Renormalization algorithm for the calculation of spectra of interacting quantum systems

We present an algorithm for the calculation of eigenstates with definite linear momentum in quantum lattices. Our method is related to the Density Matrix Renormalization Group, and makes use of the distribution of multipartite entanglement to build variational wave--functions with translational symmetry. Its virtues are shown in the study of bilinear--biquadratic S=1 chains.Comment: Corrected version. We have added an appendix with an extended explanation of the implementation of our algorith

Schwinger-Boson Mean-Field Theory of Mixed-Spin Antiferromagnet L2BaNiO5L_2BaNiO_5

The Schwinger-boson mean-field theory is used to study the three-dimensional antiferromagnetic ordering and excitations in compounds $L_2BaNiO_5$, a large family of quasi-one-dimensional mixed-spin antiferromagnet. To investigate magnetic properties of these compounds, we introduce a three-dimensional mixed-spin antiferromagnetic Heisenberg model based on experimental results for the crystal structure of $L_2BaNiO_5$. This model can explain the experimental discovery of coexistence of Haldane gap and antiferromagnetic long-range order below N\'{e}el temperature. Properties such as the low-lying excitations, magnetizations of $Ni$ and rare-earth ions, N\'{e}el temperatures of different compounds, and the behavior of Haldane gap below the N\'{e}el temperature are investigated within this model, and the results are in good agreement with neutron scattering experiments.Comment: 12 pages, 6 figure

Spin and orbital valence bond solids in a one-dimensional spin-orbital system: Schwinger boson mean field theory

A generalized one-dimensional $SU(2)\times SU(2)$ spin-orbital model is studied by Schwinger boson mean-field theory (SBMFT). We explore mainly the dimer phases and clarify how to capture properly the low temperature properties of such a system by SBMFT. The phase diagrams are exemplified. The three dimer phases, orbital valence bond solid (OVB) state, spin valence bond solid (SVB) state and spin-orbital valence bond solid (SOVB) state, are found to be favored in respectively proper parameter regions, and they can be characterized by the static spin and pseudospin susceptibilities calculated in SBMFT scheme. The result reveals that the spin-orbit coupling of $SU(2)\times SU(2)$ type serves as both the spin-Peierls and orbital-Peierles mechanisms that responsible for the spin-singlet and orbital-singlet formations respectively.Comment: 6 pages, 3 figure

Quantum antiferromagnetism and high TCT_C superconductivity: a close connection between the t-J model and the projected BCS Hamiltonian

A connection between quantum antiferromagnetism and high $T_C$ superconductivity is theoretically investigated by analyzing the t-J model and its relationships to the Gutzwiller-projected BCS Hamiltonian. After numerical corroboration via exact diagonalization, it is analytically shown that the ground state of the t-J model at half filling (i.e., the 2D antiferromagnetic Heisenberg model) is entirely equivalent to the ground state of the Gutzwiller-projected BCS Hamiltonian with strong pairing. Combined with the high wavefunction overlap between the ground states of the t-J model and the projected BCS Hamiltonian at moderate doping, this equivalence provides strong support for the existence of superconductivity in the t-J model. The relationship between the ground state of the projected BCS Hamiltonian and Anderson's resonating valence bond state (i.e., the projected BCS ground state) is discussed.Comment: 18 pages, 9 figures, the final version published in Phys. Rev.

Spin 3/2 dimer model

We present a parent Hamiltonian for weakly dimerized valence bond solid states for arbitrary half-integral S. While the model reduces for S=1/2 to the Majumdar-Ghosh Hamiltonian we discuss this model and its properties for S=3/2. Its degenerate ground state is the most popular toy model state for discussing dimerization in spin 3/2 chains. In particular, it describes the impurity induced dimer phase in Cr8Ni as proposed recently. We point out that the explicit construction of the Hamiltonian and its main features apply to arbitrary half-integral spin S.Comment: 5+ pages, 6 figures; to appear in Europhysics Letter

Low-Temperature Properties of Two-Dimensional Ideal Ferromagnets

The manifestation of the spin-wave interaction in the low-temperature series of the partition function has been investigated extensively over more than seven decades in the case of the three-dimensional ferromagnet. Surprisingly, the same problem regarding ferromagnets in two spatial dimensions, to the best of our knowledge, has never been addressed in a systematic way so far. In the present paper the low-temperature properties of two-dimensional ideal ferromagnets are analyzed within the model-independent method of effective Lagrangians. The low-temperature expansion of the partition function is evaluated up to two-loop order and the general structure of this series is discussed, including the effect of a weak external magnetic field. Our results apply to two-dimensional ideal ferromagnets which exhibit a spontaneously broken spin rotation symmetry O(3) $\to$ O(2) and are defined on a square, honeycomb, triangular or Kagom\'e lattice. Remarkably, the spin-wave interaction only sets in at three-loop order. In particular, there is no interaction term of order $T^3$ in the low-temperature series for the free energy density. This is the analog of the statement that, in the case of three-dimensional ferromagnets, there is no interaction term of order $T^4$ in the free energy density. We also provide a careful discussion of the implications of the Mermin-Wagner theorem in the present context and thereby put our low-temperature expansions on safe grounds.Comment: 24 pages, 3 figure

GROWTH AND MOVEMENT OF SMALLMOUTH BUFFALO, ICTIOBUS BUBALUS (RAFINESQUE), IN WATTS BAR RESERVOIR, TENNESSEE

The smallmouth buffalo fish, Ictiobus bubalus (Rafinesque), population of Watts Bar Reservoir, of the Tennessee River down stream from Oak Ridge National Laboratory, was investigated in order to describe its age distribution, growth rates, dispersion, and importance as an accumulator of radionuclides. Measurements and scale samples were taken from commercially-caught fish and fish caught in the ORNL tagging operations. Scale impressions were anaiyzed for age and growth phenomena. Dispersion of smallmouth buffalo was investigated by conventional of ging methods and by autoradiographic analyses of scales. Stable and radiochemicsl composition of scales was examined by spectrographic analysis, flame spectrophotometer and radiometric surveys. Calcium was the most abundance element in fish scales with at lease twenty-three other elements present in varying quantities. Fish scaless and bone were found to contain radionuclides of ruthenium, cesium, zirconium, zinc, and cobalt. Radiometric surveys of scales revealed the Watts Bar Reservoir smallmouth buffalo population was a relatively minor accumulator of radionuclides with only 0.08 per cent showing the presence of artificially produced radionuclides. Approximately 6 per cent of the Clinch River fish and 77 per cent of the White Oak Creek fish had accumulations. Limited data on dispersion were determined from conventional tags. Much more dispersion and life history data were determined from autoradiographic analyses of scales. These dispersion data were applied only to individuals because the number was too small for generalizations for the population as a whole. All normal scales containing radionuclide accumulations were found to produce identical autoradiographic patterns of concentric circles which were associated with growth of the fish in contaminated areas. This phenomenon was combined with conventional capture-recapture methods of population estimates in a proposed technique of population studies. A laboratory experiment showed that scales could be tagged with cesium-134, but this radionuclide was found to accumulate in much larger concentrations in the soft tissues than in the bony tissues. (C.H.

Chromosomal aberrations in a natural population of chironomus tentans exposed to chronic low-level environmental radiation

The salivary gland chromosomes of Chironomus tentans larvae collected from White Oak Creek, an area contaminated by radioactive waste from the Oak Ridge National Laboratory, and from six uncontaminated areas were examined for chromosomal aberrations. White Oak Creek populations were exposed to absorbed doses as high as 230 rads per year or about 1000 times background. Chromosomal maps were constructed to make a general comparison of the banding pattern of the salivary chromosomes of the C. tentans in the East Tennessee area with those of Canada and Europe. These maps were used as a reference in scoring aberrations. Fifteen different chromosomal aberrations were found in 365 larvae taken from the irradiated population as compared with five different aberrations observed in 356 larvae from six control populations, but the mean number of aberrations per larva did not differ in any of the populations. The quantitative amount of heterozygosity was essentially the same in the irradiated and the control population, but there were three times the variety of chromosomal aberrations found in the irradiated area. From this evidence it was concluded that chronic low-level irradiation from radioactive waste was increasing the variability of chromosomal aberrations without significantly increasing the frequency. It was also concluded that chromosomal polymorphism can be maintained in a natural population without superiority of the heterozygous individuals. (C.H.

Effective Spin Quantum Phases in Systems of Trapped Ions

A system of trapped ions under the action of off--resonant standing--waves can be used to simulate a variety of quantum spin models. In this work, we describe theoretically quantum phases that can be observed in the simplest realization of this idea: quantum Ising and XY models. Our numerical calculations with the Density Matrix Renormalization Group method show that experiments with ion traps should allow one to access general properties of quantum critical systems. On the other hand, ion trap quantum spin models show a few novel features due to the peculiarities of induced effective spin--spin interactions which lead to interesting effects like long--range quantum correlations and the coexistence of different spin phases.Comment: 11 pages, 13 figure

Bounds on Decoherence and Error

When a confined system interacts with its walls (treated quantum mechanically), there is an intertwining of degrees of freedom. We show that this need not lead to entanglement, hence decoherence. It will generally lead to error. The wave function optimization required to avoid decoherence is also examined.Comment: 10 pages, plain TeX, no figure