Atomic Model of Susy Hubbard Operators

We apply the recently proposed susy Hubbard operators to an atomic model. In the limiting case of free spins, we derive exact results for the entropy which are compared with a mean field + gaussian corrections description. We show how these results can be extended to the case of charge fluctuations and calculate exact results for the partition function, free energy and heat capacity of an atomic model for some simple examples. Wavefunctions of possible states are listed. We compare the accuracy of large N expansions of the susy spin operators with those obtained using `Schwinger bosons' and `Abrikosov pseudo-fermions'. For the atomic model, we compare results of slave boson, slave fermion, and susy Hubbard operator approximations in the physically interesting but uncontrolled limiting case of N->2. For a mixed representation of spins we estimate the accuracy of large N expansions of the atomic model. In the single box limit, we find that the lowest energy saddle-point solution reduces to simply either slave bosons or slave fermions, while for higher boxes this is not the case. The highest energy saddle-point solution has the interesting feature that it admits a small region of a mixed representation, which bears a superficial resemblance to that seen experimentally close to an antiferromagnetic quantum critical point.Comment: 17 pages + 7 pages Appendices, 14 figures. Substantial revision

Three dimensional resonating valence bond liquids and their excitations

We show that there are two types of RVB liquid phases present in three-dimensional quantum dimer models, corresponding to the deconfining phases of U(1) and Z_2 gauge theories in d=3+1. The former is found on the bipartite cubic lattice and is the generalization of the critical point in the square lattice quantum dimer model found originally by Rokhsar and Kivelson. The latter exists on the non-bipartite face-centred cubic lattice and generalizes the RVB phase found earlier by us on the triangular lattice. We discuss the excitation spectrum and the nature of the ordering in both cases. Both phases exhibit gapped spinons. In the U(1) case we find a collective, linearly dispersing, transverse excitation, which is the photon of the low energy Maxwell Lagrangian and we identify the ordering as quantum order in Wen's sense. In the Z_2 case all collective excitations are gapped and, as in d=2, the low energy description of this topologically ordered state is the purely topological BF action. As a byproduct of this analysis, we unearth a further gapless excitation, the pi0n, in the square lattice quantum dimer model at its critical point.Comment: 9 pages, 2 figure

Properties of the random field Ising model in a transverse magnetic field

We consider the effect of a random longitudinal field on the Ising model in a transverse magnetic field. For spatial dimension $d > 2$, there is at low strength of randomness and transverse field, a phase with true long range order which is destroyed at higher values of the randomness or transverse field. The properties of the quantum phase transition at zero temperature are controlled by a fixed point with no quantum fluctuations. This fixed point also controls the classical finite temperature phase transition in this model. Many critical properties of the quantum transition are therefore identical to those of the classical transition. In particular, we argue that the dynamical scaling is activated, i.e, the logarithm of the diverging time scale rises as a power of the diverging length scale

Schwinger boson theory of anisotropic ferromagnetic ultrathin films

Ferromagnetic thin films with magnetic single-ion anisotropies are studied within the framework of Schwinger bosonization of a quantum Heisenberg model. Two alternative bosonizations are discussed. We show that qualitatively correct results are obtained even at the mean-field level of the theory, similar to Schwinger boson results for other magnetic systems. In particular, the Mermin-Wagner theorem is satisfied: a spontaneous magnetization at finite temperatures is not found if the ground state of the anisotropic system exhibits a continuous degeneracy. We calculate the magnetization and effective anisotropies as functions of exchange interaction, magnetic anisotropies, external magnetic field, and temperature for arbitrary values of the spin quantum number. Magnetic reorientation transitions and effective anisotropies are discussed. The results obtained by Schwinger boson mean-field theory are compared with the many-body Green's function technique.Comment: 14 pages, including 7 EPS figures, minor changes, final version as publishe

Validation of martian meteorological data assimilation for MGS/TES using radio occultation measurements

We describe an assimilation of thermal profiles below about 40 km altitude and total dust opacities into a general circulation model (GCM) of the martian atmosphere. The data were provided by the Thermal Emission Spectrometer (TES) on board the Mars Global Surveyor (MGS) spacecraft. The results of the assimilation are verified against an independent source of contemporaneous data represented by radio occultation measurements with an ultra-stable radio oscillator, also aboard MGS. This paper describes a comparison between temperature profiles retrieved by the radio occultation experiments and the corresponding profiles given by both an independent, carefully tuned GCM simulation and by an assimilation of TES observations performed over the period of time from middle, northern summer in martian year 24, corresponding to May 1999, until late, northern spring in martian year 27, corresponding to August 2004. This study shows that the assimilation of TES measurements improves the overall agreement between radio occultation observations and the GCM analysis, in particular below 20 km altitude, where the radio occultation measurements are known to be most accurate. Discrepancies still remain, mostly during the global dust storm of year 2001 and at latitudes around 60° N in northern winter–early spring. These are the periods of time and locations, however, for which discrepancies between TES and radio occultation profiles are also shown to be the largest. Finally, a further direct validation is performed, comparing stationary waves at selected latitudes and time of year. Apart from biases at high latitudes in winter time, data assimilation is able to represent the correct wave behaviour, which is one major objective for martian assimilation

Lattice Pseudospin Model for ν=1\nu=1 Quantum Hall Bilayers

We present a new theoretical approach to the study of $\nu=1$ quantum Hall bilayer that is based on a systematic mapping of the microscopic Hamiltonian to an anisotropic SU(4) spin model on a lattice. To study the properties of this model we generalize the Heisenberg model Schwinger boson mean field theory (SBMFT) of Arovas and Auerbach to spin models with anisotropy. We calculate the temperature dependence of experimentally observable quantities, including the spin magnetization, and the differential interlayer capacitance. Our theory represents a substantial improvement over the conventional Hartree-Fock picture which neglects quantum and thermal fluctuations, and has advantages over long-wavelength effective models that fail to capture important microscopic physics at all realistic layer separations. The formalism we develop can be generalized to treat quantum Hall bilayers at filling factor $\nu=2$.Comment: 26 pages, 10 figures. The final version, to appear in PR

Hamiltonian Description of Composite Fermions: Magnetoexciton Dispersions

A microscopic Hamiltonian theory of the FQHE, developed by Shankar and myself based on the fermionic Chern-Simons approach, has recently been quite successful in calculating gaps in Fractional Quantum Hall states, and in predicting approximate scaling relations between the gaps of different fractions. I now apply this formalism towards computing magnetoexciton dispersions (including spin-flip dispersions) in the $\nu=1/3$, 2/5, and 3/7 gapped fractions, and find approximate agreement with numerical results. I also analyse the evolution of these dispersions with increasing sample thickness, modelled by a potential soft at high momenta. New results are obtained for instabilities as a function of thickness for 2/5 and 3/7, and it is shown that the spin-polarized 2/5 state, in contrast to the spin-polarized 1/3 state, cannot be described as a simple quantum ferromagnet.Comment: 18 pages, 18 encapsulated ps figure

Lattice gauge theory with baryons at strong coupling

We study the effective Hamiltonian for strong-coupling lattice QCD in the case of non-zero baryon density. In leading order the effective Hamiltonian is a generalized antiferromagnet. For naive fermions, the symmetry is U(4N_f) and the spins belong to a representation that depends on the local baryon number. Next-nearest-neighbor (nnn) terms in the Hamiltonian break the symmetry to U(N_f) x U(N_f). We transform the quantum problem to a Euclidean sigma model which we analyze in a 1/N_c expansion. In the vacuum sector we recover spontaneous breaking of chiral symmetry for the nearest-neighbor and nnn theories. For non-zero baryon density we study the nearest-neighbor theory only, and show that the pattern of spontaneous symmetry breaking depends on the baryon density.Comment: 31 pages, 5 EPS figures. Corrected Eq. (6.1

Fractionalization patterns in strongly correlated electron systems: Spin-charge separation and beyond

We discuss possible patterns of electron fractionalization in strongly interacting electron systems. A popular possibility is one in which the charge of the electron has been liberated from its Fermi statistics. Such a fractionalized phase contains in it the seed of superconductivity. Another possibility occurs when the spin of the electron, rather than its charge, is liberated from its Fermi statistics. Such a phase contains in it the seed of magnetism, rather than superconductivity. We consider models in which both of these phases occur and study possible phase transitions between them. We describe other fractionalized phases, distinct from these, in which fractions of the electron themselves fractionalize, and discuss the topological characterization of such phases. These ideas are illustrated with specific models of p-wave superconductors, Kondo lattices, and coexistence between d-wave superconductivity and antiferromagnetism.Comment: 28 pages, 11 fig

Theory of Two-Dimensional Quantum Heisenberg Antiferromagnets with a Nearly Critical Ground State

We present the general theory of clean, two-dimensional, quantum Heisenberg antiferromagnets which are close to the zero-temperature quantum transition between ground states with and without long-range N\'{e}el order. For N\'{e}el-ordered states, `nearly-critical' means that the ground state spin-stiffness, $\rho_s$, satisfies $\rho_s \ll J$, where $J$ is the nearest-neighbor exchange constant, while `nearly-critical' quantum-disordered ground states have a energy-gap, $\Delta$, towards excitations with spin-1, which satisfies $\Delta \ll J$. Under these circumstances, we show that the wavevector/frequency-dependent uniform and staggered spin susceptibilities, and the specific heat, are completely universal functions of just three thermodynamic parameters. Explicit results for the universal scaling functions are obtained by a $1/N$ expansion on the $O(N)$ quantum non-linear sigma model, and by Monte Carlo simulations. These calculations lead to a variety of testable predictions for neutron scattering, NMR, and magnetization measurements. Our results are in good agreement with a number of numerical simulations and experiments on undoped and lightly-doped $La_{2-\delta} Sr_{\delta}Cu O_4$.Comment: 81 pages, REVTEX 3.0, smaller updated version, YCTP-xxx