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All instances / J1-J2

J1-J2 square 6x6, J2 = 0.55

J1J2/square_36_P_0.55

Record

-0.4951670E/N (S.S)

DMRG on the L x L torus, 8192 SU(2) states

Gong, Zhu, Sheng, Motrunich & Fi · 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
36
boundary
periodic
J2
0.55
energies
8

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 (6)

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

E/N (S.S)σVar(E)V-score methodsourceyear
-0.4951670record 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
-0.4951500 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
-0.4950960 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
-0.49399(1) 1.0e-5 n/a n/a VMC + 2 Lanczos steps
peer reviewed
Hu, Becca, Parola & Sorella, Dir n/a
-0.49303(1) 1.0e-5 n/a n/a VMC + 1 Lanczos step
peer reviewed
Hu, Becca, Parola & Sorella, Dir n/a
-0.48992(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
-0.49521(7) 7.0e-5 n/a n/a VMC + Lanczos steps, extrapolated in the variance
peer reviewed
Hu, Becca, Parola & Sorella, Dir n/a
-0.495186(1) 1.0e-6 n/a n/a DMRG, extrapolated in the truncation error (4096-8192 SU(2) states)
peer reviewed
Gong, Zhu, Sheng, Motrunich & Fi n/a

How these numbers were read

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

-0.49521(7) — 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. -0.49521(7)

TABLE IV of arXiv:1304.2630 (pypdf layout text, line 384), L = 6, 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

-0.495186(1) — 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. -0.495186(1)

Table I of arXiv:1311.5962 (pypdf layout text, line 656), J2 = 0.55, L = 6, column 4 of 8 | E/J1 per site in S.S units on the L x L periodic torus (caption)

-0.4951670 ○ — 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. -0.495167

Table I of arXiv:1311.5962 (pypdf layout text, line 656), J2 = 0.55, L = 6, column 3 of 8 | E/J1 per site in S.S units on the L x L periodic torus (caption)

-0.4951500 ○ — 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. -0.495150

Table I of arXiv:1311.5962 (pypdf layout text, line 656), J2 = 0.55, L = 6, column 2 of 8 | E/J1 per site in S.S units on the L x L periodic torus (caption)

-0.4950960 ○ — 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. -0.495096

Table I of arXiv:1311.5962 (pypdf layout text, line 656), J2 = 0.55, L = 6, column 1 of 8 | E/J1 per site in S.S units on the L x L periodic torus (caption)

-0.49399(1) — 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. -0.49399(1)

TABLE III of arXiv:1304.2630 (pypdf layout text, line 364), L = 6, 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

-0.49303(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. -0.49303(1)

TABLE II of arXiv:1304.2630 (pypdf layout text, line 342), L = 6, 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

-0.48992(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. -0.48992(1)

TABLE I of arXiv:1304.2630 (pypdf layout text, line 320), L = 6, 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

No row here carries a publication year. 8 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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