Wavefunctional approach to the bilayer \nu =1 system and a possibility for a double non-chiral pseudospin liquid

We systematically discuss candidate wave functions for the ground state of the bilayer \nu = 1 as the distance between the layers is varied. Those that describe increased intralayer correlations at finite distance show a departure from the superflid description for smaller distances. They may support finite energy meron excitations and a dissipative collective mode in the place of the Goldstone mode of the ordered phase i.e. describe a vortex metal phase, or imply even an incompressible, pseudospin liquid, behavior. Therefore they describe possible outcomes of quantum disordering at finite distance between the layers. The vortex metal phase may show up in experiments in the presence of disorder at lower temperatures and explain the observed "imperfect superfluidity", and the pseudospin liquid phase may be the cause of the thermally activated (gapped) behavior of the longitudinal and Hall resistances at higher temperatures in counterflow experiments.Comment: 10 pages, 4 figure

Pairing via Index theorem

This work is motivated by a specific point of view: at short distances and high energies the undoped and underdoped cuprates resemble the $\pi$-flux phase of the t-J model. The purpose of this paper is to present a mechanism by which pairing grows out of the doped $\pi$-flux phase. According to this mechanism pairing symmetry is determined by a parameter controlling the quantum tunneling of gauge flux quanta. For zero tunneling the symmetry is $d_{x^2-y^2}+id_{xy}$, while for large tunneling it is $d_{x^2-y^2}$. A zero-temperature critical point separates these two limits

Ground state, quasi-hole, a pair of quasihole wavefunctions and instability in bilayer quantum Hall systems

Bilayer quantum Hall system (BLQH) differ from its single layer counterparts (SLQH) by its symmetry breaking ground state and associated neutral gapless mode in the pseudo-spin sector. Due to the gapless mode, qualitatively good groundstate and low energy excited state wavefunctions at any finite distance is still unknown. We investigate this important open problem by the Composite Boson (CB) theory developed by one of the authors to study BLQH systematically. We derive the ground state, quasi-hole and a pair of quasihole wavefunctions from the CB theory and its dual action. We find that the ground state wavefunction differs from the well known $(111)$ wavefunction at any finite $d$. In addition to commonly known multiplicative factors, the quasi-hole and a pair of quasi-holes wavefunctions also contain non-trivial normalization factors multiplying the correct ground state wavefunction. All the distance dependencies in all the wavefunctions are encoded in the spin part of the ground state wavefunction. The instability encoded in the spin part of the groundstate wavefunction leads to the pseudo-spin density wave formation proposed by one of the authors previously. Some subtleties related to the Lowest Landau Level (LLL) projection of the wavefunctions are briefly discussed.Comment: 9 pages, 1 figure, REVTEX, Final version to appear in Phys. Rev.

Hierarchy wave functions--from conformal correlators to Tao-Thouless states

Laughlin's wave functions, describing the fractional quantum Hall effect at filling factors $\nu=1/(2k+1)$, can be obtained as correlation functions in conformal field theory, and recently this construction was extended to Jain's composite fermion wave functions at filling factors $\nu=n/(2kn+1)$. Here we generalize this latter construction and present ground state wave functions for all quantum Hall hierarchy states that are obtained by successive condensation of quasielectrons (as opposed to quasiholes) in the original hierarchy construction. By considering these wave functions on a cylinder, we show that they approach the exact ground states, the Tao-Thouless states, when the cylinder becomes thin. We also present wave functions for the multi-hole states, make the connection to Wen's general classification of abelian quantum Hall fluids, and discuss whether the fractional statistics of the quasiparticles can be analytically determined. Finally we discuss to what extent our wave functions can be described in the language of composite fermions.Comment: 9 page

Meron excitations in the nu =1 quantum Hall bilayer and the plasma analogy

We study meron quasiparticle excitations in the \nu = 1 quantum Hall bilayer. Considering the well known single meron state, we introduce its effective form, valid in the longdistance limit. That enables us to propose two (and more) meron states in the same limit. Further, establishing a plasma analogy of the (111) ground state, we find the impurities that play the role of merons and derive meron charge distributions. Using the introduced meron constructions in generalized (mixed) ground states and corresponding plasmas for arbitrary distance between the layers, we calculate the interaction between the construction implied impurities. We also find a correspondence between the impurity interactions and meron interactions. This suggests a possible explanation of the deconfinement of the merons recently observed in the experiments.Comment: 5 pages, 3 figure

Fractional Quantum Hall Effect and vortex lattices

It is demonstrated that all observed fractions at moderate Landau level fillings for the quantum Hall effect can be obtained without recourse to the phenomenological concept of composite fermions. The possibility to have the special topologically nontrivial many-electron wave functions is considered. Their group classification indicates the special values of of electron density in the ground states separated by a gap from excited states

MACHOs, White Dwarfs, and the Age of the Universe

(Abridged Abstract) A favored interpretation of recent microlensing measurements towards the Large Magellanic Cloud implies that a large fraction (i.e. 10--50%) of the mass of the galactic halo is composed of white dwarfs. We compare model white dwarf luminosity functions to the data from the observational surveys in order to determine a lower bound on the age of any substantial white dwarf halo population (and hence possibly on the age of the Universe). We compare various theoretical white dwarf luminosity functions, in which we vary hese three parameters, with the abovementioned survey results. From this comparison, we conclude that if white dwarfs do indeed constitute more than 10% of the local halo mass density, then the Universe must be at least 10 Gyr old for our most extreme allowed values of the parameters. When we use cooling curves that account for chemical fractionation and more likely values of the IMF and the bolometric correction, we find tighter limits: a white dwarf MACHO fraction of 10% (30%) requires a minimum age of 14 Gyr (15.5 Gyr). Our analysis also indicates that the halo white dwarfs almost certainly have helium-dominated atmospheres.Comment: Final version accepted for publication, straight TeX formate, 6 figs, 22 page

Spin Susceptibility and Gap Structure of the Fractional-Statistics Gas

This paper establishes and tests procedures which can determine the electron energy gap of the high-temperature superconductors using the $t\!-\!J$ model with spinon and holon quasiparticles obeying fractional statistics. A simpler problem with similar physics, the spin susceptibility spectrum of the spin 1/2 fractional-statistics gas, is studied. Interactions with the density oscillations of the system substantially decrease the spin gap to a value of $(0.2 \pm 0.2)$ $\hbar \omega_c$, much less than the mean-field value of $\hbar\omega_c$. The lower few Landau levels remain visible, though broadened and shifted, in the spin susceptibility. As a check of the methods, the single-particle Green's function of the non-interacting Bose gas viewed in the fermionic representation, as computed by the same approximation scheme, agrees well with the exact results. The same mechanism would reduce the gap of the $t\!-\!J$ model without eliminating it.Comment: 35 pages, written in REVTeX, 16 figures available upon request from [email protected]

Quantum Hall quasielectron operators in conformal field theory

In the conformal field theory (CFT) approach to the quantum Hall effect, the multi-electron wave functions are expressed as correlation functions in certain rational CFTs. While this approach has led to a well-understood description of the fractionally charged quasihole excitations, the quasielectrons have turned out to be much harder to handle. In particular, forming quasielectron states requires non-local operators, in sharp contrast to quasiholes that can be created by local chiral vertex operators. In both cases, the operators are strongly constrained by general requirements of symmetry, braiding and fusion. Here we construct a quasielectron operator satisfying these demands and show that it reproduces known good quasiparticle wave functions, as well as predicts new ones. In particular we propose explicit wave functions for quasielectron excitations of the Moore-Read Pfaffian state. Further, this operator allows us to explicitly express the composite fermion wave functions in the positive Jain series in hierarchical form, thus settling a longtime controversy. We also critically discuss the status of the fractional statistics of quasiparticles in the Abelian hierarchical quantum Hall states, and argue that our construction of localized quasielectron states sheds new light on their statistics. At the technical level we introduce a generalized normal ordering, that allows us to "fuse" an electron operator with the inverse of an hole operator, and also an alternative approach to the background charge needed to neutralize CFT correlators. As a result we get a fully holomorphic CFT representation of a large set of quantum Hall wave functions.Comment: minor changes, publishe

Statistical Interparticle Potential between Two Anyons

The density matrix of a two-anyon system is evaluated and used to investigate the "statistical interparticle potential" following the theory of Uhlenbeck. The main purpose is to see how the statistical potential will depend on the fractional statistical parameter $\alpha$. The result shows that the statistical potential for a two-anyon system with $\alpha\ge {1\over2}$ is always repulsive. For the system with $0<\alpha< {1\over2}$, the potential is repulsive at short distances and becomes attractive at long distances. It remains only in the boson system ($\alpha=0$) that the repulsive potential arising from the exclusion principle can disappear and lead to an attractive potential at all distances.Comment: Latex 5 pages, correct typos and figur