Related papers: Competing Topological Orders in the nu=12/5 Quantu…
Observation of filling factor 6/13 is one of the surprising fractional quantum Hall states in the second Landau level because, in contrast to the standard wisdom, the fractions ($\nu < 1/2$) with lower numerators, namely 4 and 5, have not…
Nature of the fractional quantum Hall state at Landau level filling factor 5/2 remains elusive despite intensive experimental and theoretical work. While the leading theoretical candidates are Moore-Read Pfaffian (Pf) and its particle-hole…
We have studied the $\nu=5/2$ fractional quantum Hall state in a density-tunable sample at extremely low electron densities. For the densities accessed in our experiment, the Landau level mixing parameter $\kappa$ spans the…
We study an effective Hamiltonian for the standard $\nu=1/3$ fractional quantum Hall system in the thin cylinder regime. We give a complete description of its ground state space in terms of what we call Fragmented Matrix Product States,…
We present the first magneto-absorption studies of coupled electron double layers in the quantum Hall regime. Optical absorption spectra in the vicinity of total filling factor nu = 1 reveal intriguing behavior that have no analog in the…
Non-Abelian Anyons exist in certain spin models and may exist in Quantuam Hall systems at certain filling fractions. In this work we studied the ground state of dynamical SU(2) level-$\kappa$ Chern Simons non-Abelian anyons at finite…
We numerically study the fractional quantum Hall effect at filling factors $\nu=12/5$ and 13/5 (the particle-hole conjugate of 12/5) in high-quality two-dimensional GaAs heterostructures via exact diagonalization including finite well width…
The $\nu=2$ quantum Hall state at low Zeeman coupling is well-known to be a translationally invariant singlet if Landau level mixing is small. At zero Zeeman interaction, as Landau level mixing increases, the translationally invariant state…
Identifying and understanding interacting systems that can host non-Abelian topological phases with fractionalized quasiparticles have attracted intense attentions in the past twenty years. Theoretically, it is possible to realize a rich…
The structure of $3/2^{-}$ and $1/2^{+}$ states in $^{11}$B is investigated with an $\alpha+\alpha+t$ orthogonality condition model (OCM) based on the Gaussian expansion method. Full levels up to the $3/2^{-}_{3}$ and $1/2^{+}_2$ states…
We study the phase diagram of interacting electrons in a dispersionless Chern band as a function of their filling. We find hierarchy multiplets of incompressible states at fillings \nu=1/3, 2/5, 3/7, 4/9, 5/9, 4/7, 3/5 as well as…
In this work we propose a parton state as a candidate state to describe the fractional quantum Hall effect in the half-filled second Landau level. The wave function for this parton state is $\mathcal{P}_{\rm LLL}…
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…
In condensed matter physics, the study of electronic states with SU(N) symmetry has attracted considerable and growing attention in recent years, as systems with such a symmetry can often have a spontaneous symmetry-breaking effect giving…
The competing spin orders and fractional magnetization plateaus of classical Heisenberg model with long-range interactions on a Shastry-Sutherland lattice are investigated using Monte Carlo simulations, in order to understand the…
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…
The entanglement entropy of $\nu=1/2$ and $\nu=9/2$ quantum Hall states in the presence of short range disorder has been calculated by direct diagonalization. Spin polarized electrons are confined to a single Landau level and interact with…
Motivated by a recent experiment reporting the fractional quantum spin Hall effect in twisted ${\rm MoTe}_2$, we investigate microscopically the prospects of realizing exotic topologically ordered states beyond conventional quantum Hall…
We show numerically that the `deconfined' quantum critical point between the N\'eel antiferromagnet and the columnar valence-bond-solid, for a square lattice of spin-1/2s, has an emergent $SO(5)$ symmetry. This symmetry allows the N\'eel…
We use high-mobility bilayer hole systems with negligible tunneling to examine how the bilayer nu = 1 quantum Hall state evolves as charge is transferred from one layer to the other at constant total density. We map bilayer nu = 1 state…