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Despite the high overlap with the exact Coulomb ground state, the so-called Gaffnian state fails to describe the incompressibility at the 2/5 quantum Hall filling factor and consequently it was conjectured to be a quantum critical state. To…
Quantum Hall effects with multicomponent internal degrees of freedom facilitate the playground of novel emergent topological orders. Here, we explore the correlated topological phases of two-component hardcore bosons at a total filling…
We investigate the ground state properties of a bosonic Harper-Hofstadter model with local interactions on a finite cylindrical lattice with filling fraction $\nu=1/2$. We find that our system supports topologically ordered states by…
Starting from Halperin multilayer systems we develop a hierarchical scheme that generates, bosonic and fermionic, single-layer quantum Hall states (or vacua) of arbitrary filling factor. Our scheme allows for the insertion of quasiparticle…
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 theoretically examine entanglement in fractional quantum hall states, explicitly taking into account and emphasizing the quasi-two-dimensional nature of experimental quantum Hall systems. In particular, we study the entanglement entropy…
A generalized diffusion Monte Carlo method for solving the many-body Schr\"odinger equation on curved manifolds is introduced and used to perform a `fixed-phase' simulation of the fractional quantum Hall effect on the Haldane sphere. This…
The quantum Hall effect is one of the most important developments in condensed matter physics of the 20th century. The standard explanations of the famous integer quantized Hall plateaus in the transverse resistivity are qualitative, and…
While the simplest quantum Hall plateaus, such as the $\nu = 1/3$ state in GaAs, can be conveniently analyzed by assuming only a single active Landau level participates, for many phases the spin, valley, bilayer, subband, or higher Landau…
The quantum Hall effect is usually observed when the two-dimensional electron gas is subjected to an external magnetic field, so that their quantum states form Landau levels. In this work we predict that a new phenomenon, the quantum…
Fractional quantum Hall liquids can accomodate various degrees of spatial ordering. The most likely scenarios are a Hall hexatic, Hall smectic, and Hall crystal, in which respectively orientational, one--dimensional translational, and…
The coupled-wire construction provides a useful way to obtain microscopic Hamiltonians for various two-dimensional topological phases, among which fractional quantum Hall states are paradigmatic examples. Using the recently introduced flux…
The fractional quantum Hall effect is a well-known demonstration of strongly correlated topological phases in two dimensions. However, the extension of this phenomenon into a three-dimensional context has yet to be achieved. Recently, the…
Based on Haldane's spherical geometrical formalism of two-dimensional quantum Hall fluids, the relation between the noncommutative geometry of $S^2$ and the two-dimensional quantum Hall fluids is exhibited. If the number of particles $N$ is…
The fractional quantum Hall effect (FQHE) of topological surface-state particles under a tilted strong magnetic field is theoretically studied by using the exact diagonalization method. The Haldane's pseudopotentials for the Coulomb…
We have studied the partially spin-polarized fractional quantum Hall states using Chern Simon's theory and plasma picture proposed by Halperin. Using these theoretical techniques we have tried to find the stable polarized states of…
Model wave functions are essential for studying fractional quantum Hall phases, yet lattice model states have so far been limited to bosonic systems with on-site interactions. In this work, by combining analytical and numerical methods, we…
Bilayer quantum Hall states have been shown to be described by a BCS-paired state of composite fermions. However, finding a qualitatively accurate model state valid across all values of the bilayer separation is challenging. Here, we…
The quantum Hall effect realizes a quantized Hall resistance $R_{xy} = h/(\nu e^2)$ whereas the longitudinal resistance vanishes. The quantized value consists of the fundamental physical quantities, the elementary charge $e$ and the Planck…
We study non-Abelian fractional quantum Hall state in double layer systems at total filling factor $1/2$. Recent progresses in two-dimensional van der Waals materials made it possible to explore the regime with very small interlayer…