The Hamiltonian
H = −∑⟨ij⟩ σziσzj − h ∑i σxi
Transverse field h = 4. Already in Pauli operators, with no S·S term to rescale, so the per-site energy is E/N.
- lattice
- square
- sites
- 144
- boundary
- open
- h
- 4
- energies
- 4
Stored as a total energy; quoted here as
E/N (Pauli), which is what the papers report
(how the conversion works).
How these numbers were read
Where each number below was read, and how it was checked.
-4.1217979 — DMRG
Checked 2026-10-16 · source text of arXiv:2606.25600 read locally (arXiv HTML or pypdf layout text); value copied from the harvested cell and the text, no LLM transcription of numbers; single reading
Reported as. -593.5389
Table 6, row DMRG (not exact); sources/2606.25600.txt line 808; version read: arXiv v1 text (sources/2606.25600.txt); every energy string checked identical in v2 (2026-10-10); no journal version (Crossref, arXiv abs page); the paper's own DMRG, labelled 'DMRG (not exact)'; no bond dimension, code or reference given | Eq. (17): H = -J sum_<ij> sigma^z sigma^z - B_x sum_i sigma^x, Pauli matrices, J = 1, open boundaries in both directions; energies are totals (they scale with N: DMRG -202.5077/64, -316.9770/100, -457.0416/144 = -3.164, -3.170, -3.174 per site); QMBL's h is B_x.
-4.12153(5) — 2D RNN (Euclidean cells)
Checked 2026-10-16 · source text of arXiv:2606.25600 read locally (arXiv HTML or pypdf layout text); value copied from the harvested cell and the text, no LLM transcription of numbers; single reading
Reported as. −593.5006 (0.0072)
Table 6, row Euclidean 2DRNN , column Best, upper line (error in lower line); sources/2606.25600.txt line 799; version read: arXiv v1 text (sources/2606.25600.txt); every energy string checked identical in v2 (2026-10-10); no journal version (Crossref, arXiv abs page); best over runs with distinct initialisations; the line below the energy prints its standard error, 0.0072 | Eq. (17): H = -J sum_<ij> sigma^z sigma^z - B_x sum_i sigma^x, Pauli matrices, J = 1, open boundaries in both directions; energies are totals (they scale with N: DMRG -202.5077/64, -316.9770/100, -457.0416/144 = -3.164, -3.170, -3.174 per site); QMBL's h is B_x.
-4.12150(5) — 2D RNN (Lorentz (hyperbolic) cells, L_max = 2.0)
Checked 2026-10-16 · source text of arXiv:2606.25600 read locally (arXiv HTML or pypdf layout text); value copied from the harvested cell and the text, no LLM transcription of numbers; single reading
Reported as. −593.4953 (0.0077)
Table 6, row Lorentz 2DRNN Lmax=2.0, column Best, upper line (error in lower line); sources/2606.25600.txt line 802; version read: arXiv v1 text (sources/2606.25600.txt); every energy string checked identical in v2 (2026-10-10); no journal version (Crossref, arXiv abs page); best over runs with distinct initialisations; the line below the energy prints its standard error, 0.0077 | Eq. (17): H = -J sum_<ij> sigma^z sigma^z - B_x sum_i sigma^x, Pauli matrices, J = 1, open boundaries in both directions; energies are totals (they scale with N: DMRG -202.5077/64, -316.9770/100, -457.0416/144 = -3.164, -3.170, -3.174 per site); QMBL's h is B_x.
-4.12133(5) — 2D RNN (Lorentz (hyperbolic) cells, L_max = 1.5)
Checked 2026-10-16 · source text of arXiv:2606.25600 read locally (arXiv HTML or pypdf layout text); value copied from the harvested cell and the text, no LLM transcription of numbers; single reading
Reported as. −593.4719 (0.0068)
Table 6, row Lorentz 2DRNN Lmax=1.5, column Best, upper line (error in lower line); sources/2606.25600.txt line 805; version read: arXiv v1 text (sources/2606.25600.txt); every energy string checked identical in v2 (2026-10-10); no journal version (Crossref, arXiv abs page); best over runs with distinct initialisations; the line below the energy prints its standard error, 0.0068 | Eq. (17): H = -J sum_<ij> sigma^z sigma^z - B_x sum_i sigma^x, Pauli matrices, J = 1, open boundaries in both directions; energies are totals (they scale with N: DMRG -202.5077/64, -316.9770/100, -457.0416/144 = -3.164, -3.170, -3.174 per site); QMBL's h is B_x.