Uncertainty Principle and Off-Diagonal Long Range Order in the Fractional Quantum Hall Effect

A natural generalization of the Heisenberg uncertainty principle inequality holding for non hermitian operators is presented and applied to the fractional quantum Hall effect (FQHE). This inequality was used in a previous paper to prove the absence of long range order in the ground state of several 1D systems with continuous group symmetries. In this letter we use it to rule out the occurrence of Bose-Einstein condensation in the bosonic representation of the FQHE wave function proposed by Girvin and MacDonald. We show that the absence of off-diagonal long range order in this 2D problem is directly connected with the $q^2$ behavior of the static structure function $S(q)$ at small momenta.Comment: 10 pages, plain TeX, UTF-09-9

Quasi-adiabatic Continuation of Quantum States: The Stability of Topological Ground State Degeneracy and Emergent Gauge Invariance

We define for quantum many-body systems a quasi-adiabatic continuation of quantum states. The continuation is valid when the Hamiltonian has a gap, or else has a sufficiently small low-energy density of states, and thus is away from a quantum phase transition. This continuation takes local operators into local operators, while approximately preserving the ground state expectation values. We apply this continuation to the problem of gauge theories coupled to matter, and propose a new distinction, perimeter law versus "zero law" to identify confinement. We also apply the continuation to local bosonic models with emergent gauge theories. We show that local gauge invariance is topological and cannot be broken by any local perturbations in the bosonic models in either continuous or discrete gauge groups. We show that the ground state degeneracy in emergent discrete gauge theories is a robust property of the bosonic model, and we argue that the robustness of local gauge invariance in the continuous case protects the gapless gauge boson.Comment: 15 pages, 6 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

Spin transitions induced by a magnetic field in quantum dot molecules

We present a theoretical study of magnetic field driven spin transitions of electrons in coupled lateral quantum dot molecules. A detailed numerical study of spin phases of artificial molecules composed of two laterally coupled quantum dots with N=8 electrons is presented as a function of magnetic field, Zeeman energy, and the detuning using real space Hartree-Fock Configuration Interaction (HF-CI) technique. A microscopic picture of quantum Hall ferromagnetic phases corresponding to zero and full spin polarization at filling factors $\nu=2$ and $\nu=1$, and ferrimagnetic phases resulting from coupling of the two dots, is presented.Comment: 12 pages, 18 figure

Composite bosons in bilayer nu = 1 system: An application of the Murthy-Shankar formalism

We calculate the dispersion of the out-of-phase mode characteristic for the bilayer nu = 1 quantum Hall system applying the version of Chern-Simons theory of Murthy and Shankar that cures the unwanted bare electron mass dependence in the low-energy description of quantum Hall systems. The obtained value for the mode when d, distance between the layers, is zero is in a good agreement with the existing pseudospin picture of the system. For d nonzero but small we find that the mode is linearly dispersing and its velocity to a good approximation depends linearly on d. This is in agreement with the Hartree-Fock calculations of the pseudospin picture that predicts a linear dependance on d, and contrary to the naive Hartree predictions with dependence on the square-root of d. We set up a formalism that enables one to consider fluctuations around the found stationary point values. In addition we address the case of imbalanced layers in the Murthy-Shankar formalism.Comment: 10 pages, 1 figur

Hamiltonian Theory of the Composite Fermion Wigner Crystal

Experimental results indicating the existence of the high magnetic field Wigner Crystal have been available for a number of years. While variational wavefunctions have demonstrated the instability of the Laughlin liquid to a Wigner Crystal at sufficiently small filling, calculations of the excitation gaps have been hampered by the strong correlations. Recently a new Hamiltonian formulation of the fractional quantum Hall problem has been developed. In this work we extend the Hamiltonian approach to include states of nonuniform density, and use it to compute the excitation gaps of the Wigner Crystal states. We find that the Wigner Crystal states near $\nu=1/5$ are quantitatively well described as crystals of Composite Fermions with four vortices attached. Predictions for gaps and the shear modulus of the crystal are presented, and found to be in reasonable agreement with experiments.Comment: 41 page, 6 figures, 3 table

Electromagnetic characteristics and effective gauge theory of double-layer quantum Hall systems

The electromagnetic characteristics of double-layer quantum Hall systems are studied, with projection to the lowest Landau level taken into account and intra-Landau-level collective excitations treated in the single-mode approximation. It is pointed out that dipole-active excitations, both elementary and collective, govern the long-wavelength features of quantum Hall systems. In particular, the presence of the dipole-active interlayer out-of-phase collective excitations, inherent to double-layer systems, modifies the leading O(k) and O(k^{2}) long-wavelength characteristics (i.e., the transport properties and characteristic scale) of the double-layer quantum Hall states substantially. We apply bosonization techniques and construct from such electromagnetic characteristics an effective theory, which consists of three vector fields representing the three dipole-active modes, one interlayer collective mode and two inter-Landau-level cyclotron modes. This effective theory properly incorporates the spectrum of collective excitations on the right scale of the Coulomb energy and, in addition, accommodates the favorable transport properties of the standard Chern-Simons theories.Comment: 10 pages, Revtex, sec. II slightly shortened, to appear in Phys. Rev.

Generalised Chern-Simons Theory of Composite Fermions in Bilayer Hall Systems

We present a field theory of Jain's composite fermion model as generalised to the bilayer quantum Hall systems. We define operators which create composite fermions and write the Hamiltonian exactly in terms of these operators. This is seen to be a complexified version of the familiar Chern Simons theory. In the mean-field approximation, the composite fermions feel a modified effective magnetic field exactly as happens in usual Chern Simons theories, and plateaus are predicted at the same values of filling factors as Lopez and Fradkin and Halperin . But unlike normal Chern Simons theories, we obtain all features of the first-quantised wavefunctions including its phase, modulus and correct gaussian factors at the mean field level. The familiar Jain relations for monolayers and the Halperin wavefunction for bilayers come out as special cases.Comment: Revtex file; 20 pages after processing; no figure

Origin of Magic Angular Momentum in a Quantum Dot under Strong Magnetic Field

This paper investigates origin of the extra stability associated with particular values (magic numbers) of the total angular momentum of electrons in a quantum dot under strong magnetic field. The ground-state energy, distribution functions of density and angular momentum, and pair correlation function are calculated in the strong field limit by numerical diagonalization of the system containing up to seven electrons. It is shown that the composite fermion picture explains the small magic numbers well, while a simple geometrical picture does better as the magic number increases. Combination of these two pictures leads to identification of all the magic numbers. Relation of the magic-number states to the Wigner crystal and the fractional quantum Hall state is discussed.Comment: 12 pages, 9 Postscript figures, uses jpsj.st

Diffusion Thermopower at Even Denominator Fractions

We compute the electron diffusion thermopower at compressible Quantum Hall states corresponding to even denominator fractions in the framework of the composite fermion approach. It is shown that the deviation from the linear low temperature behavior of the termopower is dominated by the logarithmic temperature corrections to the conductivity and not to the thermoelectric coefficient, although such terms are present in both quantities. The enhanced magnitude of this effect compared to the zero field case may allow its observation with the existing experimental techniques.Comment: Latex, 12 pages, Nordita repor