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Matrix representation of operators in Fock space

Fock Space

Number of single particle states: 4

Particle number conservation: False

Base vectors:

Index Ket Index Ket Index Ket Index Ket
0 $\mid0000\rangle$ 4 $\mid0100\rangle$ 8 $\mid1000\rangle$ 12 $\mid1100\rangle$
1 $\mid0001\rangle$ 5 $\mid0101\rangle$ 9 $\mid1001\rangle$ 13 $\mid1101\rangle$
2 $\mid0010\rangle$ 6 $\mid0110\rangle$ 10 $\mid1010\rangle$ 14 $\mid1110\rangle$
3 $\mid0011\rangle$ 7 $\mid0111\rangle$ 11 $\mid1011\rangle$ 15 $\mid1111\rangle$

Creation operators:

  • $c_0^\dagger$
  • $c_1^\dagger$
  • $c_2^\dagger$
  • $c_3^\dagger$

Annihilation operators:

  • $c_0$
  • $c_1$
  • $c_2$
  • $c_3$

Annihilation and creation operators' matrix representation

$c_0$

Row Index Column Index Entry
0 1 1
2 3 1
4 5 1
6 7 1
8 9 1
10 11 1
12 13 1
14 15 1

$c_0^{\dagger}$

Row Index Column Index Entry
1 0 1
3 2 1
5 4 1
7 6 1
9 8 1
11 10 1
13 12 1
15 14 1

$c_1$

Row Index Column Index Entry
0 2 1
1 3 -1
4 6 1
5 7 -1
8 10 1
9 11 -1
12 14 1
13 15 -1

$c_1^{\dagger}$

Row Index Column Index Entry
2 0 1
3 1 -1
6 4 1
7 5 -1
10 8 1
11 9 -1
14 12 1
15 13 -1

$c_2$

Row Index Column Index Entry
0 4 1
1 5 -1
2 6 -1
3 7 1
8 12 1
9 13 -1
10 14 -1
11 15 1

$c_2^{\dagger}$

Row Index Column Index Entry
4 0 1
5 1 -1
6 2 -1
7 3 1
12 8 1
13 9 -1
14 10 -1
15 11 1

$c_3$

Row Index Column Index Entry
0 8 1
1 9 -1
2 10 -1
3 11 1
4 12 -1
5 13 1
6 14 1
7 15 -1

$c_3^{\dagger}$

Row Index Column Index Entry
8 0 1
9 1 -1
10 2 -1
11 3 1
12 4 -1
13 5 1
14 6 1
15 7 -1

Hopping terms' matrix representation

$c_0^{\dagger} c_0$

Row Index Column Index Entry
1 1 1
3 3 1
5 5 1
7 7 1
9 9 1
11 11 1
13 13 1
15 15 1

$c_0^{\dagger} c_1$

Row Index Column Index Entry
1 2 1
5 6 1
9 10 1
13 14 1

$c_1^{\dagger} c_0$

Row Index Column Index Entry
2 1 1
6 5 1
10 9 1
14 13 1

$c_0^{\dagger} c_2$

Row Index Column Index Entry
1 4 1
3 6 -1
9 12 1
11 14 -1

$c_2^{\dagger} c_0$

Row Index Column Index Entry
4 1 1
6 3 -1
12 9 1
14 11 -1

$c_0^{\dagger} c_3$

Row Index Column Index Entry
1 8 1
3 10 -1
5 12 -1
7 14 1

$c_3^{\dagger} c_0$

Row Index Column Index Entry
8 1 1
10 3 -1
12 5 -1
14 7 1

$c_1^{\dagger} c_1$

Row Index Column Index Entry
2 2 1
3 3 1
6 6 1
7 7 1
10 10 1
11 11 1
14 14 1
15 15 1

$c_1^{\dagger} c_2$

Row Index Column Index Entry
2 4 1
3 5 1
10 12 1
11 13 1

$c_2^{\dagger} c_1$

Row Index Column Index Entry
4 2 1
5 3 1
12 10 1
13 11 1

$c_1^{\dagger} c_3$

Row Index Column Index Entry
2 8 1
3 9 1
6 12 -1
7 13 -1

$c_3^{\dagger} c_1$

Row Index Column Index Entry
8 2 1
9 3 1
12 6 -1
13 7 -1

$c_2^{\dagger} c_2$

Row Index Column Index Entry
4 4 1
5 5 1
6 6 1
7 7 1
12 12 1
13 13 1
14 14 1
15 15 1

$c_2^{\dagger} c_3$

Row Index Column Index Entry
4 8 1
5 9 1
6 10 1
7 11 1

$c_3^{\dagger} c_2$

Row Index Column Index Entry
8 4 1
9 5 1
10 6 1
11 7 1

$c_3^{\dagger} c_3$

Row Index Column Index Entry
8 8 1
9 9 1
10 10 1
11 11 1
12 12 1
13 13 1
14 14 1
15 15 1

Hubbard term's matrix representation

$n_0 n_0$

Row Index Column Index Entry
1 1 1
3 3 1
5 5 1
7 7 1
9 9 1
11 11 1
13 13 1
15 15 1

$n_0 n_1$

Row Index Column Index Entry
3 3 1
7 7 1
11 11 1
15 15 1

$n_1 n_0$

Row Index Column Index Entry
3 3 1
7 7 1
11 11 1
15 15 1

$n_0 n_2$

Row Index Column Index Entry
5 5 1
7 7 1
13 13 1
15 15 1

$n_2 n_0$

Row Index Column Index Entry
5 5 1
7 7 1
13 13 1
15 15 1

$n_0 n_3$

Row Index Column Index Entry
9 9 1
11 11 1
13 13 1
15 15 1

$n_3 n_0$

Row Index Column Index Entry
9 9 1
11 11 1
13 13 1
15 15 1

$n_1 n_1$

Row Index Column Index Entry
2 2 1
3 3 1
6 6 1
7 7 1
10 10 1
11 11 1
14 14 1
15 15 1

$n_1 n_2$

Row Index Column Index Entry
6 6 1
7 7 1
14 14 1
15 15 1

$n_2 n_1$

Row Index Column Index Entry
6 6 1
7 7 1
14 14 1
15 15 1

$n_1 n_3$

Row Index Column Index Entry
10 10 1
11 11 1
14 14 1
15 15 1

$n_3 n_1$

Row Index Column Index Entry
10 10 1
11 11 1
14 14 1
15 15 1

$n_2 n_2$

Row Index Column Index Entry
4 4 1
5 5 1
6 6 1
7 7 1
12 12 1
13 13 1
14 14 1
15 15 1

$n_2 n_3$

Row Index Column Index Entry
12 12 1
13 13 1
14 14 1
15 15 1

$n_3 n_2$

Row Index Column Index Entry
12 12 1
13 13 1
14 14 1
15 15 1

$n_3 n_3$

Row Index Column Index Entry
8 8 1
9 9 1
10 10 1
11 11 1
12 12 1
13 13 1
14 14 1
15 15 1

Hole pairing term's matrix representation

$c_0 c_1$

Row Index Column Index Entry
0 3 -1
4 7 -1
8 11 -1
12 15 -1

$c_1 c_0$

Row Index Column Index Entry
0 3 1
4 7 1
8 11 1
12 15 1

$c_0 c_2$

Row Index Column Index Entry
0 5 -1
2 7 1
8 13 -1
10 15 1

$c_2 c_0$

Row Index Column Index Entry
0 5 1
2 7 -1
8 13 1
10 15 -1

$c_0 c_3$

Row Index Column Index Entry
0 9 -1
2 11 1
4 13 1
6 15 -1

$c_3 c_0$

Row Index Column Index Entry
0 9 1
2 11 -1
4 13 -1
6 15 1

$c_1 c_2$

Row Index Column Index Entry
0 6 -1
1 7 -1
8 14 -1
9 15 -1

$c_2 c_1$

Row Index Column Index Entry
0 6 1
1 7 1
8 14 1
9 15 1

$c_1 c_3$

Row Index Column Index Entry
0 10 -1
1 11 -1
4 14 1
5 15 1

$c_3 c_1$

Row Index Column Index Entry
0 10 1
1 11 1
4 14 -1
5 15 -1

$c_2 c_3$

Row Index Column Index Entry
0 12 -1
1 13 -1
2 14 -1
3 15 -1

$c_3 c_2$

Row Index Column Index Entry
0 12 1
1 13 1
2 14 1
3 15 1

Particle pairing term's matrix representation

$c_0^{\dagger} c_1^{\dagger}$

Row Index Column Index Entry
3 0 1
7 4 1
11 8 1
15 12 1

$c_1^{\dagger} c_0^{\dagger}$

Row Index Column Index Entry
3 0 -1
7 4 -1
11 8 -1
15 12 -1

$c_0^{\dagger} c_2^{\dagger}$

Row Index Column Index Entry
5 0 1
7 2 -1
13 8 1
15 10 -1

$c_2^{\dagger} c_0^{\dagger}$

Row Index Column Index Entry
5 0 -1
7 2 1
13 8 -1
15 10 1

$c_0^{\dagger} c_3^{\dagger}$

Row Index Column Index Entry
9 0 1
11 2 -1
13 4 -1
15 6 1

$c_3^{\dagger} c_0^{\dagger}$

Row Index Column Index Entry
9 0 -1
11 2 1
13 4 1
15 6 -1

$c_1^{\dagger} c_2^{\dagger}$

Row Index Column Index Entry
6 0 1
7 1 1
14 8 1
15 9 1

$c_2^{\dagger} c_1^{\dagger}$

Row Index Column Index Entry
6 0 -1
7 1 -1
14 8 -1
15 9 -1

$c_1^{\dagger} c_3^{\dagger}$

Row Index Column Index Entry
10 0 1
11 1 1
14 4 -1
15 5 -1

$c_3^{\dagger} c_1^{\dagger}$

Row Index Column Index Entry
10 0 -1
11 1 -1
14 4 1
15 5 1

$c_2^{\dagger} c_3^{\dagger}$

Row Index Column Index Entry
12 0 1
13 1 1
14 2 1
15 3 1

$c_3^{\dagger} c_2^{\dagger}$

Row Index Column Index Entry
12 0 -1
13 1 -1
14 2 -1
15 3 -1

Content source: wangshiphys/HamiltonianPy

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