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

2025-08-18 06:50:18,013[INFO] Use NumPy as backend
2025-08-18 06:50:18,014[INFO] numpy random seed is 9012
2025-08-18 06:50:18,015[INFO] random seed is 1092
2025-08-18 06:50:18,026[INFO] Git Commit Hash: c080e702a6ee0a055fc180ecc6ad885b0368b1c1
2025-08-18 06:50:18,027[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}")

2025-08-18 06:50:18,130[DEBUG] # of operator terms: 93
2025-08-18 06:50:18,131[DEBUG] Input operator terms: 93
2025-08-18 06:50:18,133[DEBUG] After combination of the same terms: 93
2025-08-18 06:50:18,134[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.
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))

2025-08-18 06:50:18,204[INFO] optimization method: 2site
2025-08-18 06:50:18,204[INFO] e_rtol: 1e-06
2025-08-18 06:50:18,205[INFO] e_atol: 1e-08
2025-08-18 06:50:18,206[INFO] procedure: [[30, 0.2], [30, 0], [30, 0], [30, 0], [30, 0]]
2025-08-18 06:50:18,237[DEBUG] isweep: 0
2025-08-18 06:50:18,239[DEBUG] compress config in current loop: 30, percent: 0.2
2025-08-18 06:50:18,240[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]
2025-08-18 06:50:18,242[DEBUG] optimize site: [0, 1]
2025-08-18 06:50:18,243[DEBUG] use direct eigensolver
2025-08-18 06:50:18,246[DEBUG] energy: -0.927999022689833
2025-08-18 06:50:18,248[DEBUG] optimize site: [1, 2]
2025-08-18 06:50:18,251[DEBUG] use direct eigensolver
2025-08-18 06:50:18,255[DEBUG] energy: -1.284089573410534
2025-08-18 06:50:18,257[DEBUG] optimize site: [2, 3]
2025-08-18 06:50:18,259[DEBUG] use direct eigensolver
2025-08-18 06:50:18,283[DEBUG] energy: -2.08574526474992
2025-08-18 06:50:18,285[DEBUG] optimize site: [3, 4]
2025-08-18 06:50:18,288[DEBUG] use direct eigensolver
2025-08-18 06:50:18,543[DEBUG] energy: -2.815889527237408
2025-08-18 06:50:18,545[DEBUG] optimize site: [4, 5]
2025-08-18 06:50:18,603[DEBUG] use davidson, HC hops: 34
2025-08-18 06:50:18,605[DEBUG] energy: -3.2933673155858
2025-08-18 06:50:18,607[DEBUG] optimize site: [5, 6]
2025-08-18 06:50:18,700[DEBUG] use davidson, HC hops: 42
2025-08-18 06:50:18,701[DEBUG] energy: -3.7449867503071985
2025-08-18 06:50:18,706[DEBUG] optimize site: [6, 7]
2025-08-18 06:50:18,799[DEBUG] use davidson, HC hops: 42
2025-08-18 06:50:18,801[DEBUG] energy: -4.17638557549649
2025-08-18 06:50:18,805[DEBUG] optimize site: [7, 8]
2025-08-18 06:50:18,901[DEBUG] use davidson, HC hops: 44
2025-08-18 06:50:18,903[DEBUG] energy: -4.583593477927385
2025-08-18 06:50:18,907[DEBUG] optimize site: [8, 9]
2025-08-18 06:50:19,027[DEBUG] use davidson, HC hops: 55
2025-08-18 06:50:19,029[DEBUG] energy: -4.968031845671205
2025-08-18 06:50:19,034[DEBUG] optimize site: [9, 10]
2025-08-18 06:50:19,183[DEBUG] use davidson, HC hops: 68
2025-08-18 06:50:19,185[DEBUG] energy: -5.41470636083398
2025-08-18 06:50:19,190[DEBUG] optimize site: [10, 11]
2025-08-18 06:50:19,299[DEBUG] use davidson, HC hops: 72
2025-08-18 06:50:19,300[DEBUG] energy: -5.856529754520473
2025-08-18 06:50:19,303[DEBUG] optimize site: [11, 12]
2025-08-18 06:50:19,489[DEBUG] use davidson, HC hops: 100
2025-08-18 06:50:19,491[DEBUG] energy: -6.279022467295806
2025-08-18 06:50:19,496[DEBUG] optimize site: [12, 13]
2025-08-18 06:50:19,605[DEBUG] use davidson, HC hops: 52
2025-08-18 06:50:19,607[DEBUG] energy: -6.857389012204749
2025-08-18 06:50:19,612[DEBUG] optimize site: [13, 14]
2025-08-18 06:50:19,816[DEBUG] use davidson, HC hops: 100
2025-08-18 06:50:19,819[DEBUG] energy: -7.114588022005771
2025-08-18 06:50:19,824[DEBUG] optimize site: [14, 15]
2025-08-18 06:50:19,910[DEBUG] use davidson, HC hops: 47
2025-08-18 06:50:19,910[DEBUG] energy: -7.641631783835412
2025-08-18 06:50:19,916[DEBUG] optimize site: [15, 16]
2025-08-18 06:50:19,976[DEBUG] use davidson, HC hops: 51
2025-08-18 06:50:19,978[DEBUG] energy: -8.118395338420047
2025-08-18 06:50:19,982[DEBUG] optimize site: [16, 17]
2025-08-18 06:50:20,076[DEBUG] use davidson, HC hops: 57
2025-08-18 06:50:20,077[DEBUG] energy: -8.579533430762861
2025-08-18 06:50:20,084[DEBUG] optimize site: [17, 18]
2025-08-18 06:50:20,210[DEBUG] use davidson, HC hops: 66
2025-08-18 06:50:20,213[DEBUG] energy: -8.983113190158448
2025-08-18 06:50:20,216[DEBUG] optimize site: [18, 19]
2025-08-18 06:50:20,292[DEBUG] use davidson, HC hops: 62
2025-08-18 06:50:20,294[DEBUG] energy: -9.422205404607647
2025-08-18 06:50:20,298[DEBUG] optimize site: [19, 20]
2025-08-18 06:50:20,376[DEBUG] use davidson, HC hops: 62
2025-08-18 06:50:20,377[DEBUG] energy: -9.903693680914376
2025-08-18 06:50:20,382[DEBUG] optimize site: [20, 21]
2025-08-18 06:50:20,520[DEBUG] use davidson, HC hops: 81
2025-08-18 06:50:20,521[DEBUG] energy: -10.398530611697963
2025-08-18 06:50:20,528[DEBUG] optimize site: [21, 22]
2025-08-18 06:50:20,641[DEBUG] use davidson, HC hops: 76
2025-08-18 06:50:20,642[DEBUG] energy: -10.834489434421663
2025-08-18 06:50:20,647[DEBUG] optimize site: [22, 23]
2025-08-18 06:50:20,729[DEBUG] use davidson, HC hops: 58
2025-08-18 06:50:20,732[DEBUG] energy: -11.415128707126796
2025-08-18 06:50:20,737[DEBUG] optimize site: [23, 24]
2025-08-18 06:50:20,843[DEBUG] use davidson, HC hops: 52
2025-08-18 06:50:20,844[DEBUG] energy: -12.122795879745055
2025-08-18 06:50:20,849[DEBUG] optimize site: [24, 25]
2025-08-18 06:50:20,979[DEBUG] use davidson, HC hops: 71
2025-08-18 06:50:20,982[DEBUG] energy: -12.812234874023476
2025-08-18 06:50:20,988[DEBUG] optimize site: [25, 26]
2025-08-18 06:50:21,117[DEBUG] use davidson, HC hops: 58
2025-08-18 06:50:21,121[DEBUG] energy: -13.774582804126652
2025-08-18 06:50:21,125[DEBUG] optimize site: [26, 27]
2025-08-18 06:50:21,211[DEBUG] use davidson, HC hops: 47
2025-08-18 06:50:21,214[DEBUG] energy: -13.996832655813083
2025-08-18 06:50:21,218[DEBUG] optimize site: [27, 28]
2025-08-18 06:50:21,222[DEBUG] use direct eigensolver
2025-08-18 06:50:21,491[DEBUG] energy: -13.99683265553403
2025-08-18 06:50:21,495[DEBUG] optimize site: [28, 29]
2025-08-18 06:50:21,497[DEBUG] use direct eigensolver
2025-08-18 06:50:21,546[DEBUG] energy: -13.99683265553403
2025-08-18 06:50:21,550[DEBUG] optimize site: [29, 30]
2025-08-18 06:50:21,552[DEBUG] use direct eigensolver
2025-08-18 06:50:21,560[DEBUG] energy: -13.996832655534018
2025-08-18 06:50:21,562[DEBUG] optimize site: [30, 31]
2025-08-18 06:50:21,564[DEBUG] use direct eigensolver
2025-08-18 06:50:21,567[DEBUG] energy: -13.996832655534025
2025-08-18 06:50:21,568[DEBUG] 1 sweeps are finished, lowest energy = -13.996832655813083
2025-08-18 06:50:21,571[DEBUG] isweep: 1
2025-08-18 06:50:21,571[DEBUG] compress config in current loop: 30, percent: 0
2025-08-18 06:50:21,572[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]
2025-08-18 06:50:21,574[DEBUG] optimize site: [30, 31]
2025-08-18 06:50:21,576[DEBUG] use direct eigensolver
2025-08-18 06:50:21,580[DEBUG] energy: -13.996832655534025
2025-08-18 06:50:21,581[DEBUG] optimize site: [29, 30]
2025-08-18 06:50:21,584[DEBUG] use direct eigensolver
2025-08-18 06:50:21,589[DEBUG] energy: -13.996832655534018
2025-08-18 06:50:21,590[DEBUG] optimize site: [28, 29]
2025-08-18 06:50:21,593[DEBUG] use direct eigensolver
2025-08-18 06:50:21,637[DEBUG] energy: -13.99683265553401
2025-08-18 06:50:21,638[DEBUG] optimize site: [27, 28]
2025-08-18 06:50:21,642[DEBUG] use direct eigensolver
2025-08-18 06:50:21,877[DEBUG] energy: -13.996832655534018
2025-08-18 06:50:21,881[DEBUG] optimize site: [26, 27]
2025-08-18 06:50:21,888[DEBUG] use davidson, HC hops: 4
2025-08-18 06:50:21,890[DEBUG] energy: -13.996832655813638
2025-08-18 06:50:21,894[DEBUG] optimize site: [25, 26]
2025-08-18 06:50:21,922[DEBUG] use davidson, HC hops: 22
2025-08-18 06:50:21,924[DEBUG] energy: -13.996844945038358
2025-08-18 06:50:21,927[DEBUG] optimize site: [24, 25]
2025-08-18 06:50:21,966[DEBUG] use davidson, HC hops: 28
2025-08-18 06:50:21,967[DEBUG] energy: -13.997067101658764
2025-08-18 06:50:21,971[DEBUG] optimize site: [23, 24]
2025-08-18 06:50:22,002[DEBUG] use davidson, HC hops: 25
2025-08-18 06:50:22,004[DEBUG] energy: -13.99710168471751
2025-08-18 06:50:22,008[DEBUG] optimize site: [22, 23]
2025-08-18 06:50:22,043[DEBUG] use davidson, HC hops: 23
2025-08-18 06:50:22,045[DEBUG] energy: -13.997106608213691
2025-08-18 06:50:22,052[DEBUG] optimize site: [21, 22]
2025-08-18 06:50:22,112[DEBUG] use davidson, HC hops: 23
2025-08-18 06:50:22,114[DEBUG] energy: -13.997113698271136
2025-08-18 06:50:22,120[DEBUG] optimize site: [20, 21]
2025-08-18 06:50:22,159[DEBUG] use davidson, HC hops: 26
2025-08-18 06:50:22,162[DEBUG] energy: -13.997162638323543
2025-08-18 06:50:22,165[DEBUG] optimize site: [19, 20]
2025-08-18 06:50:22,209[DEBUG] use davidson, HC hops: 23
2025-08-18 06:50:22,211[DEBUG] energy: -13.997170144965533
2025-08-18 06:50:22,216[DEBUG] optimize site: [18, 19]
2025-08-18 06:50:22,276[DEBUG] use davidson, HC hops: 26
2025-08-18 06:50:22,277[DEBUG] energy: -13.997199975427394
2025-08-18 06:50:22,282[DEBUG] optimize site: [17, 18]
2025-08-18 06:50:22,332[DEBUG] use davidson, HC hops: 22
2025-08-18 06:50:22,334[DEBUG] energy: -13.997204392621583
2025-08-18 06:50:22,338[DEBUG] optimize site: [16, 17]
2025-08-18 06:50:22,396[DEBUG] use davidson, HC hops: 25
2025-08-18 06:50:22,398[DEBUG] energy: -13.997225037523817
2025-08-18 06:50:22,402[DEBUG] optimize site: [15, 16]
2025-08-18 06:50:22,468[DEBUG] use davidson, HC hops: 26
2025-08-18 06:50:22,469[DEBUG] energy: -13.997284918121185
2025-08-18 06:50:22,474[DEBUG] optimize site: [14, 15]
2025-08-18 06:50:22,526[DEBUG] use davidson, HC hops: 22
2025-08-18 06:50:22,528[DEBUG] energy: -13.997290859971244
2025-08-18 06:50:22,532[DEBUG] optimize site: [13, 14]
2025-08-18 06:50:22,581[DEBUG] use davidson, HC hops: 20
2025-08-18 06:50:22,582[DEBUG] energy: -13.99729325765379
2025-08-18 06:50:22,587[DEBUG] optimize site: [12, 13]
2025-08-18 06:50:22,640[DEBUG] use davidson, HC hops: 23
2025-08-18 06:50:22,641[DEBUG] energy: -13.997306225086666
2025-08-18 06:50:22,646[DEBUG] optimize site: [11, 12]
2025-08-18 06:50:22,696[DEBUG] use davidson, HC hops: 21
2025-08-18 06:50:22,697[DEBUG] energy: -13.997311145595598
2025-08-18 06:50:22,702[DEBUG] optimize site: [10, 11]
2025-08-18 06:50:22,750[DEBUG] use davidson, HC hops: 20
2025-08-18 06:50:22,752[DEBUG] energy: -13.997313132707491
2025-08-18 06:50:22,758[DEBUG] optimize site: [9, 10]
2025-08-18 06:50:22,800[DEBUG] use davidson, HC hops: 17
2025-08-18 06:50:22,802[DEBUG] energy: -13.997314428626352
2025-08-18 06:50:22,806[DEBUG] optimize site: [8, 9]
2025-08-18 06:50:22,835[DEBUG] use davidson, HC hops: 11
2025-08-18 06:50:22,836[DEBUG] energy: -13.997314715468672
2025-08-18 06:50:22,841[DEBUG] optimize site: [7, 8]
2025-08-18 06:50:22,861[DEBUG] use davidson, HC hops: 7
2025-08-18 06:50:22,862[DEBUG] energy: -13.997314712669782
2025-08-18 06:50:22,866[DEBUG] optimize site: [6, 7]
2025-08-18 06:50:22,897[DEBUG] use davidson, HC hops: 12
2025-08-18 06:50:22,899[DEBUG] energy: -13.997314999750017
2025-08-18 06:50:22,904[DEBUG] optimize site: [5, 6]
2025-08-18 06:50:22,924[DEBUG] use davidson, HC hops: 7
2025-08-18 06:50:22,925[DEBUG] energy: -13.997315003811455
2025-08-18 06:50:22,930[DEBUG] optimize site: [4, 5]
2025-08-18 06:50:22,943[DEBUG] use davidson, HC hops: 5
2025-08-18 06:50:22,945[DEBUG] energy: -13.997315004767785
2025-08-18 06:50:22,947[DEBUG] optimize site: [3, 4]
2025-08-18 06:50:22,952[DEBUG] use direct eigensolver
2025-08-18 06:50:23,222[DEBUG] energy: -13.997315004467081
2025-08-18 06:50:23,225[DEBUG] optimize site: [2, 3]
2025-08-18 06:50:23,226[DEBUG] use direct eigensolver
2025-08-18 06:50:23,292[DEBUG] energy: -13.99731500446707
2025-08-18 06:50:23,295[DEBUG] optimize site: [1, 2]
2025-08-18 06:50:23,298[DEBUG] use direct eigensolver
2025-08-18 06:50:23,306[DEBUG] energy: -13.997315004467076
2025-08-18 06:50:23,308[DEBUG] optimize site: [0, 1]
2025-08-18 06:50:23,310[DEBUG] use direct eigensolver
2025-08-18 06:50:23,313[DEBUG] energy: -13.997315004467062
2025-08-18 06:50:23,315[DEBUG] 2 sweeps are finished, lowest energy = -13.997315004767785
2025-08-18 06:50:23,316[DEBUG] isweep: 2
2025-08-18 06:50:23,318[DEBUG] compress config in current loop: 30, percent: 0
2025-08-18 06:50:23,320[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]
2025-08-18 06:50:23,321[DEBUG] optimize site: [0, 1]
2025-08-18 06:50:23,323[DEBUG] use direct eigensolver
2025-08-18 06:50:23,326[DEBUG] energy: -13.997315004467062
2025-08-18 06:50:23,329[DEBUG] optimize site: [1, 2]
2025-08-18 06:50:23,331[DEBUG] use direct eigensolver
2025-08-18 06:50:23,339[DEBUG] energy: -13.997315004467065
2025-08-18 06:50:23,341[DEBUG] optimize site: [2, 3]
2025-08-18 06:50:23,341[DEBUG] use direct eigensolver
2025-08-18 06:50:23,416[DEBUG] energy: -13.99731500446707
2025-08-18 06:50:23,419[DEBUG] optimize site: [3, 4]
2025-08-18 06:50:23,422[DEBUG] use direct eigensolver
2025-08-18 06:50:23,687[DEBUG] energy: -13.997315004467094
2025-08-18 06:50:23,690[DEBUG] optimize site: [4, 5]
2025-08-18 06:50:23,698[DEBUG] use davidson, HC hops: 4
2025-08-18 06:50:23,699[DEBUG] energy: -13.99731500476786
2025-08-18 06:50:23,702[DEBUG] optimize site: [5, 6]
2025-08-18 06:50:23,718[DEBUG] use davidson, HC hops: 4
2025-08-18 06:50:23,720[DEBUG] energy: -13.99731500466774
2025-08-18 06:50:23,723[DEBUG] optimize site: [6, 7]
2025-08-18 06:50:23,740[DEBUG] use davidson, HC hops: 6
2025-08-18 06:50:23,741[DEBUG] energy: -13.997315012470631
2025-08-18 06:50:23,744[DEBUG] optimize site: [7, 8]
2025-08-18 06:50:23,758[DEBUG] use davidson, HC hops: 5
2025-08-18 06:50:23,760[DEBUG] energy: -13.99731500606661
2025-08-18 06:50:23,764[DEBUG] optimize site: [8, 9]
2025-08-18 06:50:23,782[DEBUG] use davidson, HC hops: 7
2025-08-18 06:50:23,783[DEBUG] energy: -13.997315033374507
2025-08-18 06:50:23,787[DEBUG] optimize site: [9, 10]
2025-08-18 06:50:23,804[DEBUG] use davidson, HC hops: 6
2025-08-18 06:50:23,805[DEBUG] energy: -13.997315010121923
2025-08-18 06:50:23,810[DEBUG] optimize site: [10, 11]
2025-08-18 06:50:23,831[DEBUG] use davidson, HC hops: 8
2025-08-18 06:50:23,833[DEBUG] energy: -13.99731505577685
2025-08-18 06:50:23,837[DEBUG] optimize site: [11, 12]
2025-08-18 06:50:23,856[DEBUG] use davidson, HC hops: 7
2025-08-18 06:50:23,857[DEBUG] energy: -13.99731501589044
2025-08-18 06:50:23,861[DEBUG] optimize site: [12, 13]
2025-08-18 06:50:23,881[DEBUG] use davidson, HC hops: 8
2025-08-18 06:50:23,883[DEBUG] energy: -13.997315076759387
2025-08-18 06:50:23,887[DEBUG] optimize site: [13, 14]
2025-08-18 06:50:23,905[DEBUG] use davidson, HC hops: 7
2025-08-18 06:50:23,906[DEBUG] energy: -13.997315021063734
2025-08-18 06:50:23,910[DEBUG] optimize site: [14, 15]
2025-08-18 06:50:23,931[DEBUG] use davidson, HC hops: 8
2025-08-18 06:50:23,932[DEBUG] energy: -13.99731508916345
2025-08-18 06:50:23,936[DEBUG] optimize site: [15, 16]
2025-08-18 06:50:23,958[DEBUG] use davidson, HC hops: 8
2025-08-18 06:50:23,961[DEBUG] energy: -13.997315023237677
2025-08-18 06:50:23,965[DEBUG] optimize site: [16, 17]
2025-08-18 06:50:23,990[DEBUG] use davidson, HC hops: 9
2025-08-18 06:50:23,992[DEBUG] energy: -13.997315090211584
2025-08-18 06:50:23,998[DEBUG] optimize site: [17, 18]
2025-08-18 06:50:24,020[DEBUG] use davidson, HC hops: 8
2025-08-18 06:50:24,022[DEBUG] energy: -13.997315022014194
2025-08-18 06:50:24,028[DEBUG] optimize site: [18, 19]
2025-08-18 06:50:24,051[DEBUG] use davidson, HC hops: 8
2025-08-18 06:50:24,054[DEBUG] energy: -13.997315079212491
2025-08-18 06:50:24,060[DEBUG] optimize site: [19, 20]
2025-08-18 06:50:24,081[DEBUG] use davidson, HC hops: 7
2025-08-18 06:50:24,082[DEBUG] energy: -13.997315018389617
2025-08-18 06:50:24,087[DEBUG] optimize site: [20, 21]
2025-08-18 06:50:24,108[DEBUG] use davidson, HC hops: 8
2025-08-18 06:50:24,109[DEBUG] energy: -13.997315060471486
2025-08-18 06:50:24,114[DEBUG] optimize site: [21, 22]
2025-08-18 06:50:24,132[DEBUG] use davidson, HC hops: 6
2025-08-18 06:50:24,133[DEBUG] energy: -13.99731501422291
2025-08-18 06:50:24,139[DEBUG] optimize site: [22, 23]
2025-08-18 06:50:24,161[DEBUG] use davidson, HC hops: 8
2025-08-18 06:50:24,162[DEBUG] energy: -13.99731503638069
2025-08-18 06:50:24,168[DEBUG] optimize site: [23, 24]
2025-08-18 06:50:24,185[DEBUG] use davidson, HC hops: 6
2025-08-18 06:50:24,187[DEBUG] energy: -13.997315009063273
2025-08-18 06:50:24,194[DEBUG] optimize site: [24, 25]
2025-08-18 06:50:24,210[DEBUG] use davidson, HC hops: 6
2025-08-18 06:50:24,211[DEBUG] energy: -13.997315015431766
2025-08-18 06:50:24,217[DEBUG] optimize site: [25, 26]
2025-08-18 06:50:24,231[DEBUG] use davidson, HC hops: 5
2025-08-18 06:50:24,232[DEBUG] energy: -13.997315007630444
2025-08-18 06:50:24,237[DEBUG] optimize site: [26, 27]
2025-08-18 06:50:24,247[DEBUG] use davidson, HC hops: 4
2025-08-18 06:50:24,249[DEBUG] energy: -13.997315007727401
2025-08-18 06:50:24,253[DEBUG] optimize site: [27, 28]
2025-08-18 06:50:24,257[DEBUG] use direct eigensolver
2025-08-18 06:50:24,529[DEBUG] energy: -13.99731500742737
2025-08-18 06:50:24,532[DEBUG] optimize site: [28, 29]
2025-08-18 06:50:24,534[DEBUG] use direct eigensolver
2025-08-18 06:50:24,613[DEBUG] energy: -13.997315007427373
2025-08-18 06:50:24,617[DEBUG] optimize site: [29, 30]
2025-08-18 06:50:24,620[DEBUG] use direct eigensolver
2025-08-18 06:50:24,630[DEBUG] energy: -13.997315007427378
2025-08-18 06:50:24,632[DEBUG] optimize site: [30, 31]
2025-08-18 06:50:24,634[DEBUG] use direct eigensolver
2025-08-18 06:50:24,637[DEBUG] energy: -13.997315007427373
2025-08-18 06:50:24,638[DEBUG] 3 sweeps are finished, lowest energy = -13.997315090211584
2025-08-18 06:50:24,641[INFO] DMRG has converged!
2025-08-18 06:50:24,675[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: -13.997315090211584

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