our spacetime is devised as a four-dimensional hypersurface {\it orthogonal} to the extra dimension in a five-dimensional bulk. We show that the FRW line element can be "reinvented" on a dynamical four-dimensional hypersurface, which is {\it not} orthogonal to the extra dimension, without any internal contradiction. This hypersurface is selected by the requirement of continuity of the metric and depends explicitly on the evolution of the extra dimension. The main difference between the "conventional" FRW, on an orthogonal hypersurface, and the new one is that the later contains higher-dimensional modifications to the regular matter density and pressure in 4D. We compare the evolution of the spacetime in these two interpretations. We find that a wealth of "new" physics can be derived from a five-dimensional metric if it is interpreted on a dynamical (non-orthogonal) 4D hypersurface. In particular, in the context of a well-known cosmological metric in $5D$, we construct a FRW model which is consistent with the late accelerated expansion of the universe, while fitting simultaneously the observational data for the deceleration parameter. The model predicts an effective equation of state for the universe, which is consistent with observations.Comment: References added to the Introduction, and Abstract modified. Accepted for publication in Mod. Phys. Lett.

Three field tests of a gas filter correlation radiometer

Test flights to remotely measure nonurban carbon monoxide (CO) concentrations by gas filter correlation radiometry are discussed. The inferred CO concentrations obtained through use of the Gas Filter Correlation Radiometer (GFCR) agreed with independent measurements obtained by gas chromatography air sample bottle analysis to within 20 percent. The equipment flown on board the aircraft, the flight test procedure, the gas chromatograph direct air sampling procedure, and the GFCR data analysis procedure are reported

Effects of P-wave Annihilation on the Angular Power Spectrum of Extragalactic Gamma-rays from Dark Matter Annihilation

We present a formalism for estimating the angular power spectrum of extragalactic gamma-rays produced by dark matter annihilating with any general velocity-dependent cross section. The relevant density and velocity distribution of dark matter is modeled as an ensemble of smooth, universal, rigid, disjoint, spherical halos with distribution and universal properties constrained by simulation data. We apply this formalism to theories of dark matter with p-wave annihilation, for which the relative-velocity-weighted annihilation cross section is \sigma v=a+bv^2. We determine that this significantly increases the gamma-ray power if b/a >> 10^6. The effect of p-wave annihilation on the angular power spectrum is very similar for the sample of particle physics models we explored, suggesting that the important effect for a given b/a is largely determined by the cosmic dark matter distribution. If the dark matter relic from strong p-wave theories is thermally produced, the intensities of annihilation gamma-rays are strongly p-wave suppressed, making them difficult to observe. If an angular power spectrum consistent with a strong p-wave were to be observed, it would likely indicate non-thermal production of dark matter in the early Universe.Comment: 20 pages, 3 figure