Spin density wave selection in the one-dimensional Hubbard model

The Hartree-Fock ground state phase diagram of the one-dimensional Hubbard model is calculated, constrained to uniform phases, which have no charge density modulation. The allowed solutions are saturated ferromagnetism (FM), a spiral spin density wave (SSDW) and a double spin density wave} (DSDW). The DSDW phase comprises two canted interpenetrating antiferromagnetic sublattices. FM occurs for small filling, SSDW in most of the remainder of the phase diagram, and DSDW in a narrow tongue near quarter (and three-quarter) filling. Itinerant electrons lift the degeneracy with respect to canting angle in the DSDW. The Hartree-Fock states are metallic except at multiples of a quarter filling. Near half filling the uniform SSDW phase is unstable against phase separation into a half-filled antiferromagnetic phase and a hole-rich SSDW phase. The dependence of the ground state wave number on chemical potential is conjectured to be a staircase. Comparison is made with higher dimensional Hubbard models and the $J_{1}-J_{2}$ Heisenberg model.Comment: 15 pages LaTeX, 5 Postscript figures in uuencoded file. To appear in J Phys: Condensed Matter. Requires files ioplppt.sty, iopl10.sty, iopl12.sty (available at http://www.ioppublishing.com/Journals/texstyle.html

Phase-space path-integral calculation of the Wigner function

The Wigner function W(q,p) is formulated as a phase-space path integral, whereby its sign oscillations can be seen to follow from interference between the geometrical phases of the paths. The approach has similarities to the path-centroid method in the configuration-space path integral. Paths can be classified by the mid-point of their ends; short paths where the mid-point is close to (q,p) and which lie in regions of low energy (low P function of the Hamiltonian) will dominate, and the enclosed area will determine the sign of the Wigner function. As a demonstration, the method is applied to a sequence of density matrices interpolating between a Poissonian number distribution and a number state, each member of which can be represented exactly by a discretized path integral with a finite number of vertices. Saddle point evaluation of these integrals recovers (up to a constant factor) the WKB approximation to the Wigner function of a number state.Comment: 16 pages. Small number of typos corrected, including sign in eq A2

Exact Classical Effective Potential

A quantum spin system can be modelled by an equivalent classical system, with an effective Hamiltonian obtained by integrating all non-zero frequency modes out of the path integral. The effective Hamiltonian H_eff(S_i) derived from the coherent-state integral is highly singular: the quasiprobability density exp(-beta H_eff), a Wigner function, imposes quantisation through derivatives of delta functions. This quasiprobability is the distribution of the time-averaged lower symbol of the spin in the coherent-state integral. We relate the quantum Monte Carlo minus-sign problem to the non-positivity of this quasiprobability, both analytically and by Monte Carlo integration.Comment: 4 page

Electron energy analyzer

Electrostatic deflection analyzer with three spherically concentric grids allows production of electrons within a small volume at the center of the inner sphere. By applying a retarding potential between the middle and inner spheres, the energies of the electrons can be measured

Absorption cross sections of minor constituents in planetary atmospheres from 1050 to 2100 angstrom

Absorption cross sections of minor constituent gases in planetary atmospheres from 1050 to 2100

On the ionization potential of molecular oxygen

The ionization potential of O2 was measured by the technique of high resolution photoelectron spectroscopy taking into account the influence of rotational structure on the shape of the vibrational bands. A value of 12.071 + or - .001 eV (1027.1 + or - 0.1 A) was found for the ionization potential. A lowering of the ionization potential caused by a branch-head when delta N = -2 gave an appearance potential for ionization of 12.068 + or - .001 eV (1027.4 + or - 0.1 A)

Vibrational intensity distributions for continuum photoionization of oxygen

Results from measurements of vibrational intensity distributions for continuum photoionization of O2 are reported. Measurements were made using the 584 and 304 A He lines. The photoionization cross section of O2 shows a substantial dip in magnitude over a 20 A band centered about 590 A; thus the possibility exists that a 584 A photoelectron spectrum of O2 includes an autoionized contribution and the vibrational intensity distributions may not correspond to those of continuum ionization. Oxygen photoionization cross section shows no structure around 304 A and purley continuum ionization is expected

Collecting efficiency of a cylindrical mirror electron energy analyzer with preretarding lens

The electron collecting efficiency of a cylindrical mirror energy analyzer incorporating retardation of the electrons prior to analysis has been determined over the range 0 to 30 eV by two methods. The first method requires the use of a vacuum ultraviolet monochromator to produce monoenergetic electrons of different energies; the second method involves measuring the energy-brightness relationship of the retarding optics and should be applicable to any deflection analyzer with pre-retarding optics. The results of the two methods are compared and the limitations of the latter method are discussed