J1-J2 triangular, 48 sites, J2 = 0.125

J1J2/triangular_48_P_0.125

No record

—

solved exactly (rules §6). Every row is still listed below.

The Hamiltonian

H = ∑_⟨ij⟩ σ_i·σ_j + J₂ ∑_{⟨⟨ij⟩⟩} σ_i·σ_j

J₁ = 1, J₂ = 0.125, nearest and next-nearest neighbours, written with Pauli matrices.

lattice: triangular
sites: 48
boundary: periodic
J2: 0.125
energies: 48

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.

Numerically exact (48)

Exact diagonalization, an exact solution, or sign-problem-free QMC where that is established: the answer, not a claim about it.

E/N (S.S)	σ	Var(E)	V-score	method	source	year
-0.517314443433854(2)	1.7e-15	n/a	n/a	Exact Diagonalization Gamma.D6.A1 1	Wietek et al. (2024)	2024
-0.51408058(3)	2.9e-8	n/a	n/a	Exact Diagonalization Gamma.D6.E2 1	Wietek et al. (2024)	2024
-0.50955439(2)	2.1e-8	n/a	n/a	Exact Diagonalization X2.D1.A 1	Wietek et al. (2024)	2024
-0.508609893179167(2)	1.8e-15	n/a	n/a	Exact Diagonalization X1.D1.A 1	Wietek et al. (2024)	2024
-0.507890014740104(1)	1.4e-15	n/a	n/a	Exact Diagonalization Gamma.D6.A2 1	Wietek et al. (2024)	2024
-0.5076903098(2)	2.3e-10	n/a	n/a	Exact Diagonalization K.D3.A1 -1	Wietek et al. (2024)	2024
-0.506347037525521(2)	1.9e-15	n/a	n/a	Exact Diagonalization M.D2.B2 1	Wietek et al. (2024)	2024
-0.506216380308854(2)	1.9e-15	n/a	n/a	Exact Diagonalization M.D2.A1 -1	Wietek et al. (2024)	2024
-0.505708(1)	1.3e-6	n/a	n/a	Exact Diagonalization Z.D1.A -1	Wietek et al. (2024)	2024
-0.5053562(3)	2.8e-7	n/a	n/a	Exact Diagonalization 0.C1.A 1	Wietek et al. (2024)	2024
-0.5049362(9)	8.7e-7	n/a	n/a	Exact Diagonalization Y.D1.B 1	Wietek et al. (2024)	2024
-0.504760982093750(2)	1.9e-15	n/a	n/a	Exact Diagonalization Gamma.D6.B1 -1	Wietek et al. (2024)	2024
-0.504384051535417(2)	1.9e-15	n/a	n/a	Exact Diagonalization M.D2.B1 1	Wietek et al. (2024)	2024
-0.50376542(2)	1.8e-8	n/a	n/a	Exact Diagonalization X2.D1.B 1	Wietek et al. (2024)	2024
-0.503414383221354(2)	1.6e-15	n/a	n/a	Exact Diagonalization X1.D1.B 1	Wietek et al. (2024)	2024
-0.5030326(3)	2.6e-7	n/a	n/a	Exact Diagonalization Y.D1.A 1	Wietek et al. (2024)	2024
-0.502679109800521(2)	2.0e-15	n/a	n/a	Exact Diagonalization Gamma.D6.E1 -1	Wietek et al. (2024)	2024
-0.502507643972396(2)	1.8e-15	n/a	n/a	Exact Diagonalization M.D2.A2 -1	Wietek et al. (2024)	2024
-0.5024183(2)	2.2e-7	n/a	n/a	Exact Diagonalization 0.C1.A -1	Wietek et al. (2024)	2024
-0.50227500(2)	1.8e-8	n/a	n/a	Exact Diagonalization X2.D1.A -1	Wietek et al. (2024)	2024
-0.502234207926042(4)	3.6e-15	n/a	n/a	Exact Diagonalization X1.D1.A -1	Wietek et al. (2024)	2024
-0.5022173(8)	7.6e-7	n/a	n/a	Exact Diagonalization K.D3.E -1	Wietek et al. (2024)	2024
-0.50182790(3)	3.2e-8	n/a	n/a	Exact Diagonalization Z.D1.B 1	Wietek et al. (2024)	2024
-0.501685421021354(2)	1.9e-15	n/a	n/a	Exact Diagonalization X0.D1.A 1	Wietek et al. (2024)	2024
-0.5015143(5)	5.1e-7	n/a	n/a	Exact Diagonalization Z.D1.A 1	Wietek et al. (2024)	2024
-0.500745032976562(2)	1.8e-15	n/a	n/a	Exact Diagonalization X0.D1.A -1	Wietek et al. (2024)	2024
-0.500346608323437(5)	4.7e-15	n/a	n/a	Exact Diagonalization X0.D1.B 1	Wietek et al. (2024)	2024
-0.50006456649583(2)	1.9e-14	n/a	n/a	Exact Diagonalization K.D3.E 1	Wietek et al. (2024)	2024
-0.499787436691146(2)	1.8e-15	n/a	n/a	Exact Diagonalization X0.D1.B -1	Wietek et al. (2024)	2024
-0.499455668416667(2)	1.9e-15	n/a	n/a	Exact Diagonalization M.D2.A1 1	Wietek et al. (2024)	2024
-0.49932390(7)	7.1e-8	n/a	n/a	Exact Diagonalization Y.D1.A -1	Wietek et al. (2024)	2024
-0.498833(2)	1.6e-6	n/a	n/a	Exact Diagonalization Y.D1.B -1	Wietek et al. (2024)	2024
-0.498554(4)	4.3e-6	n/a	n/a	Exact Diagonalization Z.D1.B -1	Wietek et al. (2024)	2024
-0.49811449(2)	1.7e-8	n/a	n/a	Exact Diagonalization X2.D1.B -1	Wietek et al. (2024)	2024
-0.497800870026563(2)	1.8e-15	n/a	n/a	Exact Diagonalization X1.D1.B -1	Wietek et al. (2024)	2024
-0.496925641207292(2)	1.7e-15	n/a	n/a	Exact Diagonalization K.D3.A1 1	Wietek et al. (2024)	2024
-0.496453775061458(2)	1.8e-15	n/a	n/a	Exact Diagonalization M.D2.B2 -1	Wietek et al. (2024)	2024
-0.495366985686979(2)	1.7e-15	n/a	n/a	Exact Diagonalization M.D2.A2 1	Wietek et al. (2024)	2024
-0.494824510020833(2)	1.8e-15	n/a	n/a	Exact Diagonalization K.D3.A2 1	Wietek et al. (2024)	2024
-0.494807(3)	3.2e-6	n/a	n/a	Exact Diagonalization K.D3.A2 -1	Wietek et al. (2024)	2024
-0.4938707(2)	1.7e-7	n/a	n/a	Exact Diagonalization Gamma.D6.B2 -1	Wietek et al. (2024)	2024
-0.493285813240625(2)	2.4e-15	n/a	n/a	Exact Diagonalization M.D2.B1 -1	Wietek et al. (2024)	2024
-0.492765100647917(2)	1.7e-15	n/a	n/a	Exact Diagonalization Gamma.D6.E2 -1	Wietek et al. (2024)	2024
-0.492708955941667(2)	1.9e-15	n/a	n/a	Exact Diagonalization Gamma.D6.A1 -1	Wietek et al. (2024)	2024
-0.491663208422396(2)	1.6e-15	n/a	n/a	Exact Diagonalization Gamma.D6.B1 1	Wietek et al. (2024)	2024
-0.4902970569760(1)	1.1e-13	n/a	n/a	Exact Diagonalization Gamma.D6.B2 1	Wietek et al. (2024)	2024
-0.490204(2)	1.5e-6	n/a	n/a	Exact Diagonalization Gamma.D6.E1 1	Wietek et al. (2024)	2024
-0.489564953143229(2)	1.7e-15	n/a	n/a	Exact Diagonalization Gamma.D6.A2 -1	Wietek et al. (2024)	2024

Coverage

Newest published number here: 2024. Nothing has been added to this instance since the VarBench snapshot of 2024-10-22.

This instance as data

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