相关论文: Large N Limit in the Quantum Hall Effect
We show the low-lying excitations at filling factor $\nu=n+1/3$ with realistic interactions are contained completely within the well-defined Hilbert space of "Gaffnian quasiholes". Each Laughlin quasihole can thus be understood as a bound…
A two-dimensional array of quantum dots in a magnetic field is considered. The electrons in the quantum dots are described as unitary random matrix ensembles. The strength of the magnetic field is such that there is half a flux quantum per…
Possible phase transitions between incompressible quantum Hall states and compressible three-dimensional states are discussed for infinite-layer electron systems in strong magnetic field. By variational Monte Carlo calculation, relative…
In a previous paper, we have developed a general theory of thermodynamic limits. We apply it here to three different Coulomb quantum systems, for which we prove the convergence of the free energy per unit volume. The first system is the…
The localization behavior of noninteracting two-dimensional electrons in a random potential and strong magnetic field is of fundamental interest for the physics of the quantum Hall effect. In order to understand the emergence of power-law…
We show that the Lorentz shear modulus of macroscopically homogeneous electronic states in the lowest Landau level is proportional to the bulk modulus of an equivalent system of interacting classical particles in the thermodynamic limit.…
We study quantum Hall effect within the framework of a newly proposed approach, which captures the principal results of some proposals. This can be established by considering a system of particles living on the non-commutative plane in the…
Strongly interacting topological matter exhibits fundamentally new phenomena with potential applications in quantum information technology. Emblematic instances are fractional quantum Hall states, where the interplay of magnetic fields and…
In the context of the fractional quantum Hall effect, we investigate Laughlin's celebrated ansatz for the groud state wave function at fractional filling of the lowest Landau level. Interpreting its normalization in terms of a one component…
We present a quantitative study of most prominent incompressible quantum Hall states in the partially filled first excited Landau level (LL1) which have been recently studied experimentally by Choi et al. The pseudopotential describing the…
Fractional quantum Hall-superconductor heterostructures may provide a platform towards non-abelian topological modes beyond Majoranas. However their quantitative theoretical study remains extremely challenging. We propose and implement a…
It has recently been pointed out that phases of matter with intrinsic topological order, like the fractional quantum Hall states, have an extra dynamical degree of freedom that corresponds to quantum geometry. Here we perform extensive…
The exactness and universality observed in the quantum Hall effect suggests the existence of a symmetry principle underlying Laughlin's theory. We review the role played by the infinite $W_{\infty }$ and conformal algebras as dynamical…
We demonstrate that the two-dimensonal electron system in a strong perpendicular magnetic field has stable states which break rotational but not translational symmetry. The Laughlin fluid becomes unstable to these states in quantum wells…
New trial wave functions corresponding to half filling quantum Hall states are proposed. These wave functions are constructed by first pairing up the quasielectrons of the 1/3 Laughlin quantum Hall state, with the same relative angular…
We present a consistent treatment of the quantum Hall effect within the electrostatic approximation. We derive the form of the density of states (DOS) which differs from the usual gaussian shape valid for non-interacting electrons. Below a…
Explicit relation between Laughlin state of the quantum Hall effect and one-dimensional(1D) model with long-ranged interaction ($1/r^2$) is discussed. By rewriting lowest Landau level wave functions in terms of 1D representation, Laughlin…
We analyse the inner products of edge state wavefunctions in the fractional quantum Hall effect, specifically for the Laughlin and Moore-Read states. We use an effective description for these inner products given by a large-$N$ expansion…
We demonstrate the experimental feasibility of incompressible fractional quantum Hall-like states in ultra-cold two dimensional rapidly rotating dipolar Fermi gases. In particular, we argue that the state of the system at filling fraction…
We employ the exact diagonalization method to analyze the possibility of generating strongly correlated states in two-dimensional clouds of ultracold bosonic atoms which are subjected to a geometric gauge field created by coupling two…