Symmetry breaking in Laughlin's state on a cylinder

Abstract

We investigate Laughlin's fractional quantum Hall effect wave function on a cylinder. We show that it displays translational symmetry breaking in the axial direction for sufficiently thin cylinders. At filling factor 1/p, the period is p times the period of the filled lowest Landau level. The proof uses a connection with one-dimensional polymer systems and discrete renewal equations.

34 pages, 5 figures. A few explanations added

References in corpus (11)

• Incompressible Quantum Liquids and New Conservation Laws
• Quantum Hall system in Tao-Thouless limit
• Laughlin State on Stretched and Squeezed Cylinders and Edge Excitations in Quantum Hall Effect
• Laughlin's wave functions, Coulomb gases and expansions of the discriminant
• One-Dimensional Theory of the Quantum Hall System
• Mott Insulators Without Symmetry Breaking
• Slater Decomposition of Laughlin States
• Entropy-driven phase transition in a polydisperse hard-rods lattice system
• Translation Symmetry Breaking in the One-Component Plasma on the Cylinder
• Quantum Mechanics on Thin Cylinders
• Laughlin's function on a cylinder: plasma analogy and representation as a quantum polymer

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• Spin-chain description of fractional quantum Hall states in the Jain series
• Low-complexity eigenstates of a $\nu =1/3$ fractional quantum Hall system
• Link between the hierarchy of fractional quantum Hall states and Haldane's conjecture for quantum spin chains
• Repulsion in low temperature $\beta$-ensembles
• Symmetry breaking in quasi-1D Coulomb systems
• Fermionic and bosonic Laughlin state on thick cylinders
• The Monte Carlo simulation of the topological quantities in FQH systems
• Supersymmetric gauge theories, Coulomb gases and Chern-Simons matrix models
• Exclusion statistics for quantum Hall states in Tao-Thouless limit
• Dynamical abelian anyons with bound states and scattering states
• Vortex and fractional quantum Hall phases in a rotating anisotropic Bose gas
• Excitation and tunneling spectra of a fractional quantum Hall system in the thin cylinder limit