Ground state of the Heisenberg model#

Overview#

This notebook will give an example how to use Renormalizer to calculate the ground state energy of the open boundary spin 1/2 1-D Heisenberg model.

\[H = J \sum_i [S_i^z S_{i+1}^z + \frac{1}{2}(S_i^+ S_{i+1}^- + S_i^- S_{i+1}^+)]\]

Exact result via Bethe Anstatz:

\(L\)

\(E/J\)

16

-6.9117371455749

24

-10.4537857604096

32

-13.9973156182243

48

-21.0859563143863

64

-28.1754248597421

Setup#

[1]:

from renormalizer import Model, Op, BasisHalfSpin,  Mps, Mpo, optimize_mps

2026-05-20 02:56:09,042[INFO] Use NumPy as backend
2026-05-20 02:56:09,043[INFO] numpy random seed is 9012
2026-05-20 02:56:09,044[INFO] random seed is 1092
2026-05-20 02:56:09,053[INFO] Git Commit Hash: 956ad15b6be989049c1a009a0050334f3d774d43
2026-05-20 02:56:09,054[INFO] use 64 bits

Define the Model#

In Renormalizer, models are defined by the Hamiltonian terms and the a list of basis sets. The basis also defines the ordering in DMRG.

The spin operators can be represented by Pauli operators

\[S^+ = \sigma^+\]
\[S^- = \sigma^-\]
\[S^{\{x,y,z\}} = \frac{1}{2} \sigma^{\{x,y,z\}}\]
[2]:

# define the # of spins
nspin = 32

# define the model

ham_terms = []
for ispin in range(nspin-1):
    op1 = Op("sigma_z sigma_z", [ispin, ispin+1], 1.0/4)
    op2 = Op("sigma_+ sigma_-", [ispin, ispin+1], 1.0/2)
    op3 = Op("sigma_- sigma_+", [ispin, ispin+1], 1.0/2)
    ham_terms.extend([op1, op2, op3])

# set the spin order and local basis
basis = [BasisHalfSpin(i) for i in range(nspin)]
# construct Hamiltonian MPO
model = Model(basis, ham_terms)
mpo = Mpo(model)
print(f"mpo_bond_dims:{mpo.bond_dims}")

2026-05-20 02:56:09,166[DEBUG] # of operator terms: 93
2026-05-20 02:56:09,167[DEBUG] Input operator terms: 93
2026-05-20 02:56:09,169[DEBUG] After combination of the same terms: 93
2026-05-20 02:56:09,169[DEBUG] symbolic mpo algorithm: qr

mpo_bond_dims:[1, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 4, 1]

DMRG Sweeps#

[3]:

# set the sweep paramter
M = 30
# sweep for 5 rounds. For each round, the bond dimension is M.
# in the first round, 20% of the kept states are chosen randomly to avoid
# stucking in local minimum.
# More rounds are preferred since early-stopping is enabled
procedure = [[M, 0.2], [M, 0], [M, 0], [M,0], [M,0]]

# initialize a random MPS
qntot = 0
mps = Mps.random(model, qntot, M)

mps.optimize_config.procedure = procedure
mps.optimize_config.method = "2site"

# optimize MPS
energies, _ = optimize_mps(mps.copy(), mpo)
print("gs energy:", min(energies))

2026-05-20 02:56:09,239[INFO] optimization method: 2site
2026-05-20 02:56:09,240[INFO] e_rtol: 1e-06
2026-05-20 02:56:09,241[INFO] e_atol: 1e-08
2026-05-20 02:56:09,241[INFO] procedure: [[30, 0.2], [30, 0], [30, 0], [30, 0], [30, 0]]
2026-05-20 02:56:09,268[DEBUG] isweep: 0
2026-05-20 02:56:09,268[DEBUG] compress config in current loop: 30, percent: 0.2
2026-05-20 02:56:09,270[DEBUG] mps current size: 329.7KiB, Matrix product bond dim:[1, 2, 4, 8, 16, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 16, 8, 4, 2, 1]
2026-05-20 02:56:09,271[DEBUG] optimize site: [0, 1]
2026-05-20 02:56:09,272[DEBUG] use direct eigensolver
2026-05-20 02:56:09,275[DEBUG] energy: -0.927999022689833
2026-05-20 02:56:09,277[DEBUG] optimize site: [1, 2]
2026-05-20 02:56:09,277[DEBUG] use direct eigensolver
2026-05-20 02:56:09,281[DEBUG] energy: -1.284089573410534
2026-05-20 02:56:09,283[DEBUG] optimize site: [2, 3]
2026-05-20 02:56:09,284[DEBUG] use direct eigensolver
2026-05-20 02:56:09,297[DEBUG] energy: -2.08574526474992
2026-05-20 02:56:09,299[DEBUG] optimize site: [3, 4]
2026-05-20 02:56:09,300[DEBUG] use direct eigensolver
2026-05-20 02:56:09,510[DEBUG] energy: -2.815889527237408
2026-05-20 02:56:09,512[DEBUG] optimize site: [4, 5]
2026-05-20 02:56:09,543[DEBUG] use davidson, HC hops: 34
2026-05-20 02:56:09,545[DEBUG] energy: -3.293367315585801
2026-05-20 02:56:09,547[DEBUG] optimize site: [5, 6]
2026-05-20 02:56:09,595[DEBUG] use davidson, HC hops: 42
2026-05-20 02:56:09,597[DEBUG] energy: -3.744986750307196
2026-05-20 02:56:09,600[DEBUG] optimize site: [6, 7]
2026-05-20 02:56:09,649[DEBUG] use davidson, HC hops: 42
2026-05-20 02:56:09,649[DEBUG] energy: -4.176385575496487
2026-05-20 02:56:09,652[DEBUG] optimize site: [7, 8]
2026-05-20 02:56:09,702[DEBUG] use davidson, HC hops: 44
2026-05-20 02:56:09,703[DEBUG] energy: -4.583593477927382
2026-05-20 02:56:09,707[DEBUG] optimize site: [8, 9]
2026-05-20 02:56:09,767[DEBUG] use davidson, HC hops: 55
2026-05-20 02:56:09,768[DEBUG] energy: -4.968031845671196
2026-05-20 02:56:09,772[DEBUG] optimize site: [9, 10]
2026-05-20 02:56:09,844[DEBUG] use davidson, HC hops: 68
2026-05-20 02:56:09,846[DEBUG] energy: -5.4147063608339785
2026-05-20 02:56:09,849[DEBUG] optimize site: [10, 11]
2026-05-20 02:56:09,927[DEBUG] use davidson, HC hops: 72
2026-05-20 02:56:09,929[DEBUG] energy: -5.856529754520464
2026-05-20 02:56:09,933[DEBUG] optimize site: [11, 12]
2026-05-20 02:56:10,039[DEBUG] use davidson, HC hops: 100
2026-05-20 02:56:10,040[DEBUG] energy: -6.279022467295797
2026-05-20 02:56:10,045[DEBUG] optimize site: [12, 13]
2026-05-20 02:56:10,102[DEBUG] use davidson, HC hops: 52
2026-05-20 02:56:10,104[DEBUG] energy: -6.857389012204739
2026-05-20 02:56:10,107[DEBUG] optimize site: [13, 14]
2026-05-20 02:56:10,213[DEBUG] use davidson, HC hops: 100
2026-05-20 02:56:10,215[DEBUG] energy: -7.114588022005757
2026-05-20 02:56:10,218[DEBUG] optimize site: [14, 15]
2026-05-20 02:56:10,270[DEBUG] use davidson, HC hops: 47
2026-05-20 02:56:10,272[DEBUG] energy: -7.641631783835388
2026-05-20 02:56:10,275[DEBUG] optimize site: [15, 16]
2026-05-20 02:56:10,331[DEBUG] use davidson, HC hops: 51
2026-05-20 02:56:10,332[DEBUG] energy: -8.118395338420026
2026-05-20 02:56:10,335[DEBUG] optimize site: [16, 17]
2026-05-20 02:56:10,397[DEBUG] use davidson, HC hops: 57
2026-05-20 02:56:10,397[DEBUG] energy: -8.579533430762844
2026-05-20 02:56:10,400[DEBUG] optimize site: [17, 18]
2026-05-20 02:56:10,472[DEBUG] use davidson, HC hops: 66
2026-05-20 02:56:10,473[DEBUG] energy: -8.983113190158438
2026-05-20 02:56:10,477[DEBUG] optimize site: [18, 19]
2026-05-20 02:56:10,544[DEBUG] use davidson, HC hops: 62
2026-05-20 02:56:10,545[DEBUG] energy: -9.422205404607638
2026-05-20 02:56:10,548[DEBUG] optimize site: [19, 20]
2026-05-20 02:56:10,616[DEBUG] use davidson, HC hops: 62
2026-05-20 02:56:10,617[DEBUG] energy: -9.903693680914373
2026-05-20 02:56:10,620[DEBUG] optimize site: [20, 21]
2026-05-20 02:56:10,706[DEBUG] use davidson, HC hops: 81
2026-05-20 02:56:10,707[DEBUG] energy: -10.398530611697943
2026-05-20 02:56:10,711[DEBUG] optimize site: [21, 22]
2026-05-20 02:56:10,792[DEBUG] use davidson, HC hops: 76
2026-05-20 02:56:10,793[DEBUG] energy: -10.834489434421654
2026-05-20 02:56:10,796[DEBUG] optimize site: [22, 23]
2026-05-20 02:56:10,858[DEBUG] use davidson, HC hops: 58
2026-05-20 02:56:10,859[DEBUG] energy: -11.415128707126794
2026-05-20 02:56:10,863[DEBUG] optimize site: [23, 24]
2026-05-20 02:56:10,920[DEBUG] use davidson, HC hops: 52
2026-05-20 02:56:10,921[DEBUG] energy: -12.12279587974504
2026-05-20 02:56:10,925[DEBUG] optimize site: [24, 25]
2026-05-20 02:56:11,001[DEBUG] use davidson, HC hops: 71
2026-05-20 02:56:11,003[DEBUG] energy: -12.812234874023469
2026-05-20 02:56:11,006[DEBUG] optimize site: [25, 26]
2026-05-20 02:56:11,070[DEBUG] use davidson, HC hops: 58
2026-05-20 02:56:11,071[DEBUG] energy: -13.774582804126652
2026-05-20 02:56:11,075[DEBUG] optimize site: [26, 27]
2026-05-20 02:56:11,123[DEBUG] use davidson, HC hops: 47
2026-05-20 02:56:11,125[DEBUG] energy: -13.99683265581308
2026-05-20 02:56:11,128[DEBUG] optimize site: [27, 28]
2026-05-20 02:56:11,130[DEBUG] use direct eigensolver
2026-05-20 02:56:11,352[DEBUG] energy: -13.996832655534009
2026-05-20 02:56:11,355[DEBUG] optimize site: [28, 29]
2026-05-20 02:56:11,358[DEBUG] use direct eigensolver
2026-05-20 02:56:11,401[DEBUG] energy: -13.996832655534003
2026-05-20 02:56:11,403[DEBUG] optimize site: [29, 30]
2026-05-20 02:56:11,404[DEBUG] use direct eigensolver
2026-05-20 02:56:11,411[DEBUG] energy: -13.99683265553401
2026-05-20 02:56:11,413[DEBUG] optimize site: [30, 31]
2026-05-20 02:56:11,415[DEBUG] use direct eigensolver
2026-05-20 02:56:11,418[DEBUG] energy: -13.996832655534003
2026-05-20 02:56:11,420[DEBUG] 1 sweeps are finished, lowest energy = -13.99683265581308
2026-05-20 02:56:11,422[DEBUG] isweep: 1
2026-05-20 02:56:11,422[DEBUG] compress config in current loop: 30, percent: 0
2026-05-20 02:56:11,424[DEBUG] mps current size: 343.7KiB, Matrix product bond dim:[1, 2, 4, 8, 16, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 16, 8, 4, 1]
2026-05-20 02:56:11,425[DEBUG] optimize site: [30, 31]
2026-05-20 02:56:11,426[DEBUG] use direct eigensolver
2026-05-20 02:56:11,429[DEBUG] energy: -13.996832655534003
2026-05-20 02:56:11,432[DEBUG] optimize site: [29, 30]
2026-05-20 02:56:11,434[DEBUG] use direct eigensolver
2026-05-20 02:56:11,439[DEBUG] energy: -13.996832655534014
2026-05-20 02:56:11,442[DEBUG] optimize site: [28, 29]
2026-05-20 02:56:11,444[DEBUG] use direct eigensolver
2026-05-20 02:56:11,485[DEBUG] energy: -13.99683265553399
2026-05-20 02:56:11,488[DEBUG] optimize site: [27, 28]
2026-05-20 02:56:11,490[DEBUG] use direct eigensolver
2026-05-20 02:56:11,709[DEBUG] energy: -13.996832655534003
2026-05-20 02:56:11,713[DEBUG] optimize site: [26, 27]
2026-05-20 02:56:11,719[DEBUG] use davidson, HC hops: 4
2026-05-20 02:56:11,721[DEBUG] energy: -13.996832655813623
2026-05-20 02:56:11,725[DEBUG] optimize site: [25, 26]
2026-05-20 02:56:11,751[DEBUG] use davidson, HC hops: 22
2026-05-20 02:56:11,753[DEBUG] energy: -13.996844945038351
2026-05-20 02:56:11,756[DEBUG] optimize site: [24, 25]
2026-05-20 02:56:11,788[DEBUG] use davidson, HC hops: 28
2026-05-20 02:56:11,790[DEBUG] energy: -13.997067101658748
2026-05-20 02:56:11,792[DEBUG] optimize site: [23, 24]
2026-05-20 02:56:11,822[DEBUG] use davidson, HC hops: 25
2026-05-20 02:56:11,824[DEBUG] energy: -13.9971016847175
2026-05-20 02:56:11,827[DEBUG] optimize site: [22, 23]
2026-05-20 02:56:11,854[DEBUG] use davidson, HC hops: 23
2026-05-20 02:56:11,855[DEBUG] energy: -13.997106608213704
2026-05-20 02:56:11,859[DEBUG] optimize site: [21, 22]
2026-05-20 02:56:11,886[DEBUG] use davidson, HC hops: 23
2026-05-20 02:56:11,887[DEBUG] energy: -13.997113698271137
2026-05-20 02:56:11,891[DEBUG] optimize site: [20, 21]
2026-05-20 02:56:11,921[DEBUG] use davidson, HC hops: 26
2026-05-20 02:56:11,922[DEBUG] energy: -13.997162638323548
2026-05-20 02:56:11,926[DEBUG] optimize site: [19, 20]
2026-05-20 02:56:11,953[DEBUG] use davidson, HC hops: 23
2026-05-20 02:56:11,955[DEBUG] energy: -13.997170144965555
2026-05-20 02:56:11,958[DEBUG] optimize site: [18, 19]
2026-05-20 02:56:11,989[DEBUG] use davidson, HC hops: 26
2026-05-20 02:56:11,990[DEBUG] energy: -13.997199975427405
2026-05-20 02:56:11,994[DEBUG] optimize site: [17, 18]
2026-05-20 02:56:12,020[DEBUG] use davidson, HC hops: 22
2026-05-20 02:56:12,021[DEBUG] energy: -13.997204392621608
2026-05-20 02:56:12,025[DEBUG] optimize site: [16, 17]
2026-05-20 02:56:12,054[DEBUG] use davidson, HC hops: 25
2026-05-20 02:56:12,056[DEBUG] energy: -13.997225037523815
2026-05-20 02:56:12,058[DEBUG] optimize site: [15, 16]
2026-05-20 02:56:12,090[DEBUG] use davidson, HC hops: 26
2026-05-20 02:56:12,090[DEBUG] energy: -13.997284918121167
2026-05-20 02:56:12,095[DEBUG] optimize site: [14, 15]
2026-05-20 02:56:12,121[DEBUG] use davidson, HC hops: 22
2026-05-20 02:56:12,121[DEBUG] energy: -13.997290859971228
2026-05-20 02:56:12,126[DEBUG] optimize site: [13, 14]
2026-05-20 02:56:12,150[DEBUG] use davidson, HC hops: 20
2026-05-20 02:56:12,152[DEBUG] energy: -13.997293257653773
2026-05-20 02:56:12,155[DEBUG] optimize site: [12, 13]
2026-05-20 02:56:12,182[DEBUG] use davidson, HC hops: 23
2026-05-20 02:56:12,184[DEBUG] energy: -13.997306225086646
2026-05-20 02:56:12,187[DEBUG] optimize site: [11, 12]
2026-05-20 02:56:12,212[DEBUG] use davidson, HC hops: 21
2026-05-20 02:56:12,214[DEBUG] energy: -13.997311145595594
2026-05-20 02:56:12,217[DEBUG] optimize site: [10, 11]
2026-05-20 02:56:12,240[DEBUG] use davidson, HC hops: 20
2026-05-20 02:56:12,240[DEBUG] energy: -13.997313132707486
2026-05-20 02:56:12,245[DEBUG] optimize site: [9, 10]
2026-05-20 02:56:12,265[DEBUG] use davidson, HC hops: 17
2026-05-20 02:56:12,267[DEBUG] energy: -13.997314428626355
2026-05-20 02:56:12,270[DEBUG] optimize site: [8, 9]
2026-05-20 02:56:12,285[DEBUG] use davidson, HC hops: 11
2026-05-20 02:56:12,286[DEBUG] energy: -13.997314715468686
2026-05-20 02:56:12,290[DEBUG] optimize site: [7, 8]
2026-05-20 02:56:12,300[DEBUG] use davidson, HC hops: 7
2026-05-20 02:56:12,300[DEBUG] energy: -13.997314712669796
2026-05-20 02:56:12,305[DEBUG] optimize site: [6, 7]
2026-05-20 02:56:12,320[DEBUG] use davidson, HC hops: 12
2026-05-20 02:56:12,320[DEBUG] energy: -13.99731499975004
2026-05-20 02:56:12,325[DEBUG] optimize site: [5, 6]
2026-05-20 02:56:12,335[DEBUG] use davidson, HC hops: 7
2026-05-20 02:56:12,336[DEBUG] energy: -13.997315003811472
2026-05-20 02:56:12,340[DEBUG] optimize site: [4, 5]
2026-05-20 02:56:12,347[DEBUG] use davidson, HC hops: 5
2026-05-20 02:56:12,347[DEBUG] energy: -13.997315004767806
2026-05-20 02:56:12,350[DEBUG] optimize site: [3, 4]
2026-05-20 02:56:12,353[DEBUG] use direct eigensolver
2026-05-20 02:56:12,591[DEBUG] energy: -13.997315004467106
2026-05-20 02:56:12,595[DEBUG] optimize site: [2, 3]
2026-05-20 02:56:12,597[DEBUG] use direct eigensolver
2026-05-20 02:56:12,638[DEBUG] energy: -13.997315004467104
2026-05-20 02:56:12,641[DEBUG] optimize site: [1, 2]
2026-05-20 02:56:12,642[DEBUG] use direct eigensolver
2026-05-20 02:56:12,648[DEBUG] energy: -13.997315004467112
2026-05-20 02:56:12,650[DEBUG] optimize site: [0, 1]
2026-05-20 02:56:12,652[DEBUG] use direct eigensolver
2026-05-20 02:56:12,656[DEBUG] energy: -13.997315004467112
2026-05-20 02:56:12,658[DEBUG] 2 sweeps are finished, lowest energy = -13.997315004767806
2026-05-20 02:56:12,660[DEBUG] isweep: 2
2026-05-20 02:56:12,662[DEBUG] compress config in current loop: 30, percent: 0
2026-05-20 02:56:12,662[DEBUG] mps current size: 343.7KiB, Matrix product bond dim:[1, 4, 8, 16, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 16, 8, 4, 2, 1]
2026-05-20 02:56:12,664[DEBUG] optimize site: [0, 1]
2026-05-20 02:56:12,665[DEBUG] use direct eigensolver
2026-05-20 02:56:12,669[DEBUG] energy: -13.997315004467112
2026-05-20 02:56:12,670[DEBUG] optimize site: [1, 2]
2026-05-20 02:56:12,673[DEBUG] use direct eigensolver
2026-05-20 02:56:12,679[DEBUG] energy: -13.997315004467094
2026-05-20 02:56:12,680[DEBUG] optimize site: [2, 3]
2026-05-20 02:56:12,683[DEBUG] use direct eigensolver
2026-05-20 02:56:12,721[DEBUG] energy: -13.997315004467106
2026-05-20 02:56:12,722[DEBUG] optimize site: [3, 4]
2026-05-20 02:56:12,725[DEBUG] use direct eigensolver
2026-05-20 02:56:12,939[DEBUG] energy: -13.997315004467128
2026-05-20 02:56:12,942[DEBUG] optimize site: [4, 5]
2026-05-20 02:56:12,948[DEBUG] use davidson, HC hops: 4
2026-05-20 02:56:12,948[DEBUG] energy: -13.997315004767872
2026-05-20 02:56:12,951[DEBUG] optimize site: [5, 6]
2026-05-20 02:56:12,958[DEBUG] use davidson, HC hops: 4
2026-05-20 02:56:12,959[DEBUG] energy: -13.997315004667778
2026-05-20 02:56:12,961[DEBUG] optimize site: [6, 7]
2026-05-20 02:56:12,970[DEBUG] use davidson, HC hops: 6
2026-05-20 02:56:12,970[DEBUG] energy: -13.997315012470661
2026-05-20 02:56:12,973[DEBUG] optimize site: [7, 8]
2026-05-20 02:56:12,981[DEBUG] use davidson, HC hops: 5
2026-05-20 02:56:12,981[DEBUG] energy: -13.997315006066657
2026-05-20 02:56:12,985[DEBUG] optimize site: [8, 9]
2026-05-20 02:56:12,995[DEBUG] use davidson, HC hops: 7
2026-05-20 02:56:12,995[DEBUG] energy: -13.997315033374523
2026-05-20 02:56:12,999[DEBUG] optimize site: [9, 10]
2026-05-20 02:56:13,007[DEBUG] use davidson, HC hops: 6
2026-05-20 02:56:13,008[DEBUG] energy: -13.997315010121959
2026-05-20 02:56:13,011[DEBUG] optimize site: [10, 11]
2026-05-20 02:56:13,021[DEBUG] use davidson, HC hops: 8
2026-05-20 02:56:13,022[DEBUG] energy: -13.997315055776896
2026-05-20 02:56:13,024[DEBUG] optimize site: [11, 12]
2026-05-20 02:56:13,034[DEBUG] use davidson, HC hops: 7
2026-05-20 02:56:13,035[DEBUG] energy: -13.997315015890461
2026-05-20 02:56:13,038[DEBUG] optimize site: [12, 13]
2026-05-20 02:56:13,049[DEBUG] use davidson, HC hops: 8
2026-05-20 02:56:13,049[DEBUG] energy: -13.997315076759374
2026-05-20 02:56:13,052[DEBUG] optimize site: [13, 14]
2026-05-20 02:56:13,062[DEBUG] use davidson, HC hops: 7
2026-05-20 02:56:13,062[DEBUG] energy: -13.99731502106373
2026-05-20 02:56:13,067[DEBUG] optimize site: [14, 15]
2026-05-20 02:56:13,078[DEBUG] use davidson, HC hops: 8
2026-05-20 02:56:13,078[DEBUG] energy: -13.997315089163447
2026-05-20 02:56:13,083[DEBUG] optimize site: [15, 16]
2026-05-20 02:56:13,094[DEBUG] use davidson, HC hops: 8
2026-05-20 02:56:13,094[DEBUG] energy: -13.997315023237693
2026-05-20 02:56:13,098[DEBUG] optimize site: [16, 17]
2026-05-20 02:56:13,111[DEBUG] use davidson, HC hops: 9
2026-05-20 02:56:13,111[DEBUG] energy: -13.9973150902116
2026-05-20 02:56:13,116[DEBUG] optimize site: [17, 18]
2026-05-20 02:56:13,127[DEBUG] use davidson, HC hops: 8
2026-05-20 02:56:13,127[DEBUG] energy: -13.997315022014211
2026-05-20 02:56:13,132[DEBUG] optimize site: [18, 19]
2026-05-20 02:56:13,142[DEBUG] use davidson, HC hops: 8
2026-05-20 02:56:13,144[DEBUG] energy: -13.997315079212514
2026-05-20 02:56:13,147[DEBUG] optimize site: [19, 20]
2026-05-20 02:56:13,157[DEBUG] use davidson, HC hops: 7
2026-05-20 02:56:13,158[DEBUG] energy: -13.997315018389642
2026-05-20 02:56:13,162[DEBUG] optimize site: [20, 21]
2026-05-20 02:56:13,173[DEBUG] use davidson, HC hops: 8
2026-05-20 02:56:13,175[DEBUG] energy: -13.99731506047155
2026-05-20 02:56:13,178[DEBUG] optimize site: [21, 22]
2026-05-20 02:56:13,187[DEBUG] use davidson, HC hops: 6
2026-05-20 02:56:13,189[DEBUG] energy: -13.997315014222956
2026-05-20 02:56:13,192[DEBUG] optimize site: [22, 23]
2026-05-20 02:56:13,204[DEBUG] use davidson, HC hops: 8
2026-05-20 02:56:13,206[DEBUG] energy: -13.997315036380726
2026-05-20 02:56:13,209[DEBUG] optimize site: [23, 24]
2026-05-20 02:56:13,218[DEBUG] use davidson, HC hops: 6
2026-05-20 02:56:13,220[DEBUG] energy: -13.997315009063295
2026-05-20 02:56:13,223[DEBUG] optimize site: [24, 25]
2026-05-20 02:56:13,232[DEBUG] use davidson, HC hops: 6
2026-05-20 02:56:13,234[DEBUG] energy: -13.997315015431777
2026-05-20 02:56:13,237[DEBUG] optimize site: [25, 26]
2026-05-20 02:56:13,245[DEBUG] use davidson, HC hops: 5
2026-05-20 02:56:13,246[DEBUG] energy: -13.997315007630469
2026-05-20 02:56:13,250[DEBUG] optimize site: [26, 27]
2026-05-20 02:56:13,256[DEBUG] use davidson, HC hops: 4
2026-05-20 02:56:13,258[DEBUG] energy: -13.997315007727428
2026-05-20 02:56:13,260[DEBUG] optimize site: [27, 28]
2026-05-20 02:56:13,262[DEBUG] use direct eigensolver
2026-05-20 02:56:13,480[DEBUG] energy: -13.997315007427376
2026-05-20 02:56:13,484[DEBUG] optimize site: [28, 29]
2026-05-20 02:56:13,486[DEBUG] use direct eigensolver
2026-05-20 02:56:13,528[DEBUG] energy: -13.997315007427368
2026-05-20 02:56:13,531[DEBUG] optimize site: [29, 30]
2026-05-20 02:56:13,533[DEBUG] use direct eigensolver
2026-05-20 02:56:13,538[DEBUG] energy: -13.997315007427371
2026-05-20 02:56:13,541[DEBUG] optimize site: [30, 31]
2026-05-20 02:56:13,543[DEBUG] use direct eigensolver
2026-05-20 02:56:13,545[DEBUG] energy: -13.99731500742738
2026-05-20 02:56:13,547[DEBUG] 3 sweeps are finished, lowest energy = -13.9973150902116
2026-05-20 02:56:13,549[INFO] DMRG has converged!
2026-05-20 02:56:13,586[INFO] mps current size: 329.7KiB, Matrix product bond dim:[1, 2, 4, 8, 16, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 16, 8, 4, 2, 1]

gs energy: -13.9973150902116

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