Table 1 Quantum numbers and overlap on the plane.
From: Local models of fractional quantum Hall states in lattices and physical implementation
N | L x × L y |
| f | r | D |
|
|
|---|---|---|---|---|---|---|---|
12 | 4 × 3 | 0 | +1 | +1 | 252 | 0.9866 | 0.9989 |
16 | 4 × 4 | 0 | +1 | +1 | 3,299 | 0.9886 | 0.9993 |
20 | 4 × 5 | 0 | +1 | +1 | 46,508 | 0.9848 | 0.9992 |
- The table provides the overlap |〈ψP0|
›| and the overlap per site |〈ψP0|
›|1/N between the ground state ψP0 of the local Hamiltonian in equation (3) with φ1=0.07 × 2π, φ2=0.03 × 2π, and open boundary conditions and the CFT state 
in equation (2). 
is the eigenvalue of the z component of the total spin of ψP0 and 
, f is the eigenvalue of the operator that flips all the spins, r is the eigenvalue of the operator that rotates the lattice by 180° and D is the dimension of the subspace of Hilbert space that consists of all states with the given eigenvalues. In general, 
=0, f=(−1)N/2 and r=(−1)N/2 for the CFT state. The overlaps are remarkably high, in particular when taking the large dimension of the involved Hilbert spaces into account.
›| and the overlap per site |〈ψP0|
›|1/N between the ground state ψP0 of the local Hamiltonian in equation (3) with φ1=0.07 × 2π, φ2=0.03 × 2π, and open boundary conditions and the CFT state 
in equation (2). 
is the eigenvalue of the z component of the total spin of ψP0 and 
, f is the eigenvalue of the operator that flips all the spins, r is the eigenvalue of the operator that rotates the lattice by 180° and D is the dimension of the subspace of Hilbert space that consists of all states with the given eigenvalues. In general, 
=0, f=(−1)N/2 and r=(−1)N/2 for the CFT state. The overlaps are remarkably high, in particular when taking the large dimension of the involved Hilbert spaces into account.