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All instances / J1-J2

J1-J2 square 10x10, J2 = 0.55

J1J2/square_100_P_0.55

Record

-0.48693(3) E/N (S.S)

VMC + 2 Lanczos steps

Hu, Becca, Parola & Sorella, Dir · lowest eligible strict variational bound (rules §6)

The Hamiltonian

H = ∑⟨ij⟩ σi·σj + J2⟨⟨ij⟩⟩ σi·σj

J1 = 1, J2 = 0.55, nearest and next-nearest neighbours, written with Pauli matrices.

lattice
square
sites
100
boundary
periodic
J2
0.55
energies
9

Stored as a total energy in the convention of VarBench; quoted here as E/N (S.S), 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 (7)

The record is the lowest eligible energy in this group, and only this group.

E/N (S.S)σVar(E)V-score methodsourceyear
-0.48693(3)record 3.0e-5 n/a n/a VMC + 2 Lanczos steps
peer reviewed
Hu, Becca, Parola & Sorella, Dir n/a
-0.48677(1) 1.1e-5 n/a n/a GCNN (deep group-convolutional network)
peer reviewed
Roth et al. (2022) 2022
-0.48622(1) 1.0e-5 n/a n/a VMC + 1 Lanczos step
peer reviewed
Hu, Becca, Parola & Sorella, Dir n/a
-0.4854340 n/a n/a n/a DMRG on the L x L torus, 8192 SU(2) states
peer reviewed
Gong, Zhu, Sheng, Motrunich & Fi n/a
-0.4852390 n/a n/a n/a DMRG on the L x L torus, 6144 SU(2) states
peer reviewed
Gong, Zhu, Sheng, Motrunich & Fi n/a
-0.4848900 n/a n/a n/a DMRG on the L x L torus, 4096 SU(2) states
peer reviewed
Gong, Zhu, Sheng, Motrunich & Fi n/a
-0.48335(1) 1.0e-5 n/a n/a VMC, p = 0 Lanczos steps
peer reviewed
Hu, Becca, Parola & Sorella, Dir n/a

Extrapolations (2)

Zero-variance, bond-dimension or Trotter-error extrapolations. Not a bound: no ansatz ever reached the number, so it cannot hold the record.

E/N (S.S)σVar(E)V-score methodsourceyear
-0.4880000 n/a n/a n/a DMRG, extrapolated in the truncation error (4096-8192 SU(2) states)
peer reviewed
Gong, Zhu, Sheng, Motrunich & Fi n/a
-0.48766(6) 6.0e-5 n/a n/a VMC + Lanczos steps, extrapolated in the variance
peer reviewed
Hu, Becca, Parola & Sorella, Dir n/a

How these numbers were read

Rows added after the VarBench import record where the number came from.

-0.4880000 ○ — DMRG, extrapolated in the truncation error (4096-8192 SU(2)...

Checked 2026-09-15 · source text of arXiv:1311.5962 read locally (arXiv HTML or pypdf layout text); value copied from the harvested cell and the text, no LLM transcription of numbers; parsed by column from the primary table

Reported as. -0.4880

Table I of arXiv:1311.5962 (pypdf layout text, line 658), J2 = 0.55, L = 10, column 4 of 8 | E/J1 per site in S.S units on the L x L periodic torus (caption)

-0.48766(6) — VMC + Lanczos steps, extrapolated in the variance

Checked 2026-09-15 · source text of arXiv:1304.2630 read locally (arXiv HTML or pypdf layout text); value copied from the harvested cell and the text, no LLM transcription of numbers; parsed by column from the primary table

Reported as. -0.48766(6)

TABLE IV of arXiv:1304.2630 (pypdf layout text, line 390), L = 10, S = 0, J2/J1 = 0.55 | E/J1 per site in S.S units on the L x L periodic torus; the S = 0 row is the ground state

-0.48693(3) — VMC + 2 Lanczos steps

Checked 2026-09-15 · source text of arXiv:1304.2630 read locally (arXiv HTML or pypdf layout text); value copied from the harvested cell and the text, no LLM transcription of numbers; parsed by column from the primary table

Reported as. -0.48693(3)

TABLE III of arXiv:1304.2630 (pypdf layout text, line 370), L = 10, S = 0, J2/J1 = 0.55 | E/J1 per site in S.S units on the L x L periodic torus; the S = 0 row is the ground state

-0.48677(1) — GCNN (deep group-convolutional network)

Checked 2026-09-15 · source text of arXiv:2211.07749 read locally (arXiv HTML or pypdf layout text); value copied from the harvested cell and the text, no LLM transcription of numbers; parsed by column from the primary table

Reported as. -0.486772(11)

Table I of arXiv:2211.07749 (pypdf layout text, line 188), J2/J1 = 0.55, 10x10, Our work | E/J1 per site in S.S units on the L x L periodic torus (caption: units of J1/spin)

-0.48622(1) — VMC + 1 Lanczos step

Checked 2026-09-15 · source text of arXiv:1304.2630 read locally (arXiv HTML or pypdf layout text); value copied from the harvested cell and the text, no LLM transcription of numbers; parsed by column from the primary table

Reported as. -0.48622(1)

TABLE II of arXiv:1304.2630 (pypdf layout text, line 348), L = 10, S = 0, J2/J1 = 0.55 | E/J1 per site in S.S units on the L x L periodic torus; the S = 0 row is the ground state

-0.4854340 ○ — DMRG on the L x L torus, 8192 SU(2) states

Checked 2026-09-15 · source text of arXiv:1311.5962 read locally (arXiv HTML or pypdf layout text); value copied from the harvested cell and the text, no LLM transcription of numbers; parsed by column from the primary table

Reported as. -0.485434

Table I of arXiv:1311.5962 (pypdf layout text, line 658), J2 = 0.55, L = 10, column 3 of 8 | E/J1 per site in S.S units on the L x L periodic torus (caption)

-0.4852390 ○ — DMRG on the L x L torus, 6144 SU(2) states

Checked 2026-09-15 · source text of arXiv:1311.5962 read locally (arXiv HTML or pypdf layout text); value copied from the harvested cell and the text, no LLM transcription of numbers; parsed by column from the primary table

Reported as. -0.485239

Table I of arXiv:1311.5962 (pypdf layout text, line 658), J2 = 0.55, L = 10, column 2 of 8 | E/J1 per site in S.S units on the L x L periodic torus (caption)

-0.4848900 ○ — DMRG on the L x L torus, 4096 SU(2) states

Checked 2026-09-15 · source text of arXiv:1311.5962 read locally (arXiv HTML or pypdf layout text); value copied from the harvested cell and the text, no LLM transcription of numbers; parsed by column from the primary table

Reported as. -0.484890

Table I of arXiv:1311.5962 (pypdf layout text, line 658), J2 = 0.55, L = 10, column 1 of 8 | E/J1 per site in S.S units on the L x L periodic torus (caption)

-0.48335(1) — VMC, p = 0 Lanczos steps

Checked 2026-09-15 · source text of arXiv:1304.2630 read locally (arXiv HTML or pypdf layout text); value copied from the harvested cell and the text, no LLM transcription of numbers; parsed by column from the primary table

Reported as. -0.48335(1)

TABLE I of arXiv:1304.2630 (pypdf layout text, line 326), L = 10, S = 0, J2/J1 = 0.55 | E/J1 per site in S.S units on the L x L periodic torus; the S = 0 row is the ground state

Coverage

Newest published number here: 2022. 9 rows added from the 2026-09 literature sweep, on top of the VarBench snapshot of 2024-10-22.

This instance as data

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