Strong Correlation to Weak Correlation Phase Transition in Bilayer Quantum Hall Systems

At small layer separations, the ground state of a nu=1 bilayer quantum Hall system exhibits spontaneous interlayer phase coherence and has a charged-excitation gap E_g. The evolution of this state with increasing layer separation d has been a matter of controversy. In this letter we report on small system exact diagonalization calculations which suggest that a single phase transition, likely of first order, separates coherent incompressible (E_g >0) states with strong interlayer correlations from incoherent compressible states with weak interlayer correlations. We find a dependence of the phase boundary on d and interlayer tunneling amplitude that is in very good agreement with recent experiments.Comment: 4 pages, 4 figures included, version to appear in Phys. Rev. Let

Electromagnetic field near cosmic string

The retarded Green function of the electromagnetic field in spacetime of a straight thin cosmic string is found. It splits into a geodesic part (corresponding to the propagation along null rays) and to the field scattered on the string. With help of the Green function the electric and magnetic fields of simple sources are constructed. It is shown that these sources are influenced by the cosmic string through a self-interaction with their field. The distant field of static sources is studied and it is found that it has a different multipole structure than in Minkowski spacetime. On the other hand, the string suppresses the electric and magnetic field of distant sources--the field is expelled from regions near the string.Comment: 12 pages, 8 figures (low-resolution figures; for the version with high-resolution figures see http://utf.mff.cuni.cz/~krtous/papers/), v2: two references added, typos correcte

Field Theoretical Description of Quantum Hall Edge Reconstruction

We propose a generalization of the chiral Luttinger liquid theory to allow for a unified description of quantum Hall edges with or without edge reconstruction. Within this description edge reconstruction is found to be a quantum phase transition in the universality class of one-dimensional dilute Bose gas transition, whose critical behavior can be obtained exactly. At principal filling factors $\nu=1/m$, we show the additional edge modes due to edge reconstruction modifies the point contact tunneling exponent in the low energy limit, by a small and non-universal amount.Comment: 4 pages with 1 ps figure embedde

Noise spectroscopy and interlayer phase-coherence in bilayer quantum Hall systems

Bilayer quantum Hall systems develop strong interlayer phase-coherence when the distance between layers is comparable to the typical distance between electrons within a layer. The phase-coherent state has until now been investigated primarily via transport measurements. We argue here that interlayer current and charge-imbalance noise studies in these systems will be able to address some of the key experimental questions. We show that the characteristic frequency of current-noise is that of the zero wavevector collective mode, which is sensitive to the degree of order in the system. Local electric potential noise measured in a plane above the bilayer system on the other hand is sensitive to finite-wavevector collective modes and hence to the soft-magnetoroton picture of the order-disorder phase transition.Comment: 5 pages, 2 figure

Superanalogs of the Calogero operators and Jack polynomials

A depending on a complex parameter $k$ superanalog ${\mathcal S}{\mathcal L}$ of Calogero operator is constructed; it is related with the root system of the Lie superalgebra ${\mathfrak{gl}}(n|m)$. For $m=0$ we obtain the usual Calogero operator; for $m=1$ we obtain, up to a change of indeterminates and parameter $k$ the operator constructed by Veselov, Chalykh and Feigin [2,3]. For $k=1, \frac12$ the operator ${\mathcal S}{\mathcal L}$ is the radial part of the 2nd order Laplace operator for the symmetric superspaces corresponding to pairs $(GL(V)\times GL(V), GL(V))$ and $(GL(V), OSp(V))$, respectively. We will show that for the generic $m$ and $n$ the superanalogs of the Jack polynomials constructed by Kerov, Okunkov and Olshanskii [5] are eigenfunctions of ${\mathcal S}{\mathcal L}$; for $k=1, \frac12$ they coinside with the spherical functions corresponding to the above mentioned symmetric superspaces. We also study the inner product induced by Berezin's integral on these superspaces