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Acta Physica Polonica A

Excitations of the Moore-Readν=5/2 State: Three-Body Correlations and Finite-Size Effects on a Sphere

A. Wόjs, J. J. Quinn

Published Jun 1, 2004• 0 citations
Publisher

Abstract

a a U ni versit y of T ennessee , Kno xvi l le, T ennessee37996, U SA b Wro cl aw Uni versi ty of T echno lo gy, 50-370 Wro cl aw, Po l and Corr el at ions in partiall y Ùlled electron and comp osite fermion Landa u levels are studied numerically .I nsight into the nature of the correlations is obtained by using mo del pair pseudop oten tials.Energy spectra of a mo del short-range three-b ody repulsion are calculated.Mo ore{ Read ground state at the half -Ùllin g and its quasielec tron , quasihol e, magnetoroton, and pair-brea ki ng excitation s are all identiÙed.T he quasielectron /qu asihol e excitations are describ ed by a comp osite fermion mo del for Laughlin-correla ted electron pairs.C omparison of energy spectra and wavef unction overlaps obtained for di ˜erent pseudop otentials suggests that Ùnite-size e˜ects can b e imp ortant in numerical diagonal i zati on studies on a sphere.PAC S numb ers: 71.

DOI
10.12693/aphyspola.105.575

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44 ~0 57 ~7 60 62 63 64 65 66 0. Introduct ion. 1. Cor re l a t ed Jas t row-type t r i a l wave functions. 2. Monte Carlo calculation of the energy expectat ion value. 3. Observed propert ies of l iquid 3He and some results of Monte Carlo c a l culations. 4. The Jaekson-Feenberg expression of the kinet ic energy. 5. Diagrammat ic expansion of the norm of the Jas t row wave function (local correlat ion factors). 6. Diagrammat ic expansion of the single-particle density. 7. Pointirreducible graphs: el iminat ion of ar t iculat ion points. 8. Expansion of the norm in the presence of spin-dependent correlation factors, 9. Rules for Jas t row diagrams with spin correlation bars but involving at most second-order loops. 10. Diagrammat ic expansion of the energy. 11. The Euler equations. 12. The chain equations in the absence of spin correlations. 13. A simple example of chain equations. 14. An example of chain equations in the presence of spin correlations. 141. Chain equations in the spin-0 channel. 142. Chain equations in the spin-1 channel. 15. Spin correlations in l iquid aHe. 151. Renormalizat ion of the (dashed) central correlation line. 152. Renormalizat ion of the spin correlation bar. 153. Renormalizat ion of the (central) s ta t ic L i n d h a r d f u n c t i o n S~c. 154. Renormalizat ion o f the s ta t ic L indhard function SF in the spin-i channel. 66 155. Calculation of S ' and the Euler equation. 69 16, Sound and spin waves in the collective co-ordinate approximation.

•Jan 1, 1983•0 citations
a a U ni versit y of T ennessee , Kno xvi l le, T ennessee37996, U SA b Wro cl aw Uni versi ty of T echno lo gy, 50-370 Wro cl aw, Po l and Corr el at ions in partiall y Ùlled electron and comp osite fermion Landa u levels are studied numerically .I nsight into the nature of the correlations is obtained by using mo del pair pseudop oten tials.Energy spectra of a mo del short-range three-b ody repulsion are calculated.Mo ore{ Read ground state at the half -Ùllin g and its quasielec tron , quasihol e, magnetoroton, and pair-brea ki ng excitation s are all identiÙed.T he quasielectron /qu asihol e excitations are describ ed by a comp osite fermion mo del for Laughlin-correla ted electron pairs.C omparison of energy spectra and wavef unction overlaps obtained for di ˜erent pseudop otentials suggests that Ùnite-size e˜ects can b e imp ortant in numerical diagonal i zati on studies on a sphere.PAC S numb ers: 71.
Energy spectra of a model short‐range three‐body repulsion are calculated for a half‐filled Landau level. The Moore‐Read ground state and its quasielectron (QE), quasihole (QH), magnetoroton (QE+QH), and pair‐breaking excitations are all identified. Two‐ and three‐body correlations of these states are analyzed. The QE/QH excitations are described by a composite fermion model for Laughlin‐correlated electron pairs. Comparison with the results obtained for the Coulomb interaction suggests that finite‐size effects are important in numerical diagonalization for the v = 5/2 quantum Hall state.
Two- and three-body correlations in partially filled degenerate fermion shells are studied numerically for various interactions between the particles. Three distinct correlation regimes are defined, depending on the superharmonic, subharmonic, or harmonic forms of Haldane pair pseudopotential at short range. The harmonic form applies to electrons in the first excited Landau level (LL1)({\mathrm{LL}}_{1})(LL1​). Their correlations near half filling are confirmed to have a simple three-body form characteristic of the Moore-Read (MR) Pfaffian state, consisting of the maximum avoidance of the triplet state with the smallest relative angular momentum. To study MR correlations quantitatively, three-body amplitudes and pseudopotentials are introduced and calculated. Exact sum rules derived for the amplitudes imply that MR correlations depend on the actual (pair) interaction largely through the short-range behavior of the corresponding three-body interaction. In the calculated spectra of a model three-body repulsion, higher-energy bands are identified in addition to (previously known) MR ground state and its elementary charged (quasiparticle) and neutral (pair-breaking) excitations. The pair-breaker dispersion curve is determined, and the quasiparticles are correctly described by a generalization of the composite fermion model appropriate for Halperin ppp-type electron pairing with Laughlin correlations between the pairs. The known problem of the exact few-electron ground states having small overlaps with MR trial states on a sphere is also resolved by showing that the short-range three-body pseudopotential coefficients are more sensitive to the surface curvature than the two-body ones (leading to a slow convergence of the overlaps as a function of the electron number). Hence, the MR state and its excitations are believed to be a more accurate description of the experimental $\ensuremath{\nu}=\frac{5}{2}$ quantum Hall states than could be inferred from previous, small-size calculations.
Ê I nst i t ut e of P hysi cs, Si l esian Uni versity Uni werstytec ka 4, 40-007 Ka to wi ce, Pol an d ( Recei ved December 14, 2001)W e consider t he extended H ubb ard mo del for the single cubic lattice and re w rite it in the form of interacting dimers , using the exact solutio n of the dimer problem .W e anal ytical l y deri ve the second quanti zation form of the dimer H amiltoni an elimina tin g from the consideratio ns uno ccupie d dimer energy levels in the large U limit (it is the only assumption ).T he resulting dimer H amiltonian w ritten with the use of the Hubbard op erators and spin operators contains three terms, visuali zin g explicitl y comp eting magnetic interactions (f erromagnetic, antif erromagnetic) as a generaliz atio n of the t { J mo del.T he presented, nonp erturbati ve metho d, can in principl e b e applied to the cluster of any size (e.g. one central atom and z its nearest neighb ours).T he use of the pro j ection technique can further b e appli ed in the case of a crystal to obtain the second quantization form of the extended H ubbard mo del for the sc lattice in the large U limit.
Electron correlation is studied in the special case of a single reversed spin in an otherwise fully aligned band in the one-dimensional Hubbard model for the purpose of examining our previous theory which exactly takes account of the three-body correlation. The importance of the three-body correlation is demonstrated through a comparison of our results with those of exact theories. The ground-state energy and the single particle spectra are in good agreement with McGuire-Lieb-Wu's exact solution and also with exact numerical solutions for finite size systems over a wide range of the intraatomic Coulomb integral and the electron number. The properties of the ground state are studied in detail through the calculation of pair correlation functions.
Sm ol uchow ski Insti tut e of Ph ysi cs, Jagi ell oni an Uni versi ty Reym onta 4, 30-059 Cra cow, Po l and ( Recei ved December 8, 2003; i n Ùnal for m Marc h 5, 2004)W e have observe d a Zeema n e˜e ct in an evanescent w ave absor ption in Rb v ap or with a sin gle-mo de t unable dio de laser .T he spectra are obtained for several magnetic Ùeld-and laser light-conÙgurati ons enablin g the observ ation of di˜erent ¤ and ¥ Zeeman split lines contribution.T he relative amplitud es and relative fre quencies of all Zeeman comp onents w ere calculated theoreticall y and compared w ith measured spectra.T he analysis of the data can lead to the determination of the polari zati on state of the evanescent w ave.PAC S numb ers: 42.25.Gy , 32. 60. + i
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