Fermionic and bosonic Laughlin state on thick cylinders

Abstract

We investigate a many-body wave function for particles on a cylinder known as Laughlin's function. It is the power of a Vandermonde determinant times a Gaussian. Our main result is: in a many-particle limit, at fixed radius, all correlation functions have a unique limit, and the limit state has a non-trivial period in the axial direction. The result holds regardless how large the radius is, for fermions as well as bosons. In addition, we explain how the algebraic structure used in proofs relates to a ground state perturbation series and to quasi-state decompositions, and we show that the monomer-dimer function introduced in an earlier work is an exact, zero energy, ground state of a suitable finite range Hamiltonian; this is interesting because of formal analogies with some quantum spin chains.

49 pages

References in corpus (4)

• Lieb-Robinson Bounds and the Exponential Clustering Theorem
• Symmetry breaking in Laughlin's state on a cylinder
• Symmetry breaking in quasi-1D Coulomb systems
• Laughlin's function on a cylinder: plasma analogy and representation as a quantum polymer

Cited by in corpus (8)

• Geometric construction of Quantum Hall clustering Hamiltonians
• Quantum Hall phases and plasma analogy in rotating trapped Bose gases
• Solvable models for unitary and non-unitary topological phases
• Spectral Gaps and Incompressibility in a $\nu =1/3$ Fractional Quantum Hall System
• Low-complexity eigenstates of a $\nu =1/3$ fractional quantum Hall system
• The spectral gap of a fractional quantum Hall system on a thin torus
• One-dimensional lattice model with an exact matrix-product ground state describing the Laughlin wave function
• Excitation and tunneling spectra of a fractional quantum Hall system in the thin cylinder limit