Lazy AC-Pattern Matching for Rewriting

We define a lazy pattern-matching mechanism modulo associativity and commutativity. The solutions of a pattern-matching problem are stored in a lazy list composed of a first substitution at the head and a non-evaluated object that encodes the remaining computations. We integrate the lazy AC-matching in a strategy language: rewriting rule and strategy application produce a lazy list of terms.Comment: In Proceedings WRS 2011, arXiv:1204.531

Half-Integral Spin-Singlet Quantum Hall Effect

We provide numerical evidence that the ground state of a short range interaction model at $\nu=1/2$ is incompressible and spin-singlet for a wide range of repulsive interactions. Furthermore it is accurately described by a trial wave function studied earlier. For the Coulomb interaction we find that this wave function provides a good description of the lowest lying spin-singlet state, and propose that fractional quantum Hall effect would occur at $\nu=1/2$ if this state became the global ground state.Comment: Latex 13 pages, 3 figures upon reques

Possibility of p-wave pairing of composite fermions at ν=1/2\nu=1/2

We find that for the pure Coulomb repulsion the composite Fermi sea at $\nu=1/2$ is on the verge of an instability to triplet pairing of composite fermions. It is argued that a transition into the paired state, described by a Pfaffian wave function, may be induced if the short-range part of the interaction is softened by increasing the thickness of the two-dimensional electron system.Comment: 14 pages, 3 eps figures include

Deviations from Fermi-liquid behavior above TcT_c in 2D short coherence length superconductors

We show that there are qualitative differences between the temperature dependence of the spin and charge correlations in the normal state of the 2D attractive Hubbard model using quantum Monte Carlo simulations. The one-particle density of states shows a pseudogap above \tc with a depleted $N(0)$ with decreasing $T$. The susceptibility \cs and the low frequency spin spectral weight track $N(0)$, which explains the spin-gap scaling: 1/T_1T \sim \cs(T). However the charge channel is dominated by collective behavior and the compressibility $dn/d\mu$ is $T$-independent. This anomalous ``spin-charge separation'' is shown to exist even at intermediate $|U|$ where the momentum distribution n(\bk) gives evidence for degenerate Fermi system.Comment: 4 pages (twocolumn format), 5 Postscript figure

Quantum Hall effect in single wide quantum wells

We study the quantum Hall states in the lowest Landau level for a single wide quantum well. Due to a separation of charges to opposite sides of the well, a single wide well can be modelled as an effective two level system. We provide numerical evidence of the existence of a phase transition from an incompressible to a compressible state as the electron density is increased for specific well width. Our numerical results show a critical electron density which depends on well width, beyond which a transition incompressible double layer quantum Hall state to a mono-layer compressible state occurs. We also calculate the related phase boundary corresponding to destruction of the collective mode energy gap. We show that the effective tunneling term and the interlayer separation are both renormalised by the strong magnetic field. We also exploite the local density functional techniques in the presence of strong magnetic field at $\nu=1$ to calculate renormalized $\Delta_{SAS}$. The numerical results shows good agreement between many-body calculations and local density functional techniques in the presence of a strong magnetic field at $\nu=1$. we also discuss implications of this work on the $\nu=1/2$ incompressible state observed in SWQW.Comment: 30 pages, 7 figures (figures are not included

Nonperturbative XY-model approach to strong coupling superconductivity in two and three dimensions

For an electron gas with delta-function attraction we investigate the crossover from weak- to strong-coupling supercoductivity in two and three dimensions. We derive analytic expressions for the stiffness of phase fluctuations and set up effective XY-models which serve to determine nonperturbatively the temperature of phase decoherence where superconductivity breaks down. We find the transition temperature T_c as a monotonous function of the coupling strength and carrier density both in two and three dimensions, and give analytic formulas for the merging of the temperature of phase decoherence with the temperature of pair formation in the weak-coupling limit.Comment: Few typos corrected. Emails that were sent to the address [email protected] in June and July 1999 were lost in a computer crash, so if your comments were not answered please send them once mor

Electron Correlations in Partially Filled Lowest and Excited Landau Levels

The electron correlations near the half-filling of the lowest and excited Landau levels (LL's) are studied using numerical diagonalization. It is shown that in the low lying states electrons avoid pair states with relative angular momenta ${\cal R}$ corresponding to positive anharmonicity of the interaction pseudopotential $V({\cal R})$. In the lowest LL, the super-harmonic behavior of $V({\cal R})$ causes Laughlin correlations (avoiding pairs with ${\cal R}=1$) and the Laughlin-Jain series of incompressible ground states. In the first excited LL, $V({\cal R})$ is harmonic at short range and a different series of incompressible states results. Similar correlations occur in the paired Moore-Read $\nu={5\over2}$ state and in the $\nu={7\over3}$ and ${8\over3}$ states, all having small total parentage from ${\cal R}=1$ and 3 and large parentage from ${\cal R}=5$. The $\nu={7\over3}$ and ${8\over3}$ states are different from Laughlin $\nu={1\over3}$ and ${2\over3}$ states and, in finite systems, occur at a different LL degeneracy (flux). The series of Laughlin correlated states of electron pairs at $\nu=2+2/(q_2+2)={8\over3}$, ${5\over2}$, ${12\over5}$, and ${7\over3}$ is proposed, although only in the $\nu={5\over2}$ state pairing has been confirmed numerically. In the second excited LL, $V({\cal R})$ is sub-harmonic at short range and (near the half-filling) the electrons group into spatially separated larger $\nu=1$ droplets to minimize the number of strongly repulsive pair states at ${\cal R}=3$ and 5.Comment: 10 pages, 8 figures, submitted to PR

Charge Density Wave in Two-Dimensional Electron Liquid in Weak Magnetic Field

We study the ground state of a clean two-dimensional electron liquid in a weak magnetic field where $N \gg 1$ lower Landau levels are completely filled and the upper level is partially filled. It is shown that the electrons at the upper Landau level form domains with filling factor equal to one and zero. The domains alternate with a spatial period of order of the cyclotron radius, which is much larger than the interparticle distance at the upper Landau level. The one-particle density of states, which can be probed by tunneling experiments, is shown to have a pseudogap linearly dependent on the magnetic field in the limit of large $N$.Comment: Several errors correcte

Spontaneous Interlayer Coherence in Double-Layer Quantum Hall Systems: Symmetry Breaking Interactions, In-Plane Fields and Phase Solitons

At strong magnetic fields double-layer two-dimensional-electron-gas systems can form an unusual broken symmetry state with spontaneous inter-layer phase coherence. The system can be mapped to an equivalent system of pseudospin $1/2$ particles with pseudospin-dependent interactions and easy-plane magnetic order. In this paper we discuss how the presence of a weak interlayer tunneling term alters the properties of double-layer systems when the broken symmetry is present. We use the energy functional and equations of motion derived earlier to evaluate the zero-temperature response functions of the double-layer system and use our results to discuss analogies between this system and Josephson-coupled superconducting films. We also present a qualitative picture of the low-energy charged excitations of this system. We show that parallel fields induce a highly collective phase transition to an incommensurate state with broken translational symmetry.Comment: 26 pages, RevTex, 8 postscript figures (submitted to Phys. Rev. B

Fermionic Chern-Simons theory for the Fractional Quantum Hall Effect in Bilayers

We generalize the fermion Chern-Simons theory for the Fractional Hall Effect (FQHE) which we developed before, to the case of bilayer systems. We study the complete dynamic response of these systems and predict the experimentally accessible optical properties. In general, for the so called $(m, m, n)$ states, we find that the spectrum of collective excitations has a gap, and the wave function has the Jastrow-Slater form, with the exponents determined by the coefficients $m$, and $n$. We also find that the $(m,m,m)$ states, {\it i.~e.~}, those states whose filling fraction is $1\over m$, have a gapless mode which may be related with the spontaneous appearance of the interlayer coherence. Our results also indicate that the gapless mode makes a contribution to the wave function of the $(m,m,m)$ states analogous to the phonon contribution to the wave function of superfluid $\rm{He}_4$. We calculate the Hall conductance, and the charge and statistics of the quasiparticles. We also present an $SU(2)$ generalization of this theory relevant to spin unpolarized or partially polarized single layers.Comment: 55 pages, Urbana Prepin