Fractional Quantum Hall States at 1/3 and 5/2 Filling: the Density-Matrix Renormalization Group Calculations

Abstract

In this paper, the density-matrix renormalization group method is employed to investigate the fractional quantum Hall effect at filling fractions $\nu =1/3$ and 5/2. We first present benchmark results at both filling fractions for large system sizes to show the accuracy as well as the capability of the numerical algorithm. Furthermore, we show that by keeping a large number of basis states, one can also obtain accurate entanglement spectrum at $\nu =5/2$ for large system with electron number up to $N_e=34$, much larger than systems previously studied. Based on a finite-size scaling analysis, we demonstrate that the entanglement gap defined by Li and Haldane is finite in the thermodynamic limit, which characterizes the topological order of the FQHE state.

6 pages, minor changes

References in corpus (11)

• Non-Abelian Anyons and Topological Quantum Computation
• Entanglement Spectrum as a Generalization of Entanglement Entropy: Identification of Topological Order in Non-Abelian Fractional Quantum Hall Effect States
• Particle-hole symmetry and the Pfaffian state
• Particle-Hole Symmetry and the $\nu =5/2$ Quantum Hall State
• Fractional Quantum Hall States and Jack Polynomials
• Entanglement entropy in fermionic Laughlin states
• Density Matrix Renormalization Group Study of Incompressible Fractional Quantum Hall States
• Clustering Properties and Model Wavefunctions for Non-Abelian Fractional Quantum Hall Quasielectrons
• Spin polarization of the $\nu =5/2$ quantum Hall state
• Spontaneous Particle-Hole Symmetry Breaking in the $\nu =5/2$ Fractional Quantum Hall Effect
• Entanglement signatures of quantum Hall phase transitions

Cited by in corpus (33)

• Time-dependent variational principle for quantum lattices
• Topological characterization of fractional quantum Hall ground states from microscopic Hamiltonians
• Infinite density matrix renormalization group for multicomponent quantum Hall systems
• Landau-level-mixing and the ground state of the 5/2 quantum Hall effect
• Matrix Product States for Trial Quantum Hall States
• Density matrix renormalization group on a cylinder in mixed real and momentum space
• The Fractional Quantum Hall States at $\nu =13/5$ and $12/5$ and their Non-Abelian Nature
• Fractional Quantum Hall Bilayers at Half-Filling: Tunneling-driven Non-Abelian Phase
• Comparison of the density-matrix renormalization group method applied to fractional quantum Hall systems in different geometries
• Probing the geometry of the Laughlin state
• Bulk-edge correspondence in fractional Chern insulators
• Edge Mode Combinations in the Entanglement Spectra of Non-Abelian Fractional Quantum Hall States on the Torus
• Quasiholes of 1/3 and 7/3 quantum Hall states: size estimates via exact diagonalization and density-matrix renormalization group
• Interplay between fractional quantum Hall liquid and crystal phases at low filling
• Phases of (2+1)D SO(5) non-linear sigma model with a topological term on a sphere: multicritical point and disorder phase
• Quantum Hall ferroelectrics and nematics in multivalley systems
• Energetics of the PH-Pfaffian state and the 5/2-fractional quantum Hall effect
• Disorder-driven transition and intermediate phase for $\nu =5/2$ fractional quantum Hall effect
• Entanglement Spectrum and Entanglement Hamiltonian of a Chern insulator with open boundaries
• Topological phases in small quantum Hall samples
• Entanglement Measures for Quasi-Two-Dimensional Fractional Quantum Hall States
• A Particle-Hole-Symmetric Model for a Paired Fractional Quantum Hall State in a Half-filled Landau Level
• Approximate two-body generating Hamiltonian for the PH-Pfaffian wavefunction
• Neutral excitation and bulk gap of the Fractional Quantum Hall liquids in disk geometry
• Universal Modelling of Oscillations in Fractional Quantum Hall Fluids
• Two-component parton fractional quantum Hall state in graphene
• Bubble phase at $\nu =1/3$ for a spinless hollow-core interaction
• Universal properties of the FQH state from the topological entanglement entropy and disorder effects
• Real-space entanglement spectra of projected fractional quantum Hall states using Monte Carlo methods
• Nonperturbative emergence of Dirac fermion in strongly correlated composite fermions of fractional quantum Hall effects
• Matrix-Product-State Algorithm for Finite Fractional Quantum Hall Systems
• Developments in the applications of density functional theory to fractional quantum Hall systems
• Topological states in double monolayer graphene