Spin polarization of the $\nu =5/2$ quantum Hall state

Abstract

We report on results of numerical studies of the spin polarization of the half filled second Landau level, which corresponds to the fractional quantum Hall state at filling factor $\nu =5/2$. Our studies are performed using both exact diagonalization and Density Matrix Renormalization Group (DMRG) on the sphere. We find that for the Coulomb interaction the exact finite-system ground state is fully polarized, for shifts corresponding to both the Moore-Read Pfaffian state and its particle-hole conjugate (anti-Pfaffian). This result is found to be robust against small variations of the interaction. The low-energy excitation spectrum is consistent with spin-wave excitations of a fully-magnetized ferromagnet.

Final version published on PRB

References in corpus (34)

• Non-Abelian Anyons and Topological Quantum Computation
• Paired states of fermions in two dimensions with breaking of parity and time-reversal symmetries, and the fractional quantum Hall effect
• The density-matrix renormalization group
• Non-abelian statistics of half-quantum vortices in p-wave superconductors
• Topologically-Protected Qubits from a Possible Non-Abelian Fractional Quantum Hall State
• $2n$ Quasihole States Realize $2^{n-1}$-Dimensional Spinor Braiding Statistics in Paired Quantum Hall States
• Particle-hole symmetry and the Pfaffian state
• Particle-Hole Symmetry and the $\nu =5/2$ Quantum Hall State
• Transition from quantum Hall to compressible states in the second Landau level: new light on the $\nu$=5/2 enigma
• Incompressible paired Hall state, stripe order and the composite fermion liquid phase in half-filled Landau levels
• Towards identification of a non-abelian state: observation of a quarter of electron charge at $\nu =5/2$ quantum Hall state
• Exact Quantization of Even-Denominator Fractional Quantum Hall State at $\nu$=5/2 Landau Level Filling Factor
• Electron correlation in the second Landau level; a competition between many, nearly degenerate quantum phases
• Quasiholes and fermionic zero modes of paired fractional quantum Hall states: the mechanism for nonabelian statistics
• Insulating and Fractional Quantum Hall States in the N=1 Landau Level
• Anisotropic States of Two-Dimensional Electron Systems in High Landau Levels: Effect of an In-Plane Magnetic Field
• Strongly Anisotropic Electronic Transport at Landau Level Filling Factor $\nu =9/2$ and $\nu =5/2$ Under Tilted Magnetic Field
• Experimental studies of the fractional quantum Hall effect in the first excited Landau level
• Ground state phase diagram of 2D electrons in a high Landau level: - DMRG study
• Excitation gaps in fractional quantum Hall states: An exact diagonalization study
• Density Matrix Renormalization Group Study of Incompressible Fractional Quantum Hall States
• Fractional Quantum Hall Effect in the Second Landau Level
• Fractional quantum Hall effect at $\nu =5/2$: Ground states, non-Abelian quasiholes, and edge modes in a microscopic model
• Intrinsic Gap of the nu=5/2 Fractional Quantum Hall State
• Possibility of p-wave pairing of composite fermions at $\nu =1/2$
• Paired composite fermion wavefunctions
• Orbital Landau level dependence of the fractional quantum Hall effect in quasi-two dimensional electron layers: finite-thickness effects
• Edge Excitations and Non-Abelian Statistics in the Moore-Read State: A Numerical Study in the Presence of Coulomb Interaction and Edge Confinement
• The Broken Symmetry of Two-Component $\nu =1/2$ Quantum Hall States
• Spontaneous Particle-Hole Symmetry Breaking in the $\nu =5/2$ Fractional Quantum Hall Effect
• Experimental Evidence for a Spin-Polarized Ground State in the ν=5/2 Fractional Quantum Hall Effect
• Spin Transition in the Half-Filled Landau Level
• Spin Order in Paired Quantum Hall States
• Magnetization and Spin Excitations of Non-Abelian Quantum Hall States

Cited by in corpus (68)

• Majorana Zero Modes and Topological Quantum Computation
• Particle-vortex duality of 2d Dirac fermion from electric-magnetic duality of 3d topological insulators
• Unraveling the spin polarization of the v = 5/2 fractional quantum Hall state
• Infinite density matrix renormalization group for multicomponent quantum Hall systems
• The Fractional Quantum Hall state at nu=5/2 and the Moore-Read Pfaffian
• The Effect of Landau Level-Mixing on the Effective Interaction between Electrons in the fractional quantum Hall regime
• Breaking of Particle-Hole Symmetry by Landau Level Mixing in the nu=5/2 Quantized Hall State
• The non-Abelian Interferometer
• Particle-hole symmetry without particle-hole symmetry in the quantum Hall effect at ν = 5/2
• More Realistic Hamiltonians for the Fractional Quantum Hall Regime in GaAs and Graphene
• Landau-level-mixing and the ground state of the 5/2 quantum Hall effect
• Theory of Disorder-Induced Half-Integer Thermal Hall Conductance
• Topological Order from Disorder and the Quantized Hall Thermal Metal: Possible Applications to the $\nu =5/2$ State
• The Phase Diagram of the $\nu =5/2$ Fractional Quantum Hall Effect: Effects of Landau Level Mixing and Non-Zero Width
• Valley Isospin Controlled Fractional Quantum Hall States in Bilayer Graphene
• Experimental probe of topological orders and edge excitations in the second Landau level
• Measurements of quasi-particle tunneling in the nu = 5/2 fractional quantum Hall state
• Theory of Disordered $\nu =5/2$ Quantum Thermal Hall State: Emergent Symmetry and Phase Diagram
• Recent Experimental Progress of Fractional Quantum Hall Effect: 5/2 Filling State and Graphene
• Particle-Hole Symmetry Breaking and the 5/2 Fractional Quantum Hall Effect
• Partial equilibration of integer and fractional edge channels in the thermal quantum Hall effect
• Rapid collapse of spin waves in non-uniform phases of the second Landau level
• Neutral Fermion Excitations in the Moore-Read state at ν=5/2
• Quantum Hall Phase Diagram of Second Landau-level Half-filled Bilayers: Abelian versus Non-Abelian States
• Quantum Hall Phase Diagram of Half-filled Bilayers in the Lowest and the Second Orbital Landau Levels: Abelian versus Non-Abelian Incompressible Fractional Quantum Hall States
• Influence of device geometry on tunneling in ν=5/2 quantum Hall liquid
• Noise on the Non-Abelian $\nu =5/2$ Fractional Quantum Hall Edge
• Fractional Quantum Hall States at 1/3 and 5/2 Filling: the Density-Matrix Renormalization Group Calculations
• Quantum Phase Transitions and the ν=5/2 Fractional Hall State in Wide Quantum Wells
• Numerical Calculation of the Neutral Fermion Gap at $\nu =5/2$
• Graviton Chirality and Topological Order in the Half-filled Landau Level
• Thermopower of Quantum Hall States in Corbino Geometry as a Measure of Quasiparticle Entropy
• Experimental constraints and a possible quantum Hall state at $\nu =5/2$
• Large-scale simulations of particle-hole-symmetric Pfaffian trial wavefunctions
• Domain walls, fusion rules and conformal field theory in the quantum Hall regime
• Full Classification of Transport on an Equilibrated 5/2 Edge via Shot Noise
• Skyrmions in the Moore-Read state at nu=5/2
• Energetics of the PH-Pfaffian state and the 5/2-fractional quantum Hall effect
• Enhancement of the $\nu =5/2$ Fractional Quantum Hall State in a Small In-Plane Magnetic Field
• Localized quasiholes and the Majorana fermion in fractional quantum Hall state at nu=5/2 via direct diagonalization
• Widely Tunable Quantum Phase Transition from Moore-Read to Composite Fermi Liquid in Bilayer Graphene
• Variational Monte Carlo study of spin polarization stability of fractional quantum Hall states against realistic effects in half-filled Landau levels
• Density matrix renormalization group for bosonic quantum Hall effect
• Transport in line junctions of $\nu =5/2$ quantum Hall liquids
• Quasiparticle tunneling in the Moore-Read fractional quantum Hall State
• The Pfaffian state in an electron gas with small Landau level gaps
• Identification of 331 quantum Hall states with Mach-Zehnder interferometry
• An Effective Field Theory for Fractional Quantum Hall Systems near $\nu =5/2$
• Energy Gap and Spin Polarization in the 5/2 Fractional Quantum Hall Effect
• Adiabatic Cooling with Non-Abelian Anyons
• Exploiting Geometric Degrees of Freedom in Topological Quantum Computing
• Valley Stoner Instability of the Composite Fermi Sea
• Exotic resonant level models in non-Abelian quantum Hall states coupled to quantum dots
• A Particle-Hole-Symmetric Model for a Paired Fractional Quantum Hall State in a Half-filled Landau Level
• Fractional quantum Hall effect at the filling factor $\nu =5/2$
• Paired fermions in strong magnetic fields and daughters of even-denominator Hall plateaus
• Identifying non-Abelian anyons with upstream noise
• Phase diagram of compressible and paired states in the quarter-filled Landau level
• Two-component parton fractional quantum Hall state in graphene
• Finite-thickness effect and spin polarization of the even-denominator fractional quantum Hall states
• Edge reconstruction of fractional quantum Hall liquids with spin degrees of freedom
• Charged spin textures over the Moore-Read quantum Hall state
• Universal charge conductance at Abelian--non-Abelian quantum Hall interfaces
• Non-Fermi Liquid Quantum Impurity Physics from non-Abelian Quantum Hall States
• Edge Induced Topological Phase Transition of the Quantum Hall state at Half Filling
• Cotunneling in the ν= 5/2 fractional quantum Hall regime
• Shot noise signatures of candidate states for the fractional quantum Hall $\nu =12/5$ state
• Spin texture readout of a Moore-Read topological quantum register