Peak Values of Conductivity in Integer and Fractional Quantum Hall Effect

The diagonal conductivity $\sigma_{xx}$ was measured in the Corbino geometry in both integer and fractional quantum Hall effect (QHE). We find that peak values of $\sigma_{xx}$ are approximately equal for transitions in a wide range of integer filling factors $3<\nu<16$, as expected in scaling theories of QHE. This fact allows us to compare peak values in the integer and fractional regimes within the framework of the law of corresponding states.Comment: 8 pages (revtex format), 3 postscript figure

Logarithmic temperature dependence of conductivity at half-integer filling factors: Evidence for interaction between composite fermions

We have studied the temperature dependence of diagonal conductivity in high-mobility two-dimensional samples at filling factors $\nu=1/2$ and 3/2 at low temperatures. We observe a logarithmic dependence on temperature, from our lowest temperature of 13 mK up to 400 mK. We attribute the logarithmic correction to the effects of interaction between composite fermions, analogous to the Altshuler-Aronov type correction for electrons at zero magnetic field. The paper is accepted for publication in Physical Review B, Rapid Communications.Comment: uses revtex macro

Characterization of fractional-quantum-Hall-effect quasiparticles

Composite fermions in a partially filled quasi-Landau level may be viewed as quasielectrons of the underlying fractional quantum Hall state, suggesting that a quasielectron is simply a dressed electron, as often is true in other interacting electron systems, and as a result has the same intrinsic charge and exchange statistics as an electron. This paper discusses how this result is reconciled with the earlier picture in which quasiparticles are viewed as fractionally-charged fractional-statistics ``solitons". While the two approaches provide the same answers for the long-range interactions between the quasiparticles, the dressed-electron description is more conventional and unifies the view of quasiparticle dynamics in and beyond the fractional quantum Hall regime.Comment: 11 pages, latex, no figure

Composite-fermion crystallites in quantum dots

The correlations in the ground state of interacting electrons in a two-dimensional quantum dot in a high magnetic field are known to undergo a qualitative change from liquid-like to crystal-like as the total angular momentum becomes large. We show that the composite-fermion theory provides an excellent account of the states in both regimes. The quantum mechanical formation of composite fermions with a large number of attached vortices automatically generates omposite fermion crystallites in finite quantum dots.Comment: 5 pages, 3 figure

A Multicritical Point with Infinite Fractal Symmetries

Recently a ``Pascal's triangle model" constructed with $\text{U}(1)$ rotor degrees of freedom was introduced, and it was shown that ($\textit{i}$.) this model possesses an infinite series of fractal symmetries; and ($\textit{ii}$.) it is the parent model of a series of $Z_p$ fractal models each with its own distinct fractal symmetry. In this work we discuss a multi-critical point of the Pascal's triangle model that is analogous to the Rokhsar-Kivelson (RK) point of the better known quantum dimer model. We demonstrate that the expectation value of the characteristic operator of each fractal symmetry at this multi-critical point decays as a power-law of space, and this multi-critical point is shared by the family of descendent $Z_p$ fractal models. Afterwards, we generalize our discussion to a $(3+1)d$ model termed the ``Pascal's tetrahedron model" that has both planar and fractal subsystem symmetries. We also establish a connection between the Pascal's tetrahedron model and the $\text{U}(1)$ Haah's code.Comment: 10.5 pages, 4 figure

Conformal Field Theories generated by Chern Insulators under Quantum Decoherence

We demonstrate that the fidelity between a pure state trivial insulator and the mixed state density matrix of a Chern insulator under decoherence can be mapped to a variety of two-dimensional conformal field theories (CFT); more specifically, the quantity $\mathcal{Z} = \text{tr}\{ \hat{\rho}^D_c \hat{\rho}_\Omega \}$ is mapped to the partition function of the desired CFT, where $\hat{\rho}^D_c$ and $\hat{\rho}_\Omega$ are respectively the density matrices of the decohered Chern insulator and a pure state trivial insulator. For a pure state Chern insulator with Chern number $2N$, the fidelity $\mathcal{Z}$ is mapped to the partition function of the $\text{U}(2N)_1$ CFT; under weak decoherence, the Chern insulator density matrix can experience certain instability, and the "partition function" $\mathcal{Z}$ can flow to other interacting CFTs with smaller central charges. The R\'{e}nyi relative entropy $\mathcal{F} = - \log \text{tr}\{ \hat{\rho}^D_c \hat{\rho}_\Omega \}$ is mapped to the free energy of the CFT, and we demonstrate that the central charge of the CFT can be extracted from the finite size scaling of $\mathcal{F}$, analogous to the well-known finite size scaling of $2d$ CFT.Comment: 8.5 pages, including reference

3-[(2-Formyl­thio­phen-3-yl)(hy­droxy)meth­yl]thio­phene-2-carbaldehyde

In the title compound, C11H8O3S2, the dihedral angle between the mean planes of the two thio­phene rings is 65.10 (10)°. Intra­molecular C—H⋯O inter­actions form S(6) and S(7) ring motifs. In the crystal, chains along the a axis are formed by C—H⋯O inter­actions. Adjacent chains are connected into a three-dimensional network by C—H⋯O and O—H⋯O inter­actions

Composite Fermion Description of Correlated Electrons in Quantum Dots: Low Zeeman Energy Limit

We study the applicability of composite fermion theory to electrons in two-dimensional parabolically-confined quantum dots in a strong perpendicular magnetic field in the limit of low Zeeman energy. The non-interacting composite fermion spectrum correctly specifies the primary features of this system. Additional features are relatively small, indicating that the residual interaction between the composite fermions is weak. \footnote{Published in Phys. Rev. B {\bf 52}, 2798 (1995).}Comment: 15 pages, 7 postscript figure