Laughlin's function on a cylinder: plasma analogy and representation as a quantum polymer

Jansen, Sabine; Lieb, Élliott H.; Seiler, R.

doi:10.1002/pssb.200743516

Cited by 11 publications

(20 citation statements)

References 27 publications

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“…This is, indeed, true, as was shown in [FGIL]. Moreover, the recursive structure carries over to coefficients in Laughlin's wave function [JLS,Lemma 3]. Let us explain this in some more detail.…”

Section: Block Structure Of the Vandermonde Matrixmentioning

confidence: 54%

Fermionic and bosonic Laughlin state on thick cylinders

Jansen

2012

Journal of Mathematical Physics

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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.Comment: 49 page

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Section: Block Structure Of the Vandermonde Matrixmentioning

confidence: 54%

Fermionic and bosonic Laughlin state on thick cylinders

Jansen

2012

Journal of Mathematical Physics

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“…2. Energy spectra for one (N, Ns) = (5, 16) and two (5,17) holes at ν = 1/3 with five unit cells-these excitations, identified in the TT-limit, are shown as red lines.…”

Section: Numerics Away From Tt-limitmentioning

confidence: 99%

“…2 shows the insertion of one (5/16) and two (5/17) holes at ν = 1/3 with N c = 5 unit cells. The TT-ground state at 5/15 is (hp) 5 . Adding one hole one obtains 5/16, where the lowest energy state in Fig.…”

Section: Appendix C: Exclusion Statisticsmentioning

confidence: 99%

“…2 are found to be h(hp) 2 h(hp) 3 , h(hp)h(hp) 4 and h 2 (hp) 5 (each of them 17-fold degenerate) in the TTlimit, in order of increasing energy. To determine N hh we must keep the first hole fixed and count the number of states for the second hole h ′ -the three low-energy states (and translations of them) then give the states: hh ′ (hp) 5 , h(hp)h ′ (hp) 4 , h(hp) 2 h ′ (hp) 3 , h(hp) 3 h ′ (hp) 2 , and h(hp) 4 h ′ (hp); thus N hh = 5. (h and h ′ are of course identical so the order of them does not matter.)…”

Section: Appendix C: Exclusion Statisticsmentioning

confidence: 99%

“…The first of these is of course the 1/3 ground state, whereas the others are particle-hole excitations thereof. All these states can be obtained by inserting a hole and a particle in the 5/15 ground state (hp) 5 . Adding one hole to (hp) 5 one obtains the five low energy states h(hp) 5 according to the analysis above, thus N h = 5.…”

Section: Appendix C: Exclusion Statisticsmentioning

confidence: 99%

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Exclusion statistics for quantum Hall states in the Tao–Thouless limit

Kardell¹,

Karlhede²

2011

J. Stat. Mech.

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We consider spin-polarized abelian quantum Hall states in the Tao-Thouless limit, ie on a thin torus. For any filling factor ν = p/q a well-defined sector of low-energy states is identified and the exclusion statistics of the excitations is determined. We study numerically, at and near ν = 1/3 and 2/5, how the low energy states develop as one moves away from the TT-limit towards the physical regime. We find that the lowest energy states in the physical regime develop from states in the low energy sector but that the exclusion statistics is modified.

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Symmetry Breaking in Quasi-1D Coulomb Systems

Aizenman

Jansen

Jung

2010

Ann. Henri Poincaré

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Quasi one-dimensional systems are systems of particles in domains which are of infinite extent in one direction and of uniformly bounded size in all other directions, e.g. on a cylinder of infinite length. The main result proven here is that for such particle systems with Coulomb interactions and neutralizing background, the so-called "jellium", at any temperature and at any finite-strip width there is translation symmetry breaking. This extends the previous result on Laughlin states in thin, two-dimensional strips by Jansen, Lieb and Seiler (2009). The structural argument which is used here bypasses the question of whether the translation symmetry breaking is manifest already at the level of the one particle density function. It is akin to that employed by Aizenman and Martin (1980) for a similar statement concerning symmetry breaking at all temperatures in strictly one-dimensional Coulomb systems. The extension is enabled through bounds which establish tightness of finite-volume charge fluctuations.

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Laughlin's function on a cylinder: plasma analogy and representation as a quantum polymer

Cited by 11 publications

References 27 publications

Fermionic and bosonic Laughlin state on thick cylinders

Fermionic and bosonic Laughlin state on thick cylinders

Exclusion statistics for quantum Hall states in the Tao–Thouless limit

Symmetry Breaking in Quasi-1D Coulomb Systems

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