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Exact Diagonalization of the Fractional Quantum Hall Many-Body Hamiltonian in the Lowest Landau Level | | Detlef Lehmann
; | | Date: |
6 Dec 2001 | | Subject: | Mesoscopic Systems and Quantum Hall Effect; Statistical Mechanics; Mathematical Physics | cond-mat.mes-hall cond-mat.stat-mech math-ph math.MP | | Affiliation: | TU Berlin | | Abstract: | For a gaussian interaction V(x,y)=lambda e^{-(x^2+y^2)/r^2} with long range r>>l_B, l_B the magnetic length, we rigorously prove that the eigenvalues of the finite volume Hamiltonian H_{N,LL}=P_{LL} H_N P_{LL}, H_N=sum_{i=1}^N [-ihbar
abla_{x_i}-eA(x_i)]^2+sum_{i,j; i
e j} V(x_i-x_j),
otA=(0,0,B), and P_{LL} the projection onto the lowest Landau level, are given by the following set: Let M be the number of flux quanta flowing through the sample such that
u=N/M is the filling factor. Then each eigenvalue is given by E=E(n_1,...,n_N)=sum_{i,j=1;i
e j}^N W(n_i-n_j). Here n_iin {1,2,...,M}, n_1<... | | Source: | arXiv, cond-mat/0112092 | | Services: | Forum | Review | PDF | Favorites | |
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