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

2025-11-11 02:47:05,915[INFO] Use NumPy as backend
2025-11-11 02:47:05,916[INFO] numpy random seed is 9012
2025-11-11 02:47:05,917[INFO] random seed is 1092
2025-11-11 02:47:05,927[INFO] Git Commit Hash: 940abbe8e26a22e9345f941947c6944ed81a5f06
2025-11-11 02:47:05,929[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}")

2025-11-11 02:47:06,033[DEBUG] # of operator terms: 93
2025-11-11 02:47:06,034[DEBUG] Input operator terms: 93
2025-11-11 02:47:06,037[DEBUG] After combination of the same terms: 93
2025-11-11 02:47:06,037[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))

2025-11-11 02:47:06,113[INFO] optimization method: 2site
2025-11-11 02:47:06,114[INFO] e_rtol: 1e-06
2025-11-11 02:47:06,115[INFO] e_atol: 1e-08
2025-11-11 02:47:06,115[INFO] procedure: [[30, 0.2], [30, 0], [30, 0], [30, 0], [30, 0]]
2025-11-11 02:47:06,147[DEBUG] isweep: 0
2025-11-11 02:47:06,149[DEBUG] compress config in current loop: 30, percent: 0.2
2025-11-11 02:47:06,150[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]
2025-11-11 02:47:06,152[DEBUG] optimize site: [0, 1]
2025-11-11 02:47:06,153[DEBUG] use direct eigensolver
2025-11-11 02:47:06,156[DEBUG] energy: -0.927999022689833
2025-11-11 02:47:06,158[DEBUG] optimize site: [1, 2]
2025-11-11 02:47:06,161[DEBUG] use direct eigensolver
2025-11-11 02:47:06,165[DEBUG] energy: -1.284089573410534
2025-11-11 02:47:06,168[DEBUG] optimize site: [2, 3]
2025-11-11 02:47:06,170[DEBUG] use direct eigensolver
2025-11-11 02:47:06,194[DEBUG] energy: -2.08574526474992
2025-11-11 02:47:06,197[DEBUG] optimize site: [3, 4]
2025-11-11 02:47:06,200[DEBUG] use direct eigensolver
2025-11-11 02:47:06,442[DEBUG] energy: -2.815889527237408
2025-11-11 02:47:06,444[DEBUG] optimize site: [4, 5]
2025-11-11 02:47:06,476[DEBUG] use davidson, HC hops: 34
2025-11-11 02:47:06,479[DEBUG] energy: -3.2933673155858
2025-11-11 02:47:06,482[DEBUG] optimize site: [5, 6]
2025-11-11 02:47:06,533[DEBUG] use davidson, HC hops: 42
2025-11-11 02:47:06,536[DEBUG] energy: -3.7449867503071985
2025-11-11 02:47:06,541[DEBUG] optimize site: [6, 7]
2025-11-11 02:47:06,634[DEBUG] use davidson, HC hops: 42
2025-11-11 02:47:06,636[DEBUG] energy: -4.17638557549649
2025-11-11 02:47:06,641[DEBUG] optimize site: [7, 8]
2025-11-11 02:47:06,740[DEBUG] use davidson, HC hops: 44
2025-11-11 02:47:06,741[DEBUG] energy: -4.583593477927385
2025-11-11 02:47:06,747[DEBUG] optimize site: [8, 9]
2025-11-11 02:47:06,853[DEBUG] use davidson, HC hops: 55
2025-11-11 02:47:06,855[DEBUG] energy: -4.968031845671205
2025-11-11 02:47:06,861[DEBUG] optimize site: [9, 10]
2025-11-11 02:47:07,005[DEBUG] use davidson, HC hops: 68
2025-11-11 02:47:07,007[DEBUG] energy: -5.41470636083398
2025-11-11 02:47:07,014[DEBUG] optimize site: [10, 11]
2025-11-11 02:47:07,171[DEBUG] use davidson, HC hops: 72
2025-11-11 02:47:07,172[DEBUG] energy: -5.856529754520473
2025-11-11 02:47:07,178[DEBUG] optimize site: [11, 12]
2025-11-11 02:47:07,356[DEBUG] use davidson, HC hops: 100
2025-11-11 02:47:07,357[DEBUG] energy: -6.279022467295806
2025-11-11 02:47:07,361[DEBUG] optimize site: [12, 13]
2025-11-11 02:47:07,423[DEBUG] use davidson, HC hops: 52
2025-11-11 02:47:07,424[DEBUG] energy: -6.857389012204749
2025-11-11 02:47:07,427[DEBUG] optimize site: [13, 14]
2025-11-11 02:47:07,622[DEBUG] use davidson, HC hops: 100
2025-11-11 02:47:07,625[DEBUG] energy: -7.114588022005771
2025-11-11 02:47:07,631[DEBUG] optimize site: [14, 15]
2025-11-11 02:47:07,735[DEBUG] use davidson, HC hops: 47
2025-11-11 02:47:07,738[DEBUG] energy: -7.641631783835412
2025-11-11 02:47:07,744[DEBUG] optimize site: [15, 16]
2025-11-11 02:47:07,815[DEBUG] use davidson, HC hops: 51
2025-11-11 02:47:07,816[DEBUG] energy: -8.118395338420047
2025-11-11 02:47:07,822[DEBUG] optimize site: [16, 17]
2025-11-11 02:47:07,921[DEBUG] use davidson, HC hops: 57
2025-11-11 02:47:07,923[DEBUG] energy: -8.579533430762861
2025-11-11 02:47:07,930[DEBUG] optimize site: [17, 18]
2025-11-11 02:47:08,046[DEBUG] use davidson, HC hops: 66
2025-11-11 02:47:08,049[DEBUG] energy: -8.983113190158448
2025-11-11 02:47:08,053[DEBUG] optimize site: [18, 19]
2025-11-11 02:47:08,149[DEBUG] use davidson, HC hops: 62
2025-11-11 02:47:08,152[DEBUG] energy: -9.422205404607647
2025-11-11 02:47:08,158[DEBUG] optimize site: [19, 20]
2025-11-11 02:47:08,291[DEBUG] use davidson, HC hops: 62
2025-11-11 02:47:08,292[DEBUG] energy: -9.903693680914376
2025-11-11 02:47:08,299[DEBUG] optimize site: [20, 21]
2025-11-11 02:47:08,467[DEBUG] use davidson, HC hops: 81
2025-11-11 02:47:08,471[DEBUG] energy: -10.398530611697963
2025-11-11 02:47:08,476[DEBUG] optimize site: [21, 22]
2025-11-11 02:47:08,633[DEBUG] use davidson, HC hops: 76
2025-11-11 02:47:08,634[DEBUG] energy: -10.834489434421663
2025-11-11 02:47:08,640[DEBUG] optimize site: [22, 23]
2025-11-11 02:47:08,761[DEBUG] use davidson, HC hops: 58
2025-11-11 02:47:08,764[DEBUG] energy: -11.415128707126796
2025-11-11 02:47:08,770[DEBUG] optimize site: [23, 24]
2025-11-11 02:47:08,882[DEBUG] use davidson, HC hops: 52
2025-11-11 02:47:08,885[DEBUG] energy: -12.122795879745055
2025-11-11 02:47:08,891[DEBUG] optimize site: [24, 25]
2025-11-11 02:47:08,981[DEBUG] use davidson, HC hops: 71
2025-11-11 02:47:08,984[DEBUG] energy: -12.812234874023476
2025-11-11 02:47:08,987[DEBUG] optimize site: [25, 26]
2025-11-11 02:47:09,068[DEBUG] use davidson, HC hops: 58
2025-11-11 02:47:09,070[DEBUG] energy: -13.774582804126652
2025-11-11 02:47:09,077[DEBUG] optimize site: [26, 27]
2025-11-11 02:47:09,156[DEBUG] use davidson, HC hops: 47
2025-11-11 02:47:09,158[DEBUG] energy: -13.996832655813083
2025-11-11 02:47:09,163[DEBUG] optimize site: [27, 28]
2025-11-11 02:47:09,168[DEBUG] use direct eigensolver
2025-11-11 02:47:09,440[DEBUG] energy: -13.99683265553403
2025-11-11 02:47:09,444[DEBUG] optimize site: [28, 29]
2025-11-11 02:47:09,446[DEBUG] use direct eigensolver
2025-11-11 02:47:09,526[DEBUG] energy: -13.99683265553403
2025-11-11 02:47:09,529[DEBUG] optimize site: [29, 30]
2025-11-11 02:47:09,533[DEBUG] use direct eigensolver
2025-11-11 02:47:09,542[DEBUG] energy: -13.996832655534018
2025-11-11 02:47:09,544[DEBUG] optimize site: [30, 31]
2025-11-11 02:47:09,547[DEBUG] use direct eigensolver
2025-11-11 02:47:09,551[DEBUG] energy: -13.996832655534025
2025-11-11 02:47:09,553[DEBUG] 1 sweeps are finished, lowest energy = -13.996832655813083
2025-11-11 02:47:09,555[DEBUG] isweep: 1
2025-11-11 02:47:09,556[DEBUG] compress config in current loop: 30, percent: 0
2025-11-11 02:47:09,557[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]
2025-11-11 02:47:09,559[DEBUG] optimize site: [30, 31]
2025-11-11 02:47:09,560[DEBUG] use direct eigensolver
2025-11-11 02:47:09,563[DEBUG] energy: -13.996832655534025
2025-11-11 02:47:09,565[DEBUG] optimize site: [29, 30]
2025-11-11 02:47:09,566[DEBUG] use direct eigensolver
2025-11-11 02:47:09,570[DEBUG] energy: -13.996832655534018
2025-11-11 02:47:09,571[DEBUG] optimize site: [28, 29]
2025-11-11 02:47:09,573[DEBUG] use direct eigensolver
2025-11-11 02:47:09,643[DEBUG] energy: -13.99683265553401
2025-11-11 02:47:09,645[DEBUG] optimize site: [27, 28]
2025-11-11 02:47:09,649[DEBUG] use direct eigensolver
2025-11-11 02:47:09,902[DEBUG] energy: -13.996832655534018
2025-11-11 02:47:09,906[DEBUG] optimize site: [26, 27]
2025-11-11 02:47:09,924[DEBUG] use davidson, HC hops: 4
2025-11-11 02:47:09,928[DEBUG] energy: -13.996832655813638
2025-11-11 02:47:09,932[DEBUG] optimize site: [25, 26]
2025-11-11 02:47:09,971[DEBUG] use davidson, HC hops: 22
2025-11-11 02:47:09,972[DEBUG] energy: -13.996844945038358
2025-11-11 02:47:09,977[DEBUG] optimize site: [24, 25]
2025-11-11 02:47:10,031[DEBUG] use davidson, HC hops: 28
2025-11-11 02:47:10,034[DEBUG] energy: -13.997067101658764
2025-11-11 02:47:10,040[DEBUG] optimize site: [23, 24]
2025-11-11 02:47:10,097[DEBUG] use davidson, HC hops: 25
2025-11-11 02:47:10,100[DEBUG] energy: -13.99710168471751
2025-11-11 02:47:10,106[DEBUG] optimize site: [22, 23]
2025-11-11 02:47:10,159[DEBUG] use davidson, HC hops: 23
2025-11-11 02:47:10,160[DEBUG] energy: -13.997106608213691
2025-11-11 02:47:10,167[DEBUG] optimize site: [21, 22]
2025-11-11 02:47:10,200[DEBUG] use davidson, HC hops: 23
2025-11-11 02:47:10,200[DEBUG] energy: -13.997113698271136
2025-11-11 02:47:10,206[DEBUG] optimize site: [20, 21]
2025-11-11 02:47:10,259[DEBUG] use davidson, HC hops: 26
2025-11-11 02:47:10,261[DEBUG] energy: -13.997162638323543
2025-11-11 02:47:10,268[DEBUG] optimize site: [19, 20]
2025-11-11 02:47:10,322[DEBUG] use davidson, HC hops: 23
2025-11-11 02:47:10,324[DEBUG] energy: -13.997170144965533
2025-11-11 02:47:10,331[DEBUG] optimize site: [18, 19]
2025-11-11 02:47:10,377[DEBUG] use davidson, HC hops: 26
2025-11-11 02:47:10,378[DEBUG] energy: -13.997199975427394
2025-11-11 02:47:10,384[DEBUG] optimize site: [17, 18]
2025-11-11 02:47:10,421[DEBUG] use davidson, HC hops: 22
2025-11-11 02:47:10,424[DEBUG] energy: -13.997204392621583
2025-11-11 02:47:10,430[DEBUG] optimize site: [16, 17]
2025-11-11 02:47:10,488[DEBUG] use davidson, HC hops: 25
2025-11-11 02:47:10,490[DEBUG] energy: -13.997225037523817
2025-11-11 02:47:10,497[DEBUG] optimize site: [15, 16]
2025-11-11 02:47:10,561[DEBUG] use davidson, HC hops: 26
2025-11-11 02:47:10,563[DEBUG] energy: -13.997284918121185
2025-11-11 02:47:10,569[DEBUG] optimize site: [14, 15]
2025-11-11 02:47:10,606[DEBUG] use davidson, HC hops: 22
2025-11-11 02:47:10,607[DEBUG] energy: -13.997290859971244
2025-11-11 02:47:10,613[DEBUG] optimize site: [13, 14]
2025-11-11 02:47:10,640[DEBUG] use davidson, HC hops: 20
2025-11-11 02:47:10,642[DEBUG] energy: -13.99729325765379
2025-11-11 02:47:10,646[DEBUG] optimize site: [12, 13]
2025-11-11 02:47:10,679[DEBUG] use davidson, HC hops: 23
2025-11-11 02:47:10,680[DEBUG] energy: -13.997306225086666
2025-11-11 02:47:10,686[DEBUG] optimize site: [11, 12]
2025-11-11 02:47:10,714[DEBUG] use davidson, HC hops: 21
2025-11-11 02:47:10,716[DEBUG] energy: -13.997311145595598
2025-11-11 02:47:10,721[DEBUG] optimize site: [10, 11]
2025-11-11 02:47:10,747[DEBUG] use davidson, HC hops: 20
2025-11-11 02:47:10,748[DEBUG] energy: -13.997313132707491
2025-11-11 02:47:10,754[DEBUG] optimize site: [9, 10]
2025-11-11 02:47:10,786[DEBUG] use davidson, HC hops: 17
2025-11-11 02:47:10,789[DEBUG] energy: -13.997314428626352
2025-11-11 02:47:10,795[DEBUG] optimize site: [8, 9]
2025-11-11 02:47:10,826[DEBUG] use davidson, HC hops: 11
2025-11-11 02:47:10,828[DEBUG] energy: -13.997314715468672
2025-11-11 02:47:10,836[DEBUG] optimize site: [7, 8]
2025-11-11 02:47:10,857[DEBUG] use davidson, HC hops: 7
2025-11-11 02:47:10,861[DEBUG] energy: -13.997314712669782
2025-11-11 02:47:10,866[DEBUG] optimize site: [6, 7]
2025-11-11 02:47:10,900[DEBUG] use davidson, HC hops: 12
2025-11-11 02:47:10,904[DEBUG] energy: -13.997314999750017
2025-11-11 02:47:10,908[DEBUG] optimize site: [5, 6]
2025-11-11 02:47:10,928[DEBUG] use davidson, HC hops: 7
2025-11-11 02:47:10,930[DEBUG] energy: -13.997315003811455
2025-11-11 02:47:10,935[DEBUG] optimize site: [4, 5]
2025-11-11 02:47:10,949[DEBUG] use davidson, HC hops: 5
2025-11-11 02:47:10,951[DEBUG] energy: -13.997315004767785
2025-11-11 02:47:10,954[DEBUG] optimize site: [3, 4]
2025-11-11 02:47:10,958[DEBUG] use direct eigensolver
2025-11-11 02:47:11,233[DEBUG] energy: -13.997315004467081
2025-11-11 02:47:11,236[DEBUG] optimize site: [2, 3]
2025-11-11 02:47:11,238[DEBUG] use direct eigensolver
2025-11-11 02:47:11,286[DEBUG] energy: -13.99731500446707
2025-11-11 02:47:11,288[DEBUG] optimize site: [1, 2]
2025-11-11 02:47:11,290[DEBUG] use direct eigensolver
2025-11-11 02:47:11,296[DEBUG] energy: -13.997315004467076
2025-11-11 02:47:11,298[DEBUG] optimize site: [0, 1]
2025-11-11 02:47:11,300[DEBUG] use direct eigensolver
2025-11-11 02:47:11,302[DEBUG] energy: -13.997315004467062
2025-11-11 02:47:11,303[DEBUG] 2 sweeps are finished, lowest energy = -13.997315004767785
2025-11-11 02:47:11,304[DEBUG] isweep: 2
2025-11-11 02:47:11,305[DEBUG] compress config in current loop: 30, percent: 0
2025-11-11 02:47:11,306[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]
2025-11-11 02:47:11,307[DEBUG] optimize site: [0, 1]
2025-11-11 02:47:11,307[DEBUG] use direct eigensolver
2025-11-11 02:47:11,311[DEBUG] energy: -13.997315004467062
2025-11-11 02:47:11,315[DEBUG] optimize site: [1, 2]
2025-11-11 02:47:11,317[DEBUG] use direct eigensolver
2025-11-11 02:47:11,326[DEBUG] energy: -13.997315004467065
2025-11-11 02:47:11,329[DEBUG] optimize site: [2, 3]
2025-11-11 02:47:11,331[DEBUG] use direct eigensolver
2025-11-11 02:47:11,383[DEBUG] energy: -13.99731500446707
2025-11-11 02:47:11,385[DEBUG] optimize site: [3, 4]
2025-11-11 02:47:11,386[DEBUG] use direct eigensolver
2025-11-11 02:47:11,634[DEBUG] energy: -13.997315004467094
2025-11-11 02:47:11,636[DEBUG] optimize site: [4, 5]
2025-11-11 02:47:11,643[DEBUG] use davidson, HC hops: 4
2025-11-11 02:47:11,644[DEBUG] energy: -13.99731500476786
2025-11-11 02:47:11,647[DEBUG] optimize site: [5, 6]
2025-11-11 02:47:11,656[DEBUG] use davidson, HC hops: 4
2025-11-11 02:47:11,657[DEBUG] energy: -13.99731500466774
2025-11-11 02:47:11,661[DEBUG] optimize site: [6, 7]
2025-11-11 02:47:11,671[DEBUG] use davidson, HC hops: 6
2025-11-11 02:47:11,672[DEBUG] energy: -13.997315012470631
2025-11-11 02:47:11,676[DEBUG] optimize site: [7, 8]
2025-11-11 02:47:11,684[DEBUG] use davidson, HC hops: 5
2025-11-11 02:47:11,685[DEBUG] energy: -13.99731500606661
2025-11-11 02:47:11,690[DEBUG] optimize site: [8, 9]
2025-11-11 02:47:11,701[DEBUG] use davidson, HC hops: 7
2025-11-11 02:47:11,701[DEBUG] energy: -13.997315033374507
2025-11-11 02:47:11,706[DEBUG] optimize site: [9, 10]
2025-11-11 02:47:11,717[DEBUG] use davidson, HC hops: 6
2025-11-11 02:47:11,717[DEBUG] energy: -13.997315010121923
2025-11-11 02:47:11,723[DEBUG] optimize site: [10, 11]
2025-11-11 02:47:11,735[DEBUG] use davidson, HC hops: 8
2025-11-11 02:47:11,738[DEBUG] energy: -13.99731505577685
2025-11-11 02:47:11,742[DEBUG] optimize site: [11, 12]
2025-11-11 02:47:11,753[DEBUG] use davidson, HC hops: 7
2025-11-11 02:47:11,753[DEBUG] energy: -13.99731501589044
2025-11-11 02:47:11,759[DEBUG] optimize site: [12, 13]
2025-11-11 02:47:11,771[DEBUG] use davidson, HC hops: 8
2025-11-11 02:47:11,772[DEBUG] energy: -13.997315076759387
2025-11-11 02:47:11,777[DEBUG] optimize site: [13, 14]
2025-11-11 02:47:11,789[DEBUG] use davidson, HC hops: 7
2025-11-11 02:47:11,790[DEBUG] energy: -13.997315021063734
2025-11-11 02:47:11,796[DEBUG] optimize site: [14, 15]
2025-11-11 02:47:11,808[DEBUG] use davidson, HC hops: 8
2025-11-11 02:47:11,811[DEBUG] energy: -13.99731508916345
2025-11-11 02:47:11,815[DEBUG] optimize site: [15, 16]
2025-11-11 02:47:11,828[DEBUG] use davidson, HC hops: 8
2025-11-11 02:47:11,831[DEBUG] energy: -13.997315023237677
2025-11-11 02:47:11,834[DEBUG] optimize site: [16, 17]
2025-11-11 02:47:11,848[DEBUG] use davidson, HC hops: 9
2025-11-11 02:47:11,851[DEBUG] energy: -13.997315090211584
2025-11-11 02:47:11,855[DEBUG] optimize site: [17, 18]
2025-11-11 02:47:11,867[DEBUG] use davidson, HC hops: 8
2025-11-11 02:47:11,870[DEBUG] energy: -13.997315022014194
2025-11-11 02:47:11,874[DEBUG] optimize site: [18, 19]
2025-11-11 02:47:11,887[DEBUG] use davidson, HC hops: 8
2025-11-11 02:47:11,889[DEBUG] energy: -13.997315079212491
2025-11-11 02:47:11,893[DEBUG] optimize site: [19, 20]
2025-11-11 02:47:11,905[DEBUG] use davidson, HC hops: 7
2025-11-11 02:47:11,906[DEBUG] energy: -13.997315018389617
2025-11-11 02:47:11,911[DEBUG] optimize site: [20, 21]
2025-11-11 02:47:11,924[DEBUG] use davidson, HC hops: 8
2025-11-11 02:47:11,925[DEBUG] energy: -13.997315060471486
2025-11-11 02:47:11,931[DEBUG] optimize site: [21, 22]
2025-11-11 02:47:11,942[DEBUG] use davidson, HC hops: 6
2025-11-11 02:47:11,944[DEBUG] energy: -13.99731501422291
2025-11-11 02:47:11,948[DEBUG] optimize site: [22, 23]
2025-11-11 02:47:11,962[DEBUG] use davidson, HC hops: 8
2025-11-11 02:47:11,963[DEBUG] energy: -13.99731503638069
2025-11-11 02:47:11,968[DEBUG] optimize site: [23, 24]
2025-11-11 02:47:11,979[DEBUG] use davidson, HC hops: 6
2025-11-11 02:47:11,982[DEBUG] energy: -13.997315009063273
2025-11-11 02:47:11,986[DEBUG] optimize site: [24, 25]
2025-11-11 02:47:11,997[DEBUG] use davidson, HC hops: 6
2025-11-11 02:47:11,999[DEBUG] energy: -13.997315015431766
2025-11-11 02:47:12,003[DEBUG] optimize site: [25, 26]
2025-11-11 02:47:12,013[DEBUG] use davidson, HC hops: 5
2025-11-11 02:47:12,015[DEBUG] energy: -13.997315007630444
2025-11-11 02:47:12,019[DEBUG] optimize site: [26, 27]
2025-11-11 02:47:12,026[DEBUG] use davidson, HC hops: 4
2025-11-11 02:47:12,027[DEBUG] energy: -13.997315007727401
2025-11-11 02:47:12,031[DEBUG] optimize site: [27, 28]
2025-11-11 02:47:12,034[DEBUG] use direct eigensolver
2025-11-11 02:47:12,282[DEBUG] energy: -13.99731500742737
2025-11-11 02:47:12,286[DEBUG] optimize site: [28, 29]
2025-11-11 02:47:12,289[DEBUG] use direct eigensolver
2025-11-11 02:47:12,338[DEBUG] energy: -13.997315007427373
2025-11-11 02:47:12,342[DEBUG] optimize site: [29, 30]
2025-11-11 02:47:12,345[DEBUG] use direct eigensolver
2025-11-11 02:47:12,351[DEBUG] energy: -13.997315007427378
2025-11-11 02:47:12,353[DEBUG] optimize site: [30, 31]
2025-11-11 02:47:12,357[DEBUG] use direct eigensolver
2025-11-11 02:47:12,360[DEBUG] energy: -13.997315007427373
2025-11-11 02:47:12,363[DEBUG] 3 sweeps are finished, lowest energy = -13.997315090211584
2025-11-11 02:47:12,365[INFO] DMRG has converged!
2025-11-11 02:47:12,401[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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