The Hamiltonian
An impurity model from the upstream set (SB-DMFT-MI-HF). Its Hamiltonian is defined by VarBench rather than here, so it is identified by name rather than restated, and it has no meaningful per-site energy.
Upstream this instance is Impurity/SB-DMFT-MI-HF_9. The name's 9 is the run script's Nbath (varbench/methods scripts/Impurity/SB-DMFT-MI-HF_9.py, line 17); at U = 8 and half filling the script discretises the bath with Nb = Nbath + 1 = 10 sites per spin-orbital (lines 41-44), and the Hamiltonian file it was run on (HamParams/SB-DMFT-MI_9.h5) holds ten. Both rows were computed there: QMBL's exact diagonalization on eleven orbitals per spin (the impurity and ten bath sites; N_up = 6, N_dn = 5, dimension 213444) reproduces both to 1e-13, and the stored E_inf follows only from the ten-site bath. Evidence: checks/cost/ed/results/Impurity--SB-DMFT-MI-HF_9.json.
- lattice
- SB-DMFT-MI-HF
- sites
- 10
- boundary
- —
- energies
- 2
Stored as a total energy in the convention of
VarBench; quoted here as
E (total), which is what the papers report
(how the conversion works).
Every published energy
Grouped by what the number is. Ranking happens only inside the first group.
Strict variational upper bounds (1)
Where the instance is not solved, the record is the lowest eligible energy in this group; where it is, the lowest eligible energy here is the best variational bound and the closest challenger to the exact one.
Numerically exact (1)
Exact diagonalization, an exact solution, or sign-problem-free QMC where that is established: the answer, not a claim about it, and therefore the record wherever one exists. QMC is exact only within its statistical error bar, which it must state, and its rows read exact (stochastic); an exact diagonalization outranks it. A diagonalization resolved by symmetry sector is listed for the ground state's sector only; the lowest energies of the other sectors are the instance's spectrum, in its JSON, and hold nothing.