Quasiholes of 1/3 and 7/3 quantum Hall states: size estimates via exact diagonalization and density-matrix renormalization group

Abstract

We determine the size of the elementary quasihole in $\nu =1/3$ and $\nu =7/3$ quantum Hall states via exact-diagonalization and density-matrix renormalization group calculations on the sphere and cylinder, using a variety of short- and long-range pinning potentials. The size of the quasihole at filling factor $\nu =1/3$ is estimated to be $\approx 4{\ell }_B$, and that of $\nu =7/3$ is $\approx 7{\ell }_B$, where ${\ell }_B$ is the magnetic length. In contrast, the size of the Laughlin quasihole, expected to capture the basic physics in these two states, is around $\approx 2.5{\ell }_B$. Our work supports the earlier findings that the quasihole in the first excited Landau level is significantly larger than in the lowest Landau level.

References in corpus (11)

• Fractional Quantum Hall States and Jack Polynomials
• Realization of a Laughlin quasiparticle interferometer: Observation of fractional statistics
• Topological characterization of fractional quantum Hall ground states from microscopic Hamiltonians
• Density Matrix Renormalization Group Study of Incompressible Fractional Quantum Hall States
• Exact Matrix Product States for Quantum Hall Wave Functions
• Clustering Properties and Model Wavefunctions for Non-Abelian Fractional Quantum Hall Quasielectrons
• Orbital Landau level dependence of the fractional quantum Hall effect in quasi-two dimensional electron layers: finite-thickness effects
• Matrix Product States for Trial Quantum Hall States
• Role of exciton screening in the 7/3 fractional quantum Hall effect
• Interaction-tuned compressible-to-incompressible phase transitions in the quantum Hall systems
• Localized quasiholes and the Majorana fermion in fractional quantum Hall state at nu=5/2 via direct diagonalization

Cited by in corpus (29)

• Infinite density matrix renormalization group for multicomponent quantum Hall systems
• Competing states for the fractional quantum Hall effect in the 1/3-filled second Landau level
• Braiding non-Abelian quasiholes in fractional quantum Hall states
• Abelian and Non-Abelian States in $\nu =2/3$ Bilayer Fractional Quantum Hall Systems
• Fractional Quantum Hall Effect at $\nu =2+6/13$: The Parton Paradigm for the Second Landau Level
• Fractional Quantum Hall Effect at $\nu =2+4/9$
• Time-of-Flight Measurements as a Possible Method to Observe Anyonic Statistics
• ${\mathbb{Z}}_n$ superconductivity of composite bosons and the $7/3$ fractional quantum Hall effect
• Paired states at 5/2: PH Pfaffian and particle-hole symmetry breaking
• Characterization of quasiholes in fractional Chern insulators
• A non-Abelian fractional quantum Hall state at $3/7$ filled Landau level
• Unconventional ${\mathbb{Z}}_n$ parton states at $\nu =7/3$: The role of finite width
• Direct observation of composite fermions and their fully spin-polarized Fermi sea near $\nu =5/2$
• Characterization of quasiholes in two-component fractional quantum Hall states and fractional Chern insulators in $|C|=2$ flat bands
• Incommensurate quantum-size oscillations in acene-based molecular wires - effects of quantum fluctuations
• Shape of the magnetoroton at $\nu =1/3$ and $\nu =7/3$ in real samples
• Energy projection and modified Laughlin states
• Continuum limit of lattice models with Laughlin-like ground states containing quasiholes
• Non-Abelian quasiholes in lattice Moore-Read states and parent Hamiltonians
• Spin-statistics relation and the Abelian braiding phase for anyons in fractional quantum Hall effect
• Model wavefunctions for interfaces between lattice Laughlin states
• Squeezing anyons for braiding on small lattices
• Characterization of fractional Chern insulator quasiparticles in twisted homobilayer MoTe${}_2$
• Universal Modelling of Oscillations in Fractional Quantum Hall Fluids
• Density matrix renormalization group for a highly degenerate quantum system: Sliding environment block approach
• Numerical demonstration of Abelian fractional statistics of composite fermions in the spherical geometry
• Anisotropy and quench dynamics of quasiholes in fractional quantum Hall liquids
• Dynamics of quasiholes and quasiparticles at the edges of small lattices
• Non-quasiconvex dispersion of composite fermions and the fermionic Haffnian state in the first-excited Landau level