IMSRG flow equations:
The White generator:
Energy denominators:
Simplification of flow equation for nuclear matter:
Pairing model with 4 particles, in 4 doubly degenerate levels, for $\delta=1$ and $g=+0.5$
Solving the IMSRG flow equation with a simple Euler step method with step size $ds = 0.1$. $E_0$ is the zero-body piece of the flowing Hamiltonian $H(s)$. EMBPT2 is the second order MBPT energy using $H(s)$, and $dE/ds$ is the zero body part of $[\eta(s), H(s)]$.
$s$ | $E_0$ | EMBPT2 | $dE/ds$ |
---|---|---|---|
0.0 | 1.50000 | -0.0623932 | 0.0000000 |
0.1 | 1.48752 | -0.0531358 | -0.1247860 |
0.2 | 1.47689 | -0.0453987 | -0.1062720 |
0.3 | 1.46781 | -0.0388940 | -0.0907975 |
0.4 | 1.46004 | -0.0333983 | -0.0777880 |
0.5 | 1.45336 | -0.0287359 | -0.0667967 |
The same numbers as before, but now the $[\eta_2, H_2]_2$ particle-hole commutator term is omitted.
$s$ | $E_0$ | EMBPT2 | $dE/ds$ |
---|---|---|---|
0 | 1.5 | -0.0623932 | 0 |
0.1 | 1.48752 | -0.0531358 | -0.124786 |
0.2 | 1.47689 | -0.0453551 | -0.106272 |
0.3 | 1.46782 | -0.0387878 | -0.0907102 |
0.4 | 1.46007 | -0.0332251 | -0.0775756 |
0.5 | 1.45342 | -0.0284994 | -0.0664503 |
0.6 | 1.44772 | -0.0244746 | -0.0569988 |
0.7 | 1.44283 | -0.0210395 | -0.0489492 |
These are the same as before, but with the painful $[\eta_{2b}, H_{2b}]_{2b}$ particle-hole term omitted.
$s$ | $E0$ | EMBPT2 | $dE/ds$ |
---|---|---|---|
0.0 | 1.50000 | -0.0623932 | 0 |
0.1 | 1.48752 | -0.0531358 | -0.124786 |
0.2 | 1.47689 | -0.0453551 | -0.106272 |
0.3 | 1.46782 | -0.0387878 | -0.0907102 |
0.4 | 1.46007 | -0.0332251 | -0.0775756 |
0.5 | 1.45342 | -0.0284994 | -0.0664503 |