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

2025-12-20 11:02:19,617[INFO] Use NumPy as backend
2025-12-20 11:02:19,618[INFO] numpy random seed is 9012
2025-12-20 11:02:19,618[INFO] random seed is 1092
2025-12-20 11:02:19,630[INFO] Git Commit Hash: 06430a9cbb7af930317f368a36eff512a8d5ce70
2025-12-20 11:02:19,631[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}")

2025-12-20 11:02:19,743[DEBUG] # of operator terms: 93
2025-12-20 11:02:19,743[DEBUG] Input operator terms: 93
2025-12-20 11:02:19,745[DEBUG] After combination of the same terms: 93
2025-12-20 11:02:19,746[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))

2025-12-20 11:02:19,816[INFO] optimization method: 2site
2025-12-20 11:02:19,817[INFO] e_rtol: 1e-06
2025-12-20 11:02:19,817[INFO] e_atol: 1e-08
2025-12-20 11:02:19,818[INFO] procedure: [[30, 0.2], [30, 0], [30, 0], [30, 0], [30, 0]]
2025-12-20 11:02:19,849[DEBUG] isweep: 0
2025-12-20 11:02:19,851[DEBUG] compress config in current loop: 30, percent: 0.2
2025-12-20 11:02:19,852[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]
2025-12-20 11:02:19,853[DEBUG] optimize site: [0, 1]
2025-12-20 11:02:19,855[DEBUG] use direct eigensolver
2025-12-20 11:02:19,858[DEBUG] energy: -0.927999022689833
2025-12-20 11:02:19,861[DEBUG] optimize site: [1, 2]
2025-12-20 11:02:19,863[DEBUG] use direct eigensolver
2025-12-20 11:02:19,868[DEBUG] energy: -1.284089573410534
2025-12-20 11:02:19,869[DEBUG] optimize site: [2, 3]
2025-12-20 11:02:19,871[DEBUG] use direct eigensolver
2025-12-20 11:02:19,895[DEBUG] energy: -2.08574526474992
2025-12-20 11:02:19,897[DEBUG] optimize site: [3, 4]
2025-12-20 11:02:19,899[DEBUG] use direct eigensolver
2025-12-20 11:02:20,152[DEBUG] energy: -2.815889527237408
2025-12-20 11:02:20,155[DEBUG] optimize site: [4, 5]
2025-12-20 11:02:20,210[DEBUG] use davidson, HC hops: 34
2025-12-20 11:02:20,212[DEBUG] energy: -3.2933673155858
2025-12-20 11:02:20,214[DEBUG] optimize site: [5, 6]
2025-12-20 11:02:20,303[DEBUG] use davidson, HC hops: 42
2025-12-20 11:02:20,304[DEBUG] energy: -3.7449867503071976
2025-12-20 11:02:20,308[DEBUG] optimize site: [6, 7]
2025-12-20 11:02:20,435[DEBUG] use davidson, HC hops: 42
2025-12-20 11:02:20,437[DEBUG] energy: -4.176385575496491
2025-12-20 11:02:20,450[DEBUG] optimize site: [7, 8]
2025-12-20 11:02:20,573[DEBUG] use davidson, HC hops: 44
2025-12-20 11:02:20,574[DEBUG] energy: -4.583593477927387
2025-12-20 11:02:20,578[DEBUG] optimize site: [8, 9]
2025-12-20 11:02:20,689[DEBUG] use davidson, HC hops: 55
2025-12-20 11:02:20,691[DEBUG] energy: -4.968031845671202
2025-12-20 11:02:20,695[DEBUG] optimize site: [9, 10]
2025-12-20 11:02:20,830[DEBUG] use davidson, HC hops: 68
2025-12-20 11:02:20,832[DEBUG] energy: -5.414706360833986
2025-12-20 11:02:20,836[DEBUG] optimize site: [10, 11]
2025-12-20 11:02:20,980[DEBUG] use davidson, HC hops: 72
2025-12-20 11:02:20,982[DEBUG] energy: -5.856529754520476
2025-12-20 11:02:20,986[DEBUG] optimize site: [11, 12]
2025-12-20 11:02:21,181[DEBUG] use davidson, HC hops: 100
2025-12-20 11:02:21,183[DEBUG] energy: -6.279022467295817
2025-12-20 11:02:21,186[DEBUG] optimize site: [12, 13]
2025-12-20 11:02:21,259[DEBUG] use davidson, HC hops: 52
2025-12-20 11:02:21,261[DEBUG] energy: -6.857389012204763
2025-12-20 11:02:21,265[DEBUG] optimize site: [13, 14]
2025-12-20 11:02:21,422[DEBUG] use davidson, HC hops: 100
2025-12-20 11:02:21,422[DEBUG] energy: -7.114588022005789
2025-12-20 11:02:21,425[DEBUG] optimize site: [14, 15]
2025-12-20 11:02:21,522[DEBUG] use davidson, HC hops: 47
2025-12-20 11:02:21,524[DEBUG] energy: -7.6416317838354235
2025-12-20 11:02:21,528[DEBUG] optimize site: [15, 16]
2025-12-20 11:02:21,633[DEBUG] use davidson, HC hops: 51
2025-12-20 11:02:21,635[DEBUG] energy: -8.118395338420061
2025-12-20 11:02:21,639[DEBUG] optimize site: [16, 17]
2025-12-20 11:02:21,751[DEBUG] use davidson, HC hops: 57
2025-12-20 11:02:21,752[DEBUG] energy: -8.579533430762858
2025-12-20 11:02:21,757[DEBUG] optimize site: [17, 18]
2025-12-20 11:02:21,879[DEBUG] use davidson, HC hops: 66
2025-12-20 11:02:21,880[DEBUG] energy: -8.983113190158459
2025-12-20 11:02:21,884[DEBUG] optimize site: [18, 19]
2025-12-20 11:02:22,004[DEBUG] use davidson, HC hops: 62
2025-12-20 11:02:22,005[DEBUG] energy: -9.422205404607661
2025-12-20 11:02:22,009[DEBUG] optimize site: [19, 20]
2025-12-20 11:02:22,129[DEBUG] use davidson, HC hops: 62
2025-12-20 11:02:22,130[DEBUG] energy: -9.903693680914392
2025-12-20 11:02:22,135[DEBUG] optimize site: [20, 21]
2025-12-20 11:02:22,272[DEBUG] use davidson, HC hops: 81
2025-12-20 11:02:22,273[DEBUG] energy: -10.398530611697971
2025-12-20 11:02:22,277[DEBUG] optimize site: [21, 22]
2025-12-20 11:02:22,409[DEBUG] use davidson, HC hops: 76
2025-12-20 11:02:22,410[DEBUG] energy: -10.83448943442168
2025-12-20 11:02:22,414[DEBUG] optimize site: [22, 23]
2025-12-20 11:02:22,529[DEBUG] use davidson, HC hops: 58
2025-12-20 11:02:22,530[DEBUG] energy: -11.415128707126815
2025-12-20 11:02:22,534[DEBUG] optimize site: [23, 24]
2025-12-20 11:02:22,642[DEBUG] use davidson, HC hops: 52
2025-12-20 11:02:22,643[DEBUG] energy: -12.122795879745066
2025-12-20 11:02:22,647[DEBUG] optimize site: [24, 25]
2025-12-20 11:02:22,774[DEBUG] use davidson, HC hops: 71
2025-12-20 11:02:22,775[DEBUG] energy: -12.812234874023524
2025-12-20 11:02:22,779[DEBUG] optimize site: [25, 26]
2025-12-20 11:02:22,893[DEBUG] use davidson, HC hops: 58
2025-12-20 11:02:22,895[DEBUG] energy: -13.774582804126709
2025-12-20 11:02:22,898[DEBUG] optimize site: [26, 27]
2025-12-20 11:02:22,978[DEBUG] use davidson, HC hops: 47
2025-12-20 11:02:22,979[DEBUG] energy: -13.996832655813149
2025-12-20 11:02:22,982[DEBUG] optimize site: [27, 28]
2025-12-20 11:02:22,987[DEBUG] use direct eigensolver
2025-12-20 11:02:23,241[DEBUG] energy: -13.996832655534098
2025-12-20 11:02:23,243[DEBUG] optimize site: [28, 29]
2025-12-20 11:02:23,247[DEBUG] use direct eigensolver
2025-12-20 11:02:23,294[DEBUG] energy: -13.996832655534092
2025-12-20 11:02:23,297[DEBUG] optimize site: [29, 30]
2025-12-20 11:02:23,299[DEBUG] use direct eigensolver
2025-12-20 11:02:23,305[DEBUG] energy: -13.996832655534094
2025-12-20 11:02:23,307[DEBUG] optimize site: [30, 31]
2025-12-20 11:02:23,309[DEBUG] use direct eigensolver
2025-12-20 11:02:23,312[DEBUG] energy: -13.996832655534092
2025-12-20 11:02:23,313[DEBUG] 1 sweeps are finished, lowest energy = -13.996832655813149
2025-12-20 11:02:23,315[DEBUG] isweep: 1
2025-12-20 11:02:23,316[DEBUG] compress config in current loop: 30, percent: 0
2025-12-20 11:02:23,317[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]
2025-12-20 11:02:23,320[DEBUG] optimize site: [30, 31]
2025-12-20 11:02:23,320[DEBUG] use direct eigensolver
2025-12-20 11:02:23,324[DEBUG] energy: -13.996832655534092
2025-12-20 11:02:23,325[DEBUG] optimize site: [29, 30]
2025-12-20 11:02:23,328[DEBUG] use direct eigensolver
2025-12-20 11:02:23,334[DEBUG] energy: -13.996832655534096
2025-12-20 11:02:23,335[DEBUG] optimize site: [28, 29]
2025-12-20 11:02:23,338[DEBUG] use direct eigensolver
2025-12-20 11:02:23,388[DEBUG] energy: -13.99683265553408
2025-12-20 11:02:23,391[DEBUG] optimize site: [27, 28]
2025-12-20 11:02:23,394[DEBUG] use direct eigensolver
2025-12-20 11:02:23,649[DEBUG] energy: -13.996832655534087
2025-12-20 11:02:23,652[DEBUG] optimize site: [26, 27]
2025-12-20 11:02:23,659[DEBUG] use davidson, HC hops: 4
2025-12-20 11:02:23,661[DEBUG] energy: -13.996832655813687
2025-12-20 11:02:23,665[DEBUG] optimize site: [25, 26]
2025-12-20 11:02:23,692[DEBUG] use davidson, HC hops: 22
2025-12-20 11:02:23,694[DEBUG] energy: -13.996844945038422
2025-12-20 11:02:23,697[DEBUG] optimize site: [24, 25]
2025-12-20 11:02:23,729[DEBUG] use davidson, HC hops: 28
2025-12-20 11:02:23,731[DEBUG] energy: -13.997067101658818
2025-12-20 11:02:23,734[DEBUG] optimize site: [23, 24]
2025-12-20 11:02:23,763[DEBUG] use davidson, HC hops: 25
2025-12-20 11:02:23,764[DEBUG] energy: -13.997101684717547
2025-12-20 11:02:23,768[DEBUG] optimize site: [22, 23]
2025-12-20 11:02:23,795[DEBUG] use davidson, HC hops: 23
2025-12-20 11:02:23,796[DEBUG] energy: -13.997106608213738
2025-12-20 11:02:23,800[DEBUG] optimize site: [21, 22]
2025-12-20 11:02:23,846[DEBUG] use davidson, HC hops: 23
2025-12-20 11:02:23,848[DEBUG] energy: -13.99711369827117
2025-12-20 11:02:23,853[DEBUG] optimize site: [20, 21]
2025-12-20 11:02:23,907[DEBUG] use davidson, HC hops: 26
2025-12-20 11:02:23,908[DEBUG] energy: -13.997162638323596
2025-12-20 11:02:23,913[DEBUG] optimize site: [19, 20]
2025-12-20 11:02:23,960[DEBUG] use davidson, HC hops: 23
2025-12-20 11:02:23,961[DEBUG] energy: -13.997170144965597
2025-12-20 11:02:23,965[DEBUG] optimize site: [18, 19]
2025-12-20 11:02:23,995[DEBUG] use davidson, HC hops: 26
2025-12-20 11:02:23,996[DEBUG] energy: -13.997199975427481
2025-12-20 11:02:24,000[DEBUG] optimize site: [17, 18]
2025-12-20 11:02:24,030[DEBUG] use davidson, HC hops: 22
2025-12-20 11:02:24,032[DEBUG] energy: -13.997204392621672
2025-12-20 11:02:24,037[DEBUG] optimize site: [16, 17]
2025-12-20 11:02:24,087[DEBUG] use davidson, HC hops: 25
2025-12-20 11:02:24,088[DEBUG] energy: -13.997225037523867
2025-12-20 11:02:24,092[DEBUG] optimize site: [15, 16]
2025-12-20 11:02:24,124[DEBUG] use davidson, HC hops: 26
2025-12-20 11:02:24,125[DEBUG] energy: -13.997284918121224
2025-12-20 11:02:24,129[DEBUG] optimize site: [14, 15]
2025-12-20 11:02:24,154[DEBUG] use davidson, HC hops: 22
2025-12-20 11:02:24,155[DEBUG] energy: -13.997290859971294
2025-12-20 11:02:24,159[DEBUG] optimize site: [13, 14]
2025-12-20 11:02:24,189[DEBUG] use davidson, HC hops: 20
2025-12-20 11:02:24,191[DEBUG] energy: -13.997293257653851
2025-12-20 11:02:24,195[DEBUG] optimize site: [12, 13]
2025-12-20 11:02:24,228[DEBUG] use davidson, HC hops: 23
2025-12-20 11:02:24,229[DEBUG] energy: -13.997306225086712
2025-12-20 11:02:24,233[DEBUG] optimize site: [11, 12]
2025-12-20 11:02:24,258[DEBUG] use davidson, HC hops: 21
2025-12-20 11:02:24,259[DEBUG] energy: -13.997311145595662
2025-12-20 11:02:24,263[DEBUG] optimize site: [10, 11]
2025-12-20 11:02:24,286[DEBUG] use davidson, HC hops: 20
2025-12-20 11:02:24,287[DEBUG] energy: -13.99731313270753
2025-12-20 11:02:24,291[DEBUG] optimize site: [9, 10]
2025-12-20 11:02:24,312[DEBUG] use davidson, HC hops: 17
2025-12-20 11:02:24,313[DEBUG] energy: -13.997314428626407
2025-12-20 11:02:24,317[DEBUG] optimize site: [8, 9]
2025-12-20 11:02:24,332[DEBUG] use davidson, HC hops: 11
2025-12-20 11:02:24,333[DEBUG] energy: -13.997314715468693
2025-12-20 11:02:24,337[DEBUG] optimize site: [7, 8]
2025-12-20 11:02:24,347[DEBUG] use davidson, HC hops: 7
2025-12-20 11:02:24,349[DEBUG] energy: -13.997314712669787
2025-12-20 11:02:24,352[DEBUG] optimize site: [6, 7]
2025-12-20 11:02:24,372[DEBUG] use davidson, HC hops: 12
2025-12-20 11:02:24,374[DEBUG] energy: -13.99731499975005
2025-12-20 11:02:24,379[DEBUG] optimize site: [5, 6]
2025-12-20 11:02:24,397[DEBUG] use davidson, HC hops: 7
2025-12-20 11:02:24,398[DEBUG] energy: -13.997315003811469
2025-12-20 11:02:24,402[DEBUG] optimize site: [4, 5]
2025-12-20 11:02:24,409[DEBUG] use davidson, HC hops: 5
2025-12-20 11:02:24,411[DEBUG] energy: -13.997315004767797
2025-12-20 11:02:24,413[DEBUG] optimize site: [3, 4]
2025-12-20 11:02:24,415[DEBUG] use direct eigensolver
2025-12-20 11:02:24,664[DEBUG] energy: -13.997315004467106
2025-12-20 11:02:24,668[DEBUG] optimize site: [2, 3]
2025-12-20 11:02:24,670[DEBUG] use direct eigensolver
2025-12-20 11:02:24,717[DEBUG] energy: -13.997315004467096
2025-12-20 11:02:24,719[DEBUG] optimize site: [1, 2]
2025-12-20 11:02:24,722[DEBUG] use direct eigensolver
2025-12-20 11:02:24,728[DEBUG] energy: -13.997315004467083
2025-12-20 11:02:24,730[DEBUG] optimize site: [0, 1]
2025-12-20 11:02:24,731[DEBUG] use direct eigensolver
2025-12-20 11:02:24,734[DEBUG] energy: -13.997315004467087
2025-12-20 11:02:24,735[DEBUG] 2 sweeps are finished, lowest energy = -13.997315004767797
2025-12-20 11:02:24,738[DEBUG] isweep: 2
2025-12-20 11:02:24,739[DEBUG] compress config in current loop: 30, percent: 0
2025-12-20 11:02:24,740[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]
2025-12-20 11:02:24,743[DEBUG] optimize site: [0, 1]
2025-12-20 11:02:24,744[DEBUG] use direct eigensolver
2025-12-20 11:02:24,747[DEBUG] energy: -13.997315004467087
2025-12-20 11:02:24,748[DEBUG] optimize site: [1, 2]
2025-12-20 11:02:24,751[DEBUG] use direct eigensolver
2025-12-20 11:02:24,757[DEBUG] energy: -13.997315004467097
2025-12-20 11:02:24,758[DEBUG] optimize site: [2, 3]
2025-12-20 11:02:24,761[DEBUG] use direct eigensolver
2025-12-20 11:02:24,805[DEBUG] energy: -13.9973150044671
2025-12-20 11:02:24,807[DEBUG] optimize site: [3, 4]
2025-12-20 11:02:24,809[DEBUG] use direct eigensolver
2025-12-20 11:02:25,063[DEBUG] energy: -13.997315004467117
2025-12-20 11:02:25,065[DEBUG] optimize site: [4, 5]
2025-12-20 11:02:25,074[DEBUG] use davidson, HC hops: 4
2025-12-20 11:02:25,075[DEBUG] energy: -13.997315004767874
2025-12-20 11:02:25,079[DEBUG] optimize site: [5, 6]
2025-12-20 11:02:25,095[DEBUG] use davidson, HC hops: 4
2025-12-20 11:02:25,096[DEBUG] energy: -13.997315004667774
2025-12-20 11:02:25,100[DEBUG] optimize site: [6, 7]
2025-12-20 11:02:25,109[DEBUG] use davidson, HC hops: 6
2025-12-20 11:02:25,109[DEBUG] energy: -13.997315012470644
2025-12-20 11:02:25,114[DEBUG] optimize site: [7, 8]
2025-12-20 11:02:25,122[DEBUG] use davidson, HC hops: 5
2025-12-20 11:02:25,122[DEBUG] energy: -13.997315006066646
2025-12-20 11:02:25,126[DEBUG] optimize site: [8, 9]
2025-12-20 11:02:25,137[DEBUG] use davidson, HC hops: 7
2025-12-20 11:02:25,137[DEBUG] energy: -13.997315033374527
2025-12-20 11:02:25,141[DEBUG] optimize site: [9, 10]
2025-12-20 11:02:25,151[DEBUG] use davidson, HC hops: 6
2025-12-20 11:02:25,151[DEBUG] energy: -13.997315010121966
2025-12-20 11:02:25,155[DEBUG] optimize site: [10, 11]
2025-12-20 11:02:25,167[DEBUG] use davidson, HC hops: 8
2025-12-20 11:02:25,167[DEBUG] energy: -13.997315055776882
2025-12-20 11:02:25,172[DEBUG] optimize site: [11, 12]
2025-12-20 11:02:25,182[DEBUG] use davidson, HC hops: 7
2025-12-20 11:02:25,183[DEBUG] energy: -13.997315015890473
2025-12-20 11:02:25,187[DEBUG] optimize site: [12, 13]
2025-12-20 11:02:25,198[DEBUG] use davidson, HC hops: 8
2025-12-20 11:02:25,199[DEBUG] energy: -13.99731507675943
2025-12-20 11:02:25,203[DEBUG] optimize site: [13, 14]
2025-12-20 11:02:25,213[DEBUG] use davidson, HC hops: 7
2025-12-20 11:02:25,213[DEBUG] energy: -13.997315021063773
2025-12-20 11:02:25,218[DEBUG] optimize site: [14, 15]
2025-12-20 11:02:25,229[DEBUG] use davidson, HC hops: 8
2025-12-20 11:02:25,230[DEBUG] energy: -13.997315089163507
2025-12-20 11:02:25,234[DEBUG] optimize site: [15, 16]
2025-12-20 11:02:25,245[DEBUG] use davidson, HC hops: 8
2025-12-20 11:02:25,247[DEBUG] energy: -13.997315023237732
2025-12-20 11:02:25,250[DEBUG] optimize site: [16, 17]
2025-12-20 11:02:25,263[DEBUG] use davidson, HC hops: 9
2025-12-20 11:02:25,264[DEBUG] energy: -13.997315090211641
2025-12-20 11:02:25,267[DEBUG] optimize site: [17, 18]
2025-12-20 11:02:25,279[DEBUG] use davidson, HC hops: 8
2025-12-20 11:02:25,280[DEBUG] energy: -13.99731502201426
2025-12-20 11:02:25,284[DEBUG] optimize site: [18, 19]
2025-12-20 11:02:25,295[DEBUG] use davidson, HC hops: 8
2025-12-20 11:02:25,296[DEBUG] energy: -13.997315079212528
2025-12-20 11:02:25,300[DEBUG] optimize site: [19, 20]
2025-12-20 11:02:25,310[DEBUG] use davidson, HC hops: 7
2025-12-20 11:02:25,311[DEBUG] energy: -13.997315018389646
2025-12-20 11:02:25,315[DEBUG] optimize site: [20, 21]
2025-12-20 11:02:25,326[DEBUG] use davidson, HC hops: 8
2025-12-20 11:02:25,327[DEBUG] energy: -13.99731506047151
2025-12-20 11:02:25,331[DEBUG] optimize site: [21, 22]
2025-12-20 11:02:25,341[DEBUG] use davidson, HC hops: 6
2025-12-20 11:02:25,342[DEBUG] energy: -13.99731501422293
2025-12-20 11:02:25,345[DEBUG] optimize site: [22, 23]
2025-12-20 11:02:25,357[DEBUG] use davidson, HC hops: 8
2025-12-20 11:02:25,357[DEBUG] energy: -13.997315036380687
2025-12-20 11:02:25,362[DEBUG] optimize site: [23, 24]
2025-12-20 11:02:25,371[DEBUG] use davidson, HC hops: 6
2025-12-20 11:02:25,372[DEBUG] energy: -13.997315009063291
2025-12-20 11:02:25,376[DEBUG] optimize site: [24, 25]
2025-12-20 11:02:25,385[DEBUG] use davidson, HC hops: 6
2025-12-20 11:02:25,386[DEBUG] energy: -13.99731501543178
2025-12-20 11:02:25,390[DEBUG] optimize site: [25, 26]
2025-12-20 11:02:25,398[DEBUG] use davidson, HC hops: 5
2025-12-20 11:02:25,398[DEBUG] energy: -13.997315007630467
2025-12-20 11:02:25,403[DEBUG] optimize site: [26, 27]
2025-12-20 11:02:25,409[DEBUG] use davidson, HC hops: 4
2025-12-20 11:02:25,410[DEBUG] energy: -13.997315007727414
2025-12-20 11:02:25,413[DEBUG] optimize site: [27, 28]
2025-12-20 11:02:25,415[DEBUG] use direct eigensolver
2025-12-20 11:02:25,670[DEBUG] energy: -13.997315007427384
2025-12-20 11:02:25,674[DEBUG] optimize site: [28, 29]
2025-12-20 11:02:25,676[DEBUG] use direct eigensolver
2025-12-20 11:02:25,725[DEBUG] energy: -13.997315007427398
2025-12-20 11:02:25,728[DEBUG] optimize site: [29, 30]
2025-12-20 11:02:25,731[DEBUG] use direct eigensolver
2025-12-20 11:02:25,740[DEBUG] energy: -13.99731500742741
2025-12-20 11:02:25,742[DEBUG] optimize site: [30, 31]
2025-12-20 11:02:25,745[DEBUG] use direct eigensolver
2025-12-20 11:02:25,750[DEBUG] energy: -13.997315007427408
2025-12-20 11:02:25,752[DEBUG] 3 sweeps are finished, lowest energy = -13.997315090211641
2025-12-20 11:02:25,755[INFO] DMRG has converged!
2025-12-20 11:02:25,804[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: -13.997315090211641

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