The fractional quantum hall effect and the rotation group
- Los Alamos National Lab., NM (United States)
- Washington Univ., Seattle, WA (United States). Inst. for Nuclear Theory
The fractional quantum Hall effect is thought to be the result of correlations between electrons induced by their mutual interactions. This paper explores the consequences of these correlations numerically and analytically. The problem is mapped onto the surface of a sphere, so that the number of states in the first Landau level is finite. The following three sections review this geometry, give the matrix elements of the Coulomb interaction, and compare exact wave functions with the Laughlin/Haldane ground state ansatz for fractional fillings 1/m, m an odd integer. While this ansatz accounts for many of the J = 0 ground states found in numerical diagonalizations, it does not explain all such states. To make progress on this problem. A complete characterization of the most general four-particle J = 0 wave function is given, including an algebraic enumeration of the number of such states. This construction provides one example of a 2/3-filled state, the particle-hole conjugate of the 3-particle Laughlin/Haldane m = 3 state. This result suggests a generalization that may give the particle-hole conjugates of all Laughlin/Haldane states of arbitrary N: the construction depends on an equivalence of single-particle spinors of rank N/2 and ones formed by coupling the elementary spinors of N different particles. This result is further generalized to produce a wave function ansatz that may account for other fractional fillings of physical interest.
- Research Organization:
- Los Alamos National Lab., NM (United States); Washington Univ., Seattle, WA (United States). Inst. for Nuclear Theory
- Sponsoring Organization:
- USDOE, Washington, DC (United States)
- DOE Contract Number:
- FG06-90ER40561; FG06-88ER40427
- OSTI ID:
- 10155834
- Report Number(s):
- DOE/ER/40561-084; CONF-9208164-3; ON: DE93010348; IN: INT-92-09-04; TRN: 93:015180
- Resource Relation:
- Conference: 6. symmetries in science,Bregenz (Austria),2-7 Aug 1992; Other Information: PBD: [1992]
- Country of Publication:
- United States
- Language:
- English
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