Quantum Hall system in Tao-Thouless limit

Abstract

We consider spin-polarized electrons in a single Landau level on a torus. The quantum Hall problem is mapped onto a one-dimensional lattice model with lattice constant $2\pi /L_1$, where $L_1$ is a circumference of the torus (in units of the magnetic length). In the Tao-Thouless limit, $L_1\to 0$, the interacting many-electron problem is exactly diagonalized at any rational filling factor $\nu =p/q\le 1$. For odd $q$, the ground state has the same qualitative properties as a bulk ($L_1\to \infty$) quantum Hall hierarchy state and the lowest energy quasiparticle exitations have the same fractional charges as in the bulk. These states are the $L_1\to 0$ limits of the Laughlin/Jain wave functions for filling fractions where these exist. We argue that the exact solutions generically, for odd $q$, are continuously connected to the two-dimensional bulk quantum Hall hierarchy states, {\it ie} that there is no phase transition as $L_1\to \infty$ for filling factors where such states can be observed. For even denominator fractions, a phase transition occurs as $L_1$ increases. For $\nu =1/2$ this leads to the system being mapped onto a Luttinger liquid of neutral particles at small but finite $L_1$, this then develops continuously into the composite fermion wave function that is believed to describe the bulk $\nu =1/2$ system. The analysis generalizes to non-abelian quantum Hall states.

25 pages, 9 figures

References in corpus (36)

• Fault-tolerant quantum computation by anyons
• Topological orders and Edge excitations in FQH states
• Beyond paired quantum Hall states: parafermions and incompressible states in the first excited Landau level
• Evidence for an Anisotropic State of Two-Dimensional Electrons in High Landau Levels
• $2n$ 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
• Strongly Anisotropic Transport in Higher Two-Dimensional Landau Levels
• Incompressible paired Hall state, stripe order and the composite fermion liquid phase in half-filled Landau levels
• Quasiholes and fermionic zero modes of paired fractional quantum Hall states: the mechanism for nonabelian statistics
• Fractional Quantum Hall Effect of Composite Fermions
• Lowest-Landau-level theory of the quantum Hall effect: the Fermi-liquid-like state
• Towards a field theory of the fractional quantum Hall states
• Incompressible Quantum Liquids and New Conservation Laws
• Laughlin State on Stretched and Squeezed Cylinders and Edge Excitations in Quantum Hall Effect
• Half-Filled Lowest Landau Level on a Thin Torus
• Theory of the half-filled Landau level
• Abelian and Non-abelian Hall Liquids and Charge Density Wave: Quantum Number Fractionalization in One and Two Dimensions
• A dipole interpretation of the $\nu =1/2$ state
• Paired composite fermion wavefunctions
• The Pfaffian quantum Hall state made simple--multiple vacua and domain walls on a thin torus
• Fractional Quantum Hall States of Clustered Composite Fermions
• Microscopic theory of the quantum Hall hierarchy
• Half-filled Landau level as a Fermi liquid of dipolar quasiparticles
• Microscopic origin of the next generation fractional quantum Hall effect
• Conformal Field Theory of Composite Fermions
• The Composite Fermion Hierarchy: Condensed States of Composite Fermion Excitations?
• Wavefunctions and counting formulas for quasiholes of clustered quantum Hall states on a sphere
• Quantum Hall wave functions on the torus
• Fermion Chern Simons Theory of Hierarchical Fractional Quantum Hall States
• Microscopic formulation of the hierarchy of quantized Hall states
• Possible Reentrance of the Fractional Quantum Hall Effect in the Lowest Landau Level
• On the self-similarity in quantum Hall systems
• A First-Landau-Level Laughlin/Jain Wave Function for the Fractional Quantum Hall Effect
• Extended Bose-Hubbard model with incompressible states at fractional numbers

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