Invariants of the Haldane-Shastry SU(N)SU(N) Chain

Using a formalism developed by Polychronakos, we explicitly construct a set of invariants of the motion for the Haldane-Shastry $SU(N)$ chain.Comment: 11 pages, UVA-92-0

Electronic Structure of LuRh2Si2: "Small" Fermi Surface Reference to YbRh2Si2

We present band structure calculations and quantum oscillation measurements on LuRh2Si2, which is an ideal reference to the intensively studied quantum critical heavy-fermion system YbRh2Si2. Our band structure calculations show a strong sensitivity of the Fermi surface on the position of the silicon atoms zSi within the unit cell. Single crystal structure refinement and comparison of predicted and observed quantum oscillation frequencies and masses yield zSi = 0.379c in good agreement with numerical lattice relaxation. This value of zSi is suggested for future band structure calculations on LuRh2Si2 and YbRh2Si2. LuRh2Si2 with a full f electron shell represents the "small" Fermi surface configuration of YbRh2Si2. Our experimentally and ab initio derived quantum oscillation frequencies of LuRh2Si2 show strong differences with earlier measurements on YbRh2Si2. Consequently, our results confirm the contribution of the f electrons to the Fermi surface of YbRh2Si2 at high magnetic fields. Yet the limited agreement with refined fully itinerant local density approximation calculations highlights the need for more elaborated models to describe the Fermi surface of YbRh2Si2.Comment: 12 pages 10 figure

Starburst Galaxies: Why the Calzetti Dust Extinction Law?

The empirical reddening function for starburst galaxies generated by Calzetti and her co-workers has proven very successful, and is now used widely in the observational literature. Despite its success, however, the physical basis for this extinction law, or more correctly, attenuation law remains weak. Here we provide a physical explanation for the Calzetti Law based on a turbulent interstellar medium. In essence, this provides a log-normal distribution of column densities, giving a wide range of column densities in the dusty foreground screen. Therefore, extended sources such as starburst regions or HII regions seen through it suffer a point-to-point stochastic extinction and reddening. Regions of high column densities are "black" in the UV, but translucent in the IR, which leads to a flatter extinction law, and a larger value of the total to selective extinction, R_V. We fit the Calzetti Law, and infer that the variance sigma of the log-normal distribution lies in the range 0.6<sigma<2.2. The absolute to selective extinction R_V is found to be in the range 4.3 to 5.2 consistent with R_V=4.05+/-0.80 of the Calzetti Law.Comment: accepted for publication in ApJ

Taxonomy of particles in Ising spin chains

The statistical mechanics of particles with shapes on a one-dimensional lattice is investigated in the context of the $s=1$ Ising chain with uniform nearest-neighbor coupling, quadratic single-site potential, and magnetic field, which supports four distinct ground states: $|\uparrow\downarrow\uparrow\downarrow...>$, $|\circ\circ...>$, $|\uparrow\uparrow...>$, $|\uparrow\circ\uparrow\circ...>$. The complete spectrum is generated from each ground state by particles from a different set of six or seven species. Particles and elements of pseudo-vacuum are characterized by motifs (patterns of several consecutive site variables). Particles are floating objects that can be placed into open slots on the lattice. Open slots are recognized as permissible links between motifs. The energy of a particle varies between species but is independent of where it is placed. Placement of one particle changes the open-slot configuration for particles of all species. This statistical interaction is encoded in a generalized Pauli principle, from which the multiplicity of states for a given particle combination is determined and used for the exact statistical mechanical analysis. Particles from all species belong to one of four categories: compacts, hosts, tags, or hybrids. Compacts and hosts find open slots in segments of pseudo-vacuum. Tags find open slots inside hosts. Hybrids are tags with hosting capability. In the taxonomy of particles proposed here, `species' is indicative of structure and `category' indicative of function. The hosting function splits the Pauli principle into exclusion and accommodation parts. Near phase boundaries, the state of the Ising chain at low temperature is akin to that of miscible or immiscible liquids with particles from one species acting as surfactant molecules.Comment: 12 pages, 6 tables, 6 figure

Statistically interacting quasiparticles in Ising chains

The exclusion statistics of two complementary sets of quasiparticles, generated from opposite ends of the spectrum, are identified for Ising chains with spin s=1/2,1. In the s=1/2 case the two sets are antiferromagnetic domain walls (solitons) and ferromagnetic domains (strings). In the s=1 case they are soliton pairs and nested strings, respectively. The Ising model is equivalent to a system of two species of solitons for s=1/2 and to a system of six species of soliton pairs for s=1. Solitons exist on single bonds but soliton pairs may be spread across many bonds. The thermodynamics of a system of domains spanning up to $M$ lattice sites is amenable to exact analysis and shown to become equivalent, in the limit M -> infinity, to the thermodynamics of the s=1/2 Ising chain. A relation is presented between the solitons in the Ising limit and the spinons in the XX limit of the s=1/2 XXZ chain.Comment: 18 pages and 4 figure

Are the Narrow Line Regions in Active Galaxies Dusty and Radiation Pressure Dominated?

The remarkable similarity between emission spectra of narrow line regions (NLR) in Seyfert Galaxies has long presented a mystery. In photoionization models, this similarity implies that the ionization parameter is nearly always the same, about U ~ 0.01. Here we present dusty, radiation-pressure dominated photoionization models that can provide natural physical insight into this problem. In these models, dust and the radiation pressure acting on it provide the controlling factor in moderating the density, excitation and surface brightness of photoionized NLR structures. Additionally, photoelectric heating by the dust is important in determining the temperature structure of the models. These models can also explain the coexistence of the low-, intermediate- and coronal ionization zones within a single self-consistent physical structure. The radiation pressure acting on dust may also be capable of driving the fast (~3000 km/s) outflows such as are seen in the HST observations of NGC 1068.Comment: 23 pages, 8 figures, Accepted by Ap

Thermodynamics of statistically interacting quantum gas in D dimensions

We present the exact thermodynamics (isochores, isotherms, isobars, response functions) of a statistically interacting quantum gas in D dimensions. The results in D=1 are those of the thermodynamic Bethe ansatz for the nonlinear Schroedinger model, a gas with repulsive two-body contact potential. In all dimensions the ideal boson and fermion gases are recovered in the weak-coupling and strong-coupling limits, respectively. For all nonzero couplings ideal fermion gas behavior emerges for D>>1 and, in the limit D->infinity, a phase transition occurs at T>0. Significant deviations from ideal quantum gas behavior are found for intermediate coupling and finite D.Comment: 12 pages and 19 figure

Strong in-plane anisotropy in the electronic structure of fixed-valence β\beta-LuAlB4_4

The origin of intrinsic quantum criticality in the heavy-fermion superconductor $\beta$-YbAlB$_4$ has been attributed to strong Yb valence fluctuations and its peculiar crystal structure. Here, we assess these contributions individually by studying the isostructural but fixed-valence compound $\beta$-LuAlB$_4$. Quantum oscillation measurements and DFT calculations reveal a Fermi surface markedly different from that of $\beta$-YbAlB$_4$, consistent with a `large' Fermi surface there. We also find an unexpected in-plane anisotropy of the electronic structure, in contrast to the isotropic Kondo hybridization in $\beta$-YbAlB$_4$.Comment: 6 pages, 4 figure

Ground State and Excitations of Spin Chain with Orbital Degeneracy

The one dimensional Heisenberg model in the presence of orbital degeneracy is studied at the SU(4) symmetric viewpoint by means of Bethe ansatz. Following Sutherland's previous work on an equivalent model, we discuss the ground state and the low-lying excitations more extensively in connection to the spin systems with orbital degeneracy. We show explicitly that the ground state is a SU(4) singlet. We study the degeneracies of the elementary excitations and the spectra of the generalized magnons consisting of these excitations. We also discuss the complex 2-strings in the context of the Bethe ansatz solutions.Comment: Revtex, 9 pages, 3 figures; typos correcte