Sanjoy K. Sarker

Metal-Insulator Transition in the Hubbard Model on a Triangular Lattice

We discuss the results of an extensive mean-field investigation of the half-filled Hubbard model on a triangular lattice at zero temperature. At intermediate U we find a first-order metal-insulator transition from an incommensurate spiral magnetic metal to a semiconducting state with a commensurate linear spin density wave ordering stabilized by the competition between the kinetic energy and the frustrated nature of the magnetic interaction. At large U the ground state is that of a classical triangular antiferromagnet within our approximation. In the incommensurate spiral metallic phase the Fermi surface has parts in which the wave function renormalization Z is extremely small. The evolution of the Fermi surface and the broadening of the quasi-particle band along with the variation of the plasma frequency and a charge stiffness constant with U/t are discussed.

POSSIBLE EVIDENCE OF THERMODYNAMIC EQUILIBRIUM IN DARK MATTER HALOS

After deducing the density profiles and gravitational potential functions of eight galaxies from the rotation velocity data from THINGS, we find that the density decreases exponentially with the potential in substantial regions of the halos. This behavior is in agreement with that of a single-component isothermal Boltzmann gas, and it suggests that an effective description in terms of a Boltzmann gas is possible for dark matter in these regions. This could be an indication that dark matter self-interactions are sufficient in strength and number to lead to thermal equilibrium in these regions. We write down the dynamics and boundary conditions for a Boltzmann gas description and examine some of its qualitative and quantitative consequences. Solutions to the dynamical system are determined by three dimensionfull parameters, and they provide reasonable fits to the rotational velocity data in the regions where the Boltzmann-like behavior was found. Unlike in the usual approach to curve fitting, we do not assume a specific form for the dark matter density profile, and we do not require a detailed knowledge of the baryonic content of the galaxy.

Phase transition in the double-exchange model: a Schwinger boson approach

Local alignment of a conduction electrons spin with core spins caused by strong ferromagnetic coupling imposes a severe restriction on the Hilbert space. This is incorporated in a representation in which the electron is a composite object. Within a mean-field approximation we find a transition from a ferromagnetic metal to a paramagnetic state at a temperature , the Fermi temperature, i.e., there is a separation of energy scales. The electron Green function exhibits a two-fluid character: a Fermi liquid component associated with the ordered spins which disappears above , and an incoherent component with disordered spins which breaks particle-hole symmetry. Implications for manganites, which exhibit very large magnetoresistance, are discussed.

A mean-field approximation to the two-band model for copper oxide superconductors: normal-state properties

The normal-state properties of a high-Tc superconductor are studied using a mean-field approximation. It is found that the excess holes in the oxygen orbitals form unusual metallic bands. The spin of the moving hole is bound as a singlet to the underlying copper spins because of strong exchange interaction. Thus the charge carrier has charge e and spin zero. Binding causes the holes to be heavy, but not as heavy in a Kondo lattice system. It is also found that the condensation (or binding) temperature, the Fermi temperature and the band gap are distinct (i.e. there is no scaling).

COVALENT MOLECULAR BINDING IN A SUSY BACKGROUND

The Pauli exclusion principle plays an essential role in the structure of the current universe. However, in an exactly supersymmetric (susy) universe, the degeneracy of bosons and fermions plus the ability of fermions to convert in pairs to bosons implies that the effects of the Pauli principle would be largely absent. Such a universe may eventually occur through vacuum decay from our current positive vacuum energy universe to the zero vacuum energy universe of exact susy. It has been shown that in such a susy universe ionic molecular binding does exist but homonuclear diatomic molecules are left unbound. In this paper we provide a first look at covalent binding in a susy background and compare the properties of the homonuclear bound states with those of the corresponding molecules in our universe. We find that covalent binding of diatomic molecules is very strong in an exact susy universe and the interatomic distances are in general much smaller than in the broken susy universe.

Spin-charge separation and kinetic energy in the t-J model

The effect of spin-charge separation on the kinetic energy (KE) of the two-dimensional t-J model is examined. Using a sum rule, we derive an exact expression for the lowest possible KE (E b o u n d ) for any state without doubly occupied sites. The kinetic energies of the relevant slave-boson and Schwinger-boson mean-field (MF) states are found to be considerably larger than E b o u n d . The MF states exhibit complete spin-charge separation, and form the basis of a number of microscopic theories. An examination of the momentum distribution reveals that the large increase in KE of the MF states is due to excessive depletion of electrons from the bottom of the band (Schwinger boson states) and holes from the top of the band (slave boson states). To see whether the excess KE is simply due to the poor treatment of the local constraints, we solve the constraint problem analytically for the Schwinger boson MF states in the J=0 limit. This restores gauge invariance, incorrectly violated in the MF theories. The resulting state is a generalization of the Hartree-Fock state in the Hubbard model, but one that includes spin-wave excitations, removing a deficiency of the simple HF theory. Even after the constraints are imposed correctly, the MF kinetic energy is found to be much larger than E b o u n d . These results support the notion, advanced in earlier papers, that spin-charge separation in the MF state costs excessive kinetic energy, and makes the state unstable toward recombination processes which lead to superconductivity in d = 2 and a Fermi liquid state in higher dimensions.

The negative-U Hubbard model with long-range Coulomb interaction: metal–insulator transition far from half-filling

It is shown that a metal-insulator transition can occur far from half-filling in the negative-U Hubbard model in the presence of long-range repulsive interactions. Specifically, we consider the bcc lattice at an electron concentration of 2/3 and show that a CDW insulating state exists which is energetically favoured over the relevant metallic states. The repulsive interaction plays the same role as it does in stabilizing a Wigner crystal. Despite the absence of Fermi surface nesting, the CDW insulator appears at rather small values of the interaction, preceded by a CDW semimetal at even smaller values. This places severe restrictions on the region of the parameter space where superconductivity may exist. We believe that the model will show similar behaviour for other electron densities and other lattices.

Complex Quasi-Two-Dimensional Crystalline Order Embedded in VO 2 and Other Crystals

Metal oxides such as VO_{2} undergo structural transitions to low-symmetry phases characterized by intricate crystalline order, accompanied by rich electronic behavior. We derive a minimal ionic Hamiltonian based on symmetry and local energetics which describes structural transitions involving all four observed phases, in the correct order. An exact analysis shows that complexity results from the symmetry-induced constraints of the parent phase, which forces ionic displacements to form multiple interpenetrating groups using low-dimensional pathways and distant neighbors. Displacements within each group exhibit independent, quasi-two-dimensional order, which is frustrated and fragile. This selective ordering mechanism is not restricted to VO_{2}: it applies to other oxides that show similar complex order.

Consistent theory of underdoped cuprates: Evolution of the resonating valence bond state from half filling

Using continuity, we derive a renormalized Hamiltonian from the parent

Metallic conduction and superconductivity in the pseudogap phase

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