Magnetization process from Chern-Simons theory and its application to SrCu2_2(BO3_3)2_2

URL: http://www-spht.cea.fr/articles/T02/081 16th Nishinomiya-Yukawa Memorial Symposium, Nishinomiya, Japan, November 2001 http://fr.arxiv.org/abs/cond-mat/0204161In two-dimensional systems, it is possible transmute bosons into fermions by use of a Chern-Simons gauge field. Such a mapping is used to compute magnetization processes of two-dimensional magnets. The calculation of the magnetization curve then involves the structure of the Hofstadter problem for the lattice under consideration. Certain features of the Hofstadter butterfly are shown to imply the appearance of magnetization plateaus. While not always successfull, this approach leads to interesting results when applied to the 2D AF magnet \SrCu

Disorder and interactions in quantum Hall ferromagnets: effects of disorder in Skyrmion physics

We present a Hartree-Fock study of the competition between disorder and interactions in quantum Hall ferromagnets near $\nu=1$. We find that the ground state at $\nu=1$ evolves with increasing interaction strength from a quasi-metallic paramagnet, to a partially spin-polarized ferromagnetic Anderson insulator, and to a fully spin-polarized ferromagnet with a charge gap. Away from $\nu=1$, the ground state evolves from a conventional Anderson insulator, to a conventional quasiparticle glass, and finally to a ferromagnetic Skyrmion quasiparticle glass. These different regimes can be measured in low-temperature transport and NMR experiments. We present calculations for the NMR spectra in different disorder regimes.Comment: 3 pages, 3 figures, proceedings for EP2DS-14, Prague 200

Exotic Quantum Order in Low-Dimensional Systems

Strongly correlated quantum systems in low dimensions often exhibit novel quantum ordering. This ordering is sometimes hidden and can be revealed only by examining new `dual' types of correlations. Such ordering leads to novel collective modes and fractional quantum numbers. Examples will be presented from quantum spin chains and the quantum Hall effect.Comment: To appear in Solid State Communications, Proceedings of Symposium on the Advancing Frontiers in Condensed Matter Science. 12pages +6 PS figure

Properties of the Soliton-Lattice State in Double-Layer Quantum Hall Systems

Application of a sufficiently strong parallel magnetic field $B_\parallel > B_{c}$ produces a soliton-lattice (SL) ground state in a double-layer quantum Hall system. We calculate the ground-state properties of the SL state as a function of $B_\parallel$ for total filling factor $\nu_{T}=1$, and obtain the total energy, anisotropic SL stiffness, Kosterlitz-Thouless melting temperature, and SL magnetization. The SL magnetization might be experimentally measurable, and the magnetic susceptibility diverges as $|B_\parallel - B_{c}|^{-1}$.Comment: 4 pages LaTeX, 1 EPS figure. Proceedings of the 12th International Conference on the Electronic Properties of Two-Dimensional Electron Systems (EP2DS-12), to be published in Physica B (1998

Formation of an Edge Striped Phase in Fractional Quantum Hall Systems

We have performed an exact diagonalization study of up to N=12 interacting electrons on a disk at filling $\nu={1/3}$ for both Coulomb and $V_1$ short-range interaction for which Laughlin wave function is the exact solution. For Coulomb interaction and $N\geq 10$ we find persistent radial oscillations in electron density, which are not captured by the Laughlin wave function. Our results srongly suggest formation of a chiral edge striped phase in quantum Hall systems. The amplitude of the charge density oscillations decays slowly, perhaps as a square root of the distance from the edge; thus the spectrum of edge excitations is likely to be affected.Comment: 4 pages, 3 Figs. include

Soluble `Supersymmetric' Quantum XY Model

We present a `supersymmetric' modification of the $d$-dimensional quantum rotor model whose ground state is exactly soluble. The model undergoes a vortex-binding transition from insulator to metal as the rotor coupling is varied. The Hamiltonian contains three-site terms which are relevant: they change the universality class of the transition from that of the ($d+1$)--- to the $d$-dimensional classical XY model. The metallic phase has algebraic ODLRO but the superfluid density is identically zero. Variational wave functions for single-particle and collective excitations are presented.Comment: 12 pages, REVTEX 3.0, IUCM93-00

A Quantum Hall Fluid of Vortices

In this note we demonstrate that vortices in a non-relativistic Chern-Simons theory form a quantum Hall fluid. We show that the vortex dynamics is controlled by the matrix mechanics previously proposed by Polychronakos as a description of the quantum Hall droplet. As the number of vortices becomes large, they fill the plane and a hydrodynamic treatment becomes possible, resulting in the non-commutative theory of Susskind. Key to the story is the recent D-brane realisation of vortices and their moduli spaces.Comment: 10 pages. v2(3): (More) References adde

Phase transition and spin-wave dispersion in quantum Hall bilayers at filling factor nu=1

We present an effective Hamiltonian for a bilayer quantum Hall system at filling factor $\nu=1$ neglecting charge fluctuations. Our model is formulated in terms of spin and pseudospin operators and is an exact representation of the system within the above approximation. We analyze its low-lying excitations in terms of spin-wave theory. Moreover we add to previous first-principle exact-diagonalization studies concentrating on the quantum phase transition seen in this system.Comment: Four pages, proceedings for EP2DS-14, Prague 200

Liouvillian Approach to the Integer Quantum Hall Effect Transition

We present a novel approach to the localization-delocalization transition in the integer quantum Hall effect. The Hamiltonian projected onto the lowest Landau level can be written in terms of the projected density operators alone. This and the closed set of commutation relations between the projected densities leads to simple equations for the time evolution of the density operators. These equations can be used to map the problem of calculating the disorder averaged and energetically unconstrained density-density correlation function to the problem of calculating the one-particle density of states of a dynamical system with a novel action. At the self-consistent mean-field level, this approach yields normal diffusion and a finite longitudinal conductivity. While we have not been able to go beyond the saddle point approximation analytically, we show numerically that the critical localization exponent can be extracted from the energetically integrated correlation function yielding $\nu=2.33 \pm 0.05$ in excellent agreement with previous finite-size scaling studies.Comment: 9 pages, submitted to PR

Magnetoroton instabilities and static susceptibilities in higher Landau levels

We present analytical results concerning the magneto-roton instability in higher Landau levels evaluated in the single mode approximation. The roton gap appears at a finite wave vector, which is approximately independent of the LL index n, in agreement with numerical calculations in the composite-fermion picture. However, a large maximum in the static susceptibility indicates a charge density modulation with wave vectors $q_0(n)\sim 1/\sqrt{2n+1}$, as expected from Hartree-Fock predictions. We thus obtain a unified description of the leading charge instabilities in all LLs.Comment: 4 pages, 5 figure