All 322 instances

One page per Hamiltonian instance, at a stable URL, listing every published energy for it. 182 instances have a record; the rest say why they do not.

Heisenberg#

96 instances, 31 with a record, energies as E/N (S.S)

instance	record	method	rows
chain, 20 sites, open	-0.4341237	DMRG (max truncation error ~ 1.0E-12) run script, no paper cited	5
chain, 20 sites	-0.4452193	DMRG (max truncation error ~ 1.0E-13) run script, no paper cited	7
chain, 200 sites, open	-0.4422078	DMRG (max truncation error ~ 1.0E-14) run script, no paper cited	3
chain, 200 sites	-0.4431678	DMRG (max truncation error ~ 2.8E-12) run script, no paper cited	4
kagome-24, 24 sites	no record	solved exactly	1
kagome 2x2 (12 sites)	no record	solved exactly	1
kagome 2x3 (18 sites)	-0.4471262	DMRG (bond dimension = 368) run script, no paper cited	5
kagome-30, 30 sites	no record	solved exactly	1
kagome-36a, 36 sites	no record	solved exactly	1
kagome-36b, 36 sites	no record	solved exactly	1
kagome-36c, 36 sites	no record	solved exactly	1
kagome-36d, 36 sites	no record	solved exactly	1
kagome-42a, 42 sites	no record	solved exactly	1
kagome-42b, 42 sites	no record	solved exactly	1
kagome 4x4 (48 sites)	-0.4375(2)	GCNN (6 layers, 6 feature maps), symmetric ansatz Đurić et al. (2024)	4
kagome 6x6 (108 sites)	no record	every variational row is flagged	2
kagome 8x8 (192 sites)	-0.42987(1)	VMC with Dirac spin liquid + Jastrow run script, no paper cited	1
pyrochlore 2x2x2 (32 sites)	-0.51627(2)	mVMC with SU(2) and symmetry projections Astrakhantsev et al. (2021)	3
pyrochlore 2x2x2 (128 sites)	-0.49220(4)	mVMC (PP + RBM + 1st step Lanczos, spin-parity... Pohle et al. (2023)	1
pyrochlore 3x3x3 (108 sites)	-0.48711(9)	mVMC with SU(2) and symmetry projections Astrakhantsev et al. (2021)	3
pyrochlore 3x3x3 (432 sites)	-0.48847(3)	mVMC (PP + 1st step Lanczos, spin-parity projection... Pohle et al. (2023)	1
pyrochlore 4x4x4 (256 sites)	-0.48310(7)	mVMC with SU(2) and symmetry projections Astrakhantsev et al. (2021)	2
pyrochlore 4x4x4 (1024 sites)	-0.48800(1)	mVMC (PP + 1st step Lanczos, spin-parity projection... Pohle et al. (2023)	1
rectangular 10x20, periodic/open	no record	solved exactly	1
rectangular 12x24, periodic/open	no record	solved exactly	1
rectangular 14x28, periodic/open	no record	solved exactly	1
rectangular 16x32, periodic/open	no record	solved exactly	1
rectangular 18x36, periodic/open	no record	solved exactly	1
rectangular 20x40, periodic/open	no record	solved exactly	1
rectangular 24x48, periodic/open	no record	solved exactly	1
rectangular 32x64, periodic/open	no record	solved exactly	1
rectangular 48x96, periodic/open	no record	solved exactly	1
rectangular 4x8, periodic/open	no record	solved exactly	1
rectangular 64x128, periodic/open	no record	solved exactly	1
rectangular 6x12, periodic/open	no record	solved exactly	1
rectangular 6x8	no record	solved exactly	1
rectangular 8x16, periodic/open	no record	solved exactly	1
shuriken, 24 sites	no record	solved exactly	1
shuriken, 96 sites	-0.43826(1)	mVMC with SU(2) and point group projection Astrakhantsev et al. (2021)	1
shuriken, 216 sites	-0.4376(1)	mVMC with SU(2) and point group projection Astrakhantsev et al. (2021)	1
shuriken, 384 sites	-0.4371(1)	mVMC with SU(2) and point group projection Astrakhantsev et al. (2021)	1
square 4x4	-0.7017449	VQE + symm. circuit (64 pars., exact grad... run script, no paper cited	3
square 6x6, open	-0.6035218	DMRG (bond dimension = 2048) run script, no paper cited	5
square 6x6	-0.67887(2)	2D RNN wavefunction (best variational) Moss et al. (2025)	9
square, 40 sites	no record	solved exactly	1
square, 50 sites	no record	solved exactly	1
square 8x8, open	no record	solved exactly	1
square 8x8	no record	solved exactly	1
square 10x10, open	-0.628656(9)	2D tensorized RNN (symmetry + annealing) Hibat-Allah et al. (2022)	16
square 10x10	-0.67155260(3)	CNN + MinSR Chen & Heyl (2023)	12
square 12x12, open	no record	solved exactly	1
square 12x12	no record	solved exactly	1
square 14x14, open	no record	solved exactly	1
square 14x14	-0.668346(8)	VMC with fermions (flux+neel+Jastrow) run script, no paper cited	5
square 16x16, open	-0.643504(3)	2D minGRU (3 layers, c4v symmetry, parallel scan) Merali et al. (2026)	4
square 16x16	no record	solved exactly	1
square 18x18, open	no record	solved exactly	1
square 18x18	no record	solved exactly	1
square 20x20, open	no record	solved exactly	1
square 20x20	no record	solved exactly	1
square 22x22, open	no record	solved exactly	1
square 22x22	no record	solved exactly	1
square 24x24, open	no record	solved exactly	1
square 24x24	no record	solved exactly	1
square 26x26, open	no record	solved exactly	1
square 26x26	no record	solved exactly	1
square 28x28, open	no record	solved exactly	1
square 28x28	no record	solved exactly	1
square 30x30	no record	solved exactly	1
square 32x32, open	no record	solved exactly	1
square 32x32	no record	solved exactly	1
square 36x36	no record	solved exactly	1
square 40x40	no record	solved exactly	1
square 44x44	no record	solved exactly	1
square 48x48, open	no record	solved exactly	1
square 48x48	no record	solved exactly	1
square 52x52	no record	solved exactly	1
square 56x56	no record	solved exactly	1
square 60x60	no record	solved exactly	1
square 64x64, open	no record	solved exactly	1
square 64x64	no record	solved exactly	1
square 72x72	no record	solved exactly	1
square 80x80	no record	solved exactly	1
square 88x88	no record	solved exactly	1
square 96x96, open	no record	solved exactly	1
square 96x96	no record	solved exactly	1
square 128x128, open	no record	solved exactly	1
triangular 4x4	-0.5347197	DMRG (bond dimension = 256) run script, no paper cited	5
triangular 6x6	-0.560313(3)	Group CNN (deep, symmetry-projected) Roth et al. (2022)	8
triangular, 48 sites	no record	solved exactly	1
triangular 10x10, open	-0.5147668	DMRG (bond dimension = 4096) run script, no paper cited	7
triangular, 108 sites	-0.55315(3)	GCNN (deep group-equivariant CNN) Roth et al. (2022)	2
triangular 12x12, open	-0.5150648	DMRG (Bond dimension = 3000) run script, no paper cited	5
triangular 12x12	-0.54624(2)	VMC with Dirac+field+Jastrow run script, no paper cited	4
triangular 14x14, open	-0.5138(1)	2D Gated RNN Hibat-Allah et al. (2022)	5
triangular 16x16, open	-0.51668(9)	2D Gated RNN Hibat-Allah et al. (2022)	4

J1-J2#

56 instances, 43 with a record, energies as E/N (S.S)

instance	record	method	rows
rectangular 4x6, J2 = 0.5	-0.5225249	DMRG (bond dimension = 4096) run script, no paper cited	6
square 4x4, J2 = 0.05	-0.6805657	VQE + symm. circuit (64 pars., exact grad... run script, no paper cited	3
square 4x4, J2 = 0.1	-0.6597832	VQE + symm. circuit (64 pars., exact grad... run script, no paper cited	3
square 4x4, J2 = 0.15	-0.6395066	VQE + symm. circuit (64 pars., exact grad... run script, no paper cited	3
square 4x4, J2 = 0.2	-0.6198639	VQE + symm. circuit (64 pars., exact grad... run script, no paper cited	3
square 4x4, J2 = 0.25	-0.6009332	VQE + symm. circuit (64 pars., exact grad... run script, no paper cited	3
square 4x4, J2 = 0.3	-0.5829420	VQE + symm. circuit (64 pars., exact grad... run script, no paper cited	3
square 4x4, J2 = 0.35	-0.5662285	VQE + symm. circuit (64 pars., exact grad... run script, no paper cited	3
square 4x4, J2 = 0.4	-0.5511033	VQE + symm. circuit (64 pars., exact grad... run script, no paper cited	3
square 4x4, J2 = 0.45	-0.5382766	VQE + symm. circuit (64 pars., exact grad... run script, no paper cited	3
square 4x4, J2 = 0.5	-0.5286202	DMRG (bond dimension = 256) run script, no paper cited	6
square 4x4, J2 = 0.6	-0.5258158	VQE + symm. circuit (64 pars., exact grad... run script, no paper cited	3
square 4x4, J2 = 0.65	-0.5393444	VQE + symm. circuit (64 pars., exact grad... run script, no paper cited	3
square 4x4, J2 = 0.7	-0.5637643	VQE + symm. circuit (64 pars., exact grad... run script, no paper cited	3
square 4x4, J2 = 0.75	-0.5942152	VQE + symm. circuit (64 pars., exact grad... run script, no paper cited	3
square 4x4, J2 = 0.8	-0.6273137	VQE + symm. circuit (64 pars., exact grad... run script, no paper cited	3
square 4x4, J2 = 0.85	-0.6617069	VQE + symm. circuit (64 pars., exact grad... run script, no paper cited	3
square 4x4, J2 = 0.9	-0.6967967	VQE + symm. circuit (64 pars., exact grad... run script, no paper cited	3
square 4x4, J2 = 0.95	-0.7324804	VQE + symm. circuit (64 pars., exact grad... run script, no paper cited	3
square 4x4, J2 = 1	-0.7684501	VQE + symm. circuit (64 pars., exact grad... run script, no paper cited	3
square 6x6, J2 = 0.3	-0.5618876	DMRG (bond dimension = 2048) run script, no paper cited	4
square 6x6, J2 = 0.4	-0.529687(7)	RBM wave function Chen et al. (2022)	6
square 6x6, J2 = 0.5	-0.503800(1)	RBM+PP with momentum (K=0), spin-parity (even S)... Nomura & Imada (2021)	11
square 6x6, J2 = 0.6	-0.49318(5)	RBM wave function + 2-step Lanczos recursion Chen et al. (2022)	8
square 6x6, J2 = 0.7	-0.5299243	DMRG (bond dimension = 2048) run script, no paper cited	5
square 6x6, J2 = 0.8	-0.586411(9)	RBM wave function Chen et al. (2022)	6
square 6x6, J2 = 0.9	-0.6478705	DMRG (bond dimension = 2048) run script, no paper cited	4
square 6x6, J2 = 1	-0.71429(1)	RBM wave function Chen et al. (2022)	6
square, 40 sites, J2 = 0.1	no record	solved exactly	1
square, 40 sites, J2 = 0.2	no record	solved exactly	1
square, 40 sites, J2 = 0.3	no record	solved exactly	1
square, 40 sites, J2 = 0.4	no record	solved exactly	1
square, 40 sites, J2 = 0.5	no record	solved exactly	1
square, 40 sites, J2 = 0.55	no record	solved exactly	1
square, 40 sites, J2 = 0.6	no record	solved exactly	1
square, 40 sites, J2 = 0.65	no record	solved exactly	1
square, 40 sites, J2 = 0.7	no record	solved exactly	1
square, 40 sites, J2 = 0.8	no record	solved exactly	1
square, 40 sites, J2 = 0.9	no record	solved exactly	1
square, 40 sites, J2 = 1	no record	solved exactly	1
square 8x8, J2 = 0.5	-0.498963(2)	RBM+PP with momentum (K=0), spin-parity (even S)... Nomura & Imada (2021)	8
square 8x8, J2 = 0.55	-0.48835(8)	ClebschTree Vieijra & Nys (2021)	1
square 10x10, J2 = 0.3	-0.55485(1)	VMC with fermions (flux+neel+Jastrow) run script, no paper cited	4
square 10x10, J2 = 0.4	-0.52388(2)	RBM wave function Chen et al. (2022)	5
square 10x10, J2 = 0.5	-0.4976939(2)	CNN-MPS (h,D,l)=(32,20,20), Marshall sign... Fan et al. (2026)	15
square 10x10, J2 = 0.6	-0.4774611	DMRG (bond dimension = 1024) run script, no paper cited	5
square 10x10, J2 = 0.7	-0.51889(2)	RBM wave function Chen et al. (2022)	4
square 10x10, J2 = 0.8	-0.57404(2)	RBM wave function Chen et al. (2022)	5
square 10x10, J2 = 0.9	-0.6269664	DMRG (bond dimension = 1024) run script, no paper cited	3
square 10x10, J2 = 1	-0.69670(2)	RBM wave function Chen et al. (2022)	5
square 14x14, J2 = 0.5	-0.49443(1)	VMC with projected BCS (Z2 spin liquid) run script, no paper cited	4
square 16x16, J2 = 0.5	-0.4969140(5)	CNN-MPS Fan et al. (2026)	3
square 20x20, J2 = 0.5	-0.4967987(6)	CNN-MPS (h,D,l)=(32,15,20) Fan et al. (2026)	2
triangular, 48 sites, J2 = 0.125	no record	solved exactly	48
triangular, 108 sites, J2 = 0.125	-0.51268(9)	GCNN + Lanczos step Roth et al. (2022)	4
triangular 12x12, J2 = 0.125	-0.51218(9)	GCNN + Lanczos step Roth et al. (2022)	4

Hubbard#

137 instances, 75 with a record, energies as E/site

instance	record	method	rows
chain, 14 sites, U = 1, n ≈ 0.5714	-0.9116293	DMRG (MaxBondDim = 1550, Extrap Energy = -12.762823... run script, no paper cited	2
chain, 14 sites, U = 1.66810054, n ≈ 0.5714	no record	solved exactly	2
chain, 14 sites, U = 2.15443469, n ≈ 0.5714	-0.8542284	DMRG (MaxBondDim ~1500) run script, no paper cited	2
chain, 14 sites, U = 2.7825594, n ≈ 0.5714	-0.8300032	DMRG (MaxBondDim ~1500) run script, no paper cited	2
chain, 14 sites, U = 3.59381366, n ≈ 0.5714	-0.8043230	DMRG (MaxBondDim ~1500) run script, no paper cited	2
chain, 14 sites, U = 4.64158882, n ≈ 0.5714	-0.7783541	DMRG (MaxBondDim ~1500) run script, no paper cited	2
chain, 14 sites, U = 7.74263683, n ≈ 0.5714	-0.7304717	DMRG (MaxBondDim ~1500) run script, no paper cited	2
chain, 14 sites, U = 10, n ≈ 0.5714	-0.7103637	DMRG (MaxBondDim ~1500, Extrap Eng = -9.9450941 +/-... run script, no paper cited	2
rectangular 14x16, U = 8, n = 0.875	-0.75830(4)	VAFQMC stripe length=7 Sorella (2023)	1
rectangular 4x16, U = 8, n = 0.875	-0.76623(1)	ACE (16 conv layers) + full symmetry projection Gu et al. (2026)	8
rectangular 4x16, periodic/open, U = 2, n = 0.8125	-1.2852656	DMRG (MaxLinkDim = 6000, MaxTruncErr~1.0E-04) run script, no paper cited	1
rectangular 4x16, periodic/open, U = 8, n = 0.8125	-0.8530000	DMRG (MaxLinkDim = 4000, MaxTruncErr~5.0E-05) run script, no paper cited	1
rectangular 4x16, periodic/open, U = 2, n = 0.875	-1.2611875	DMRG (MaxLinkDim = 4000, MaxTruncErr~8.0E-05) run script, no paper cited	1
rectangular 4x16, periodic/open, U = 8, n = 0.875	-0.7508328	DMRG (MaxLinkDim = 10000, MaxTruncErr~2.0E-05... run script, no paper cited	2
rectangular 4x16, periodic/open, U = 2, n = 0.9375	-1.2199062	DMRG (MaxLinkDim = 4000, MaxTruncErr~1.2E-04) run script, no paper cited	1
rectangular 4x16, periodic/open, U = 8, n = 0.9375	-0.6378750	DMRG (MaxLinkDim = 4000, MaxTruncErr~1.5E-05) run script, no paper cited	1
rectangular 4x16, periodic/open, U = 2, n = 1	-1.1710781	DMRG (MaxLinkDim = 4000, MaxTruncErr~3.5E-05) run script, no paper cited	1
rectangular 4x16, periodic/open, U = 8, n = 1	-0.5144219	DMRG (MaxLinkDim = 4000, MaxTruncErr~4.7E-07) run script, no paper cited	1
rectangular 4x8, U = 8, n = 0.875	-0.76690(1)	HFPS (hidden-fermion Pfaffian state) Chen et al. (2025)	3
rectangular 4x8, periodic/open, U = 8, n = 0.875	-0.7363906	DMRG (MaxLinkDim = 12000, MaxTruncErr~6.6E-06... run script, no paper cited	4
rectangular 6x48, U = 8, n ≈ 0.8333	-0.82075(3)	VMC with stripe of wavelength 6 (+Jastrow and... run script, no paper cited	4
rectangular 6x48, U = 8, n = 0.875	-0.74834(3)	VMC with stripe of wavelength 8 (+Jastrow and... run script, no paper cited	4
rectangular 6x48, U = 12, n = 0.875	-0.62556(3)	VMC with stripe of wavelength 6 (+Jastrow and... run script, no paper cited	4
rectangular 6x48, U = 8, n ≈ 0.9167	-0.67269(3)	VMC with stripe of wavelength 8 (+Jastrow and... run script, no paper cited	4
square 4x4, U = 2, n = 0.5	-1.1559648	DMRG (MaxLinkDim ~ 3200) run script, no paper cited	2
square 4x4, U = 3.5981, n = 0.5	-1.1060144	DMRG (MaxBondDim ~3200) run script, no paper cited	3
square 4x4, U = 4, n = 0.5	-1.0959310	DMRG (MaxBondDim ~ 3200) run script, no paper cited	2
square 4x4, U = 6, n = 0.5	-1.0562454	DMRG (MaxBondDim ~ 3200) run script, no paper cited	2
square 4x4, U = 7.74264, n = 0.5	-1.0318221	DMRG (MaxBondDim ~3200) run script, no paper cited	3
square 4x4, U = 8, n = 0.5	-1.0287892	DMRG (MaxBondDim ~ 3200) run script, no paper cited	2
square 4x4, U = 10, n = 0.5	-1.0089505	DMRG (MaxBondDim = 3200) run script, no paper cited	3
square 4x4, U = 2, n = 0.625	-1.3360594	DMRG (MaxBondDim = 7000) run script, no paper cited	2
square 4x4, U = 2.1544, n = 0.625	-1.3257670	DMRG (MaxBondDim 7000) run script, no paper cited	3
square 4x4, U = 3.5981, n = 0.625	-1.2431527(4)	VMC Hidden Fermion Determinant State Ansatz... Moreno et al. (2022)	3
square 4x4, U = 4, n = 0.625	-1.2238086	DMRG (MaxBondDim = 7000) run script, no paper cited	2
square 4x4, U = 6, n = 0.625	-1.1473978 ○	DMRG (MaxBondDim = 7000) run script, no paper cited	2
square 4x4, U = 7.74264, n = 0.625	-1.1002331	DMRG (MaxBondDim = 7000) run script, no paper cited	3
square 4x4, U = 8, n = 0.625	-1.0943979	DMRG (MaxBondDim = 7000) run script, no paper cited	2
square 4x4, U = 10, n = 0.625	-1.0564725	DMRG (MaxBondDim = 7000) run script, no paper cited	3
square 4x4, U = 2, n = 1	no record	solved exactly	1
square 4x4, U = 4, n = 1	no record	solved exactly	1
square 4x4, U = 6, n = 1	no record	solved exactly	1
square 4x4, U = 8, n = 1	no record	solved exactly	1
square 4x4, periodic/antiperiodic, U = 2, n = 1	no record	solved exactly	1
square 4x4, periodic/antiperiodic, U = 4, n = 1	no record	solved exactly	1
square 4x4, periodic/antiperiodic, U = 6, n = 1	no record	solved exactly	1
square 4x4, periodic/antiperiodic, U = 8, n = 1	no record	solved exactly	1
square 6x6, U = 4, n ≈ 0.6667	no record	no variational row	1
square 6x6, U = 2, n = 1	no record	solved exactly	1
square 6x6, U = 4, n = 1	no record	solved exactly	1
square 6x6, U = 6, n = 1	no record	solved exactly	1
square 6x6, U = 8, n = 1	no record	solved exactly	1
square 6x6, U = 4, n ≈ 1.3333	no record	no variational row	1
square 6x6, periodic/antiperiodic, U = 2, n = 1	-1.2079(1)	VMC Hidden Fermion Determinant State Ansatz... Moreno et al. (2022)	3
square 6x6, periodic/antiperiodic, U = 4, n = 1	-0.87173(2)	VMC Hidden Fermion Determinant State Ansatz... Moreno et al. (2022)	2
square 6x6, periodic/antiperiodic, U = 6, n = 1	-0.66094(3)	VMC Hidden Fermion Determinant State Ansatz... Moreno et al. (2022)	2
square 6x6, periodic/antiperiodic, U = 8, n = 1	-0.52705(3)	VMC Hidden Fermion Determinant State Ansatz... Moreno et al. (2022)	2
square, 50 sites, U = 8, n = 0.84	-0.82328(3)	VAFQMC Sorella (2023)	1
square 8x8, U = 4, n = 0.4375	no record	no variational row	1
square 8x8, U = 4, n = 0.6875	no record	no variational row	1
square 8x8, U = -8, n ≈ 0.7813	no record	solved exactly	1
square 8x8, U = -4, n ≈ 0.7813	no record	solved exactly	1
square 8x8, U = 4, n ≈ 0.7813	-1.130375(5)	mVMC with SU(2) and momentum projections (gamma... run script, no paper cited	3
square 8x8, U = 8, n ≈ 0.7813	-0.91483(2)	mVMC with SU(2) and momentum projections (gamma... run script, no paper cited	3
square 8x8, U = -8, n = 0.875	no record	solved exactly	1
square 8x8, U = -4, n = 0.875	no record	solved exactly	1
square 8x8, U = 4, n = 0.875	-1.00580(3)	VMC with uniform BCS pairing (+Jastrow and backflow) run script, no paper cited	2
square 8x8, U = 8, n = 0.875	-0.7458(6)	Jastrow-backflow (JBf), 8x8 torus Sharma et al. (2025)	8
square 8x8, U = -8, n = 1	no record	solved exactly	1
square 8x8, U = -4, n = 1	no record	solved exactly	1
square 8x8, U = 2, n = 1	no record	solved exactly	1
square 8x8, U = 4, n = 1	-0.859156(8)	mVMC with SU(2) and momentum projections (gamma... run script, no paper cited	5
square 8x8, U = 6, n = 1	no record	solved exactly	1
square 8x8, U = 8, n = 1	-0.52459(1)	mVMC with SU(2) and momentum projections (gamma... run script, no paper cited	4
square 8x8, periodic/antiperiodic, U = 2, n = 1	-1.19003(9)	VMC Hidden Fermion Determinant State Ansatz... Moreno et al. (2022)	2
square 8x8, periodic/antiperiodic, U = 4, n = 1	-0.8622(2)	VMC Hidden Fermion Determinant State Ansatz... Moreno et al. (2022)	2
square 8x8, periodic/antiperiodic, U = 6, n = 1	-0.6574(2)	VMC Hidden Fermion Determinant State Ansatz... Moreno et al. (2022)	3
square 8x8, periodic/antiperiodic, U = 8, n = 1	-0.5245(2)	VMC Hidden Fermion Determinant State Ansatz... Moreno et al. (2022)	2
square 8x8, periodic/open, U = 8, n = 1	-0.49944(4)	VAFQMC Sorella (2023)	3
square 10x10, U = 4, n = 0.8	no record	no variational row	1
square 10x10, U = 2, n = 1	no record	solved exactly	1
square 10x10, U = 4, n = 1	no record	solved exactly	1
square 10x10, U = 6, n = 1	no record	solved exactly	1
square 10x10, U = 8, n = 1	no record	solved exactly	1
square 10x10, periodic/antiperiodic, U = 2, n = 1	no record	solved exactly	1
square 10x10, periodic/antiperiodic, U = 4, n = 1	no record	solved exactly	1
square 10x10, periodic/antiperiodic, U = 6, n = 1	no record	solved exactly	1
square 10x10, periodic/antiperiodic, U = 8, n = 1	no record	solved exactly	1
square 12x12, U = 4, n ≈ 0.8056	no record	no variational row	1
square 12x12, U = 2, n = 1	no record	solved exactly	1
square 12x12, U = 4, n = 1	no record	solved exactly	1
square 12x12, U = 6, n = 1	no record	solved exactly	1
square 12x12, U = 8, n = 1	no record	solved exactly	1
square 12x12, periodic/antiperiodic, U = 2, n = 1	no record	solved exactly	1
square 12x12, periodic/antiperiodic, U = 4, n = 1	no record	solved exactly	1
square 12x12, periodic/antiperiodic, U = 6, n = 1	no record	solved exactly	1
square 12x12, periodic/antiperiodic, U = 8, n = 1	no record	solved exactly	1
square 14x14, U = 2, n = 1	no record	solved exactly	1
square 14x14, U = 4, n = 1	no record	solved exactly	1
square 14x14, U = 6, n = 1	no record	solved exactly	1
square 14x14, U = 8, n = 1	no record	solved exactly	1
square 14x14, periodic/antiperiodic, U = 2, n = 1	no record	solved exactly	1
square 14x14, periodic/antiperiodic, U = 4, n = 1	no record	solved exactly	1
square 14x14, periodic/antiperiodic, U = 6, n = 1	no record	solved exactly	1
square 14x14, periodic/antiperiodic, U = 8, n = 1	no record	solved exactly	1
square 16x16, U = 8, n ≈ 0.8281	-0.83788(6)	VAFQMC stripe length=8 Sorella (2023)	1
square 16x16, U = 8, n ≈ 0.8438	-0.81198(6)	VAFQMC stripe length=8 Sorella (2023)	1
square 16x16, U = 8, n ≈ 0.8516	-0.79896(5)	VAFQMC stripe length=8 Sorella (2023)	1
square 16x16, U = 8, n ≈ 0.8594	-0.78530(6)	VAFQMC stripe length=8 Sorella (2023)	2
square 16x16, U = 8, n ≈ 0.8672	-0.77196(6)	VAFQMC stripe length=8 Sorella (2023)	1
square 16x16, U = -8, n = 0.875	no record	solved exactly	1
square 16x16, U = -4, n = 0.875	no record	solved exactly	1
square 16x16, U = 4, n = 0.875	-1.02916(2)	VAFQMC stripe length=8 Sorella (2023)	2
square 16x16, U = 6, n = 0.875	-0.86592(2)	VAFQMC stripe length=8 Sorella (2023)	2
square 16x16, U = 8, n = 0.875	-0.75865(3)	VAFQMC stripe length 8 Sorella (2023)	13
square 16x16, U = 8, n ≈ 0.8828	-0.74455(3)	VAFQMC stripe length=8 Sorella (2023)	1
square 16x16, U = 4, n ≈ 0.8906	-1.00849(2)	VAFQMC stripe length=8 Sorella (2023)	2
square 16x16, U = 6, n ≈ 0.8906	-0.84058(2)	VAFQMC stripe length=8 Sorella (2023)	2
square 16x16, U = 8, n ≈ 0.8906	-0.73038(5)	VAFQMC stripe length=8 Sorella (2023)	2
square 16x16, U = 8, n ≈ 0.8984	-0.71584(5)	VAFQMC stripe length=8 Sorella (2023)	1
square 16x16, U = 8, n ≈ 0.9063	-0.70135(3)	VAFQMC stripe length=8 Sorella (2023)	2
square 16x16, U = 8, n ≈ 0.9141	-0.68678(5)	VAFQMC stripe length=8 Sorella (2023)	1
square 16x16, U = 8, n ≈ 0.9219	-0.67215(5)	VAFQMC stripe length=8 Sorella (2023)	1
square 16x16, U = 8, n = 0.9375	-0.64053(5)	VAFQMC stripe length=8 Sorella (2023)	1
square 16x16, U = -8, n = 1	no record	solved exactly	1
square 16x16, U = -4, n = 1	no record	solved exactly	1
square 16x16, U = 2, n = 1	no record	solved exactly	1
square 16x16, U = 4, n = 1	no record	solved exactly	1
square 16x16, U = 6, n = 1	no record	solved exactly	1
square 16x16, U = 8, n = 1	no record	solved exactly	1
square 16x16, periodic/antiperiodic, U = 8, n ≈ 0.8359	-0.82333(3)	VAFQMC stripe length 8 APBC along the stripe Sorella (2023)	2
square 16x16, periodic/antiperiodic, U = 8, n ≈ 0.8359, t12	-0.79937(4)	mVMC with SU(2) and momentum projections (gamma... run script, no paper cited	1
square 16x16, periodic/antiperiodic, U = 8, n ≈ 0.8359, t12, UV1V2	1.25918(3)	mVMC with SU(2) and momentum projections (gamma... run script, no paper cited	1
square 16x16, periodic/antiperiodic, U = 2, n = 1	no record	solved exactly	1
square 16x16, periodic/antiperiodic, U = 4, n = 1	no record	solved exactly	1
square 16x16, periodic/antiperiodic, U = 6, n = 1	no record	solved exactly	1
square 16x16, periodic/antiperiodic, U = 8, n = 1	-0.52427(4)	VAFQMC Sorella (2023)	4

Spinless t-V#

14 instances, 14 with a record, energies as E/site

instance	record	method	rows
chain, 32 sites, V = 1, n = 0.5	-0.4983390	DMRG (maxbonddim = 573) run script, no paper cited	4
chain, 32 sites, V = 2, n = 0.5	-0.3852719 ○	DMRG (maxbonddim = 200) run script, no paper cited	3
chain, 32 sites, V = 4, n = 0.5	-0.2344426 ○	DMRG (maxbonddim = 200) run script, no paper cited	3
square 4x4, V = 0.01, n = 0.3125	-0.7487521(6)	VMC Determinant Slater-Jastrow (RBM) Ansatz Romero et al. (2024)	3
square 4x4, V = 0.1, n = 0.3125	-0.7376632(3)	VMC Determinant Slater-Backflow-Jastrow (RBM)... Romero et al. (2024)	5
square 4x4, V = 1, n = 0.3125	-0.6400407	DMRG (maxbonddim = 74) run script, no paper cited	5
square 4x4, V = 10, n = 0.3125	-0.2532535	DMRG (maxbonddim = 74) run script, no paper cited	5
square 6x6, V = 0.01, n ≈ 0.3611	-0.7759280(1)	VMC Determinant Slater-Jastrow (RBM) Ansatz with... Romero et al. (2024)	3
square 6x6, V = 0.1, n ≈ 0.3611	-0.759460(1)	VMC Determinant Slater-Jastrow (RBM) Ansatz with... Romero et al. (2024)	4
square 6x6, V = 1, n ≈ 0.3611	-0.6132263	DMRG (maxbonddim = 4096) run script, no paper cited	4
square 6x6, V = 10, n ≈ 0.3611	-0.2201239	DMRG (maxbonddim = 4096) run script, no paper cited	4
square 8x8, V = 1, n = 0.5	-0.4590635	DMRG (maxbonddim = 4096) run script, no paper cited	2
square 8x8, V = 2, n = 0.5	-0.2911555	DMRG (maxbonddim = 4096) run script, no paper cited	2
square 8x8, V = 4, n = 0.5	-0.1601344	DMRG (maxbonddim = 4096) run script, no paper cited	2

Transverse-field Ising#

7 instances, 7 with a record, energies as E/N (Pauli)

instance	record	method	rows
chain, 10 sites, open, h = 1	-1.2381490	DMRG (bond dimension = 13) run script, no paper cited	6
chain, 10 sites, h = 1	-1.2784906	DMRG (bond dimension = 28) run script, no paper cited	4
chain, 32 sites, h = 0.5	-1.0635444	DMRG (bond dimension = 24) run script, no paper cited	5
chain, 32 sites, h = 1	-1.2737510	DMRG (bond dimension = 71) run script, no paper cited	5
square 6x6, h = 3	-3.2009084	DMRG (bond dimension = 1024) run script, no paper cited	4
square 12x12, open, h = 3	-3.1739018(2)	2D Recurrent Neural Network (2DRNN) Hibat-Allah et al. (2020)	4
square 20x20, open, h = 3	-3.1819700 ○	DMRG on TPU (bond dimension = 32768) Ganahl et al. (2023)	7

Impurity#

12 instances, 12 with a record, energies as E (total)

instance	record	method	rows
SB-DMFT-MI-HF, size 9	-34.5805205	DMRG (bond dimension 100) using fork tensor product... Bauernfeind et al. (2017)	2
SB-DMFT-MT-AHF, size 9	-13.8893249	DMRG (bond dimension 100) using fork tensor product... Bauernfeind et al. (2017)	2
SB-DMFT-MT-HF, size 9	-23.3009472	DMRG (bond dimension 100) using fork tensor product... Bauernfeind et al. (2017)	2
SB-IMP, size 9	-10.4871285	DMRG (bond dimension 100) using fork tensor product... Bauernfeind et al. (2017)	2
TB-DMFT, size 9	-112.9042852	DMRG (bond dimension 350) using fork tensor product... Bauernfeind et al. (2017)	3
TB-DMFT, size 19	-224.3360713	DMRG (bond dimension 350) using fork tensor product... Bauernfeind et al. (2017)	3
TB-DMFT, size 119	-1307.5645417	DMRG (bond dimension 350) using fork tensor product... Bauernfeind et al. (2017)	3
TB-DMFT, size 309	-3378.6762368	DMRG (bond dimension 350) using fork tensor product... Bauernfeind et al. (2017)	3
TB-DMFT-SOC, size 9	-112.8717703	DMRG (bond dimension 350) using fork tensor product... Bauernfeind et al. (2017)	3
TB-DMFT-SOC, size 19	-219.7669110	DMRG (bond dimension 350) using fork tensor product... Bauernfeind et al. (2017)	3
TB-DMFT-SOC, size 119	-1305.3902308	DMRG (bond dimension 350) using fork tensor product... Bauernfeind et al. (2017)	3
TB-DMFT-SOC, size 309	-3351.7573592	DMRG (bond dimension 350) using fork tensor product... Bauernfeind et al. (2017)	3