Related papers: Laughlin Wave Function and One-Dimensional Free Fe…
We introduce a two-parameter family of strongly-correlated wave functions for bosons and fermions in lattices. One parameter, $q$, is connected to the filling fraction. The other one, $\eta$, allows us to interpolate between the lattice…
We investigate Laughlin's fractional quantum Hall effect wave function on a cylinder. We show that it displays translational symmetry breaking in the axial direction for sufficiently thin cylinders. At filling factor 1/p, the period is p…
A theory is developed for the paired even-denominator fractional quantum Hall states in the lowest Landau level. We show that electrons bind to quantized vortices to form composite fermions, interacting through an exact instantaneous…
Landau levels and states of electrons in a magnetic field are fundamental quantum entities underlying the quantum-Hall and related effects in condensed matter physics. However, the real-space properties and observation of Landau wave…
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…
We algebraically analysis the quantum Hall effect of a system of particles living on the disc ${\bf B}^1$ in the presence of an uniform magnetic field $B$. For this, we identify the non-compact disc with the coset space $SU(1,1)/U(1)$. This…
The reduction of the energy gap due to Landau level mixing, characterized by the dimensionless parameter $\lambda = (e^2/\epsilon l_0)/\hbar\omega_c$, has been calculated by variational Monte Carlo for the fractional quantum Hall effect at…
We present a novel matrix product representation of the Laughlin and related fractional quantum Hall wavefunctions based on a rigorous version of the correlators of a chiral quantum field theory. This representation enables the quantitative…
We investigate Laughlin's fractional quantum Hall effect wave function in the cylinder geometry of Laughlin's integer quantum Hall effect argument, at filling factor 1/3. We show that the plasma analogy leads to a periodic density, and that…
The Laughlin states for $N$ interacting electrons at the plateaus of the fractional Hall effect are studied in the thermodynamic limit of large $N$. It is shown that this limit leads to the semiclassical regime for these states, thereby…
The correlations that give rise to incompressible quantum liquid (IQL) states in fractional quantum Hall systems are determined by the pseudopotential $V(\mathcal R)$ describing the interaction of a pair of Fermions in a degenerate Landau…
We discuss the possibility of the quantum Hall effect at half-filled Landau level in terms of the pairing of the composite fermions. In the absence of Coulomb energy, we show that the ground state of the system is described by the {\it…
We study the entanglement properties of some fractional quantum Hall liquids. We calculate the entanglement of the Laughlin wave function and the wave functions that are generated by the K-matrix using the modified entanglement measure of…
Following recent work of Halperin, Lee, and Read, and Kalmeyer and Zhang, a double-layer electron system with total Landau-level filling factor $\nu=1/2$ is mapped onto an equivalent system of fermions in zero average magnetic field…
It is demonstrated that all observed fractions at moderate Landau level fillings for the quantum Hall effect can be obtained without recourse to the phenomenological concept of composite fermions. The possibility to have the special…
The fractional quantum Hall effect (FQHE) is theoretically investigated, with numerical and algebraic approaches, in assemblies of a few spinful ultracold neutral fermionic atoms, interacting via repulsive contact potentials and confined in…
In the framework of a recently developed model of interacting composite fermions, we calculate the energy of different solid and Laughlin-type liquid phases of spin-polarized composite fermions. The liquid phases have a lower energy than…
We consider 2D fermions on a plane with a perpendicular magnetic field, described by Landau levels. It is wellknown that, semiclassically, restriction to the lowest Landau levels (LLL) implies two constraints on a 4D phase space, that…
We present explicit expressions for a large set of hierarchy wave functions on the torus. Included are the Laughlin states, the states in the positive Jain series, and recently observed states at e.g. $\nu = 4/11$. The techniques we use…
We present improved wave functions for the ground state, Laughlin quasihole and quasiparticle excitations of the fractional quantum Hall effect. These depend explicitly on the effective strength of Coulomb interaction and reproduce…