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

2025-08-12 09:12:49,150[INFO] Use NumPy as backend
2025-08-12 09:12:49,151[INFO] numpy random seed is 9012
2025-08-12 09:12:49,152[INFO] random seed is 1092
2025-08-12 09:12:49,161[INFO] Git Commit Hash: 17d8634f55d07699b9771eb4183b519874cb7d31
2025-08-12 09:12:49,162[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}")

2025-08-12 09:12:49,258[DEBUG] # of operator terms: 93
2025-08-12 09:12:49,259[DEBUG] Input operator terms: 93
2025-08-12 09:12:49,261[DEBUG] After combination of the same terms: 93
2025-08-12 09:12:49,262[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))

2025-08-12 09:12:49,332[INFO] optimization method: 2site
2025-08-12 09:12:49,332[INFO] e_rtol: 1e-06
2025-08-12 09:12:49,333[INFO] e_atol: 1e-08
2025-08-12 09:12:49,334[INFO] procedure: [[30, 0.2], [30, 0], [30, 0], [30, 0], [30, 0]]
2025-08-12 09:12:49,363[DEBUG] isweep: 0
2025-08-12 09:12:49,365[DEBUG] compress config in current loop: 30, percent: 0.2
2025-08-12 09:12:49,365[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]
2025-08-12 09:12:49,367[DEBUG] optimize site: [0, 1]
2025-08-12 09:12:49,368[DEBUG] use direct eigensolver
2025-08-12 09:12:49,372[DEBUG] energy: -0.9279990226898331
2025-08-12 09:12:49,373[DEBUG] optimize site: [1, 2]
2025-08-12 09:12:49,376[DEBUG] use direct eigensolver
2025-08-12 09:12:49,381[DEBUG] energy: -1.284089573410534
2025-08-12 09:12:49,382[DEBUG] optimize site: [2, 3]
2025-08-12 09:12:49,384[DEBUG] use direct eigensolver
2025-08-12 09:12:49,408[DEBUG] energy: -2.085745264749922
2025-08-12 09:12:49,410[DEBUG] optimize site: [3, 4]
2025-08-12 09:12:49,413[DEBUG] use direct eigensolver
2025-08-12 09:12:49,664[DEBUG] energy: -2.815889527237411
2025-08-12 09:12:49,666[DEBUG] optimize site: [4, 5]
2025-08-12 09:12:49,721[DEBUG] use davidson, HC hops: 34
2025-08-12 09:12:49,722[DEBUG] energy: -3.2933673155858036
2025-08-12 09:12:49,724[DEBUG] optimize site: [5, 6]
2025-08-12 09:12:49,810[DEBUG] use davidson, HC hops: 42
2025-08-12 09:12:49,812[DEBUG] energy: -3.744986750307202
2025-08-12 09:12:49,817[DEBUG] optimize site: [6, 7]
2025-08-12 09:12:49,902[DEBUG] use davidson, HC hops: 42
2025-08-12 09:12:49,903[DEBUG] energy: -4.176385575496492
2025-08-12 09:12:49,908[DEBUG] optimize site: [7, 8]
2025-08-12 09:12:50,000[DEBUG] use davidson, HC hops: 44
2025-08-12 09:12:50,001[DEBUG] energy: -4.583593477927389
2025-08-12 09:12:50,005[DEBUG] optimize site: [8, 9]
2025-08-12 09:12:50,116[DEBUG] use davidson, HC hops: 55
2025-08-12 09:12:50,118[DEBUG] energy: -4.968031845671203
2025-08-12 09:12:50,123[DEBUG] optimize site: [9, 10]
2025-08-12 09:12:50,256[DEBUG] use davidson, HC hops: 68
2025-08-12 09:12:50,258[DEBUG] energy: -5.414706360833991
2025-08-12 09:12:50,262[DEBUG] optimize site: [10, 11]
2025-08-12 09:12:50,410[DEBUG] use davidson, HC hops: 72
2025-08-12 09:12:50,412[DEBUG] energy: -5.856529754520476
2025-08-12 09:12:50,416[DEBUG] optimize site: [11, 12]
2025-08-12 09:12:50,612[DEBUG] use davidson, HC hops: 100
2025-08-12 09:12:50,614[DEBUG] energy: -6.279022467295811
2025-08-12 09:12:50,619[DEBUG] optimize site: [12, 13]
2025-08-12 09:12:50,722[DEBUG] use davidson, HC hops: 52
2025-08-12 09:12:50,724[DEBUG] energy: -6.8573890122047585
2025-08-12 09:12:50,728[DEBUG] optimize site: [13, 14]
2025-08-12 09:12:50,925[DEBUG] use davidson, HC hops: 100
2025-08-12 09:12:50,927[DEBUG] energy: -7.114588022005776
2025-08-12 09:12:50,931[DEBUG] optimize site: [14, 15]
2025-08-12 09:12:51,026[DEBUG] use davidson, HC hops: 47
2025-08-12 09:12:51,027[DEBUG] energy: -7.641631783835413
2025-08-12 09:12:51,031[DEBUG] optimize site: [15, 16]
2025-08-12 09:12:51,134[DEBUG] use davidson, HC hops: 51
2025-08-12 09:12:51,135[DEBUG] energy: -8.118395338420047
2025-08-12 09:12:51,140[DEBUG] optimize site: [16, 17]
2025-08-12 09:12:51,253[DEBUG] use davidson, HC hops: 57
2025-08-12 09:12:51,254[DEBUG] energy: -8.579533430762854
2025-08-12 09:12:51,259[DEBUG] optimize site: [17, 18]
2025-08-12 09:12:51,389[DEBUG] use davidson, HC hops: 66
2025-08-12 09:12:51,391[DEBUG] energy: -8.983113190158468
2025-08-12 09:12:51,395[DEBUG] optimize site: [18, 19]
2025-08-12 09:12:51,520[DEBUG] use davidson, HC hops: 62
2025-08-12 09:12:51,522[DEBUG] energy: -9.42220540460768
2025-08-12 09:12:51,526[DEBUG] optimize site: [19, 20]
2025-08-12 09:12:51,649[DEBUG] use davidson, HC hops: 62
2025-08-12 09:12:51,651[DEBUG] energy: -9.903693680914412
2025-08-12 09:12:51,655[DEBUG] optimize site: [20, 21]
2025-08-12 09:12:51,814[DEBUG] use davidson, HC hops: 81
2025-08-12 09:12:51,816[DEBUG] energy: -10.398530611697996
2025-08-12 09:12:51,822[DEBUG] optimize site: [21, 22]
2025-08-12 09:12:51,971[DEBUG] use davidson, HC hops: 76
2025-08-12 09:12:51,974[DEBUG] energy: -10.834489434421702
2025-08-12 09:12:51,978[DEBUG] optimize site: [22, 23]
2025-08-12 09:12:52,095[DEBUG] use davidson, HC hops: 58
2025-08-12 09:12:52,097[DEBUG] energy: -11.415128707126835
2025-08-12 09:12:52,103[DEBUG] optimize site: [23, 24]
2025-08-12 09:12:52,207[DEBUG] use davidson, HC hops: 52
2025-08-12 09:12:52,209[DEBUG] energy: -12.12279587974508
2025-08-12 09:12:52,214[DEBUG] optimize site: [24, 25]
2025-08-12 09:12:52,353[DEBUG] use davidson, HC hops: 71
2025-08-12 09:12:52,355[DEBUG] energy: -12.812234874023524
2025-08-12 09:12:52,361[DEBUG] optimize site: [25, 26]
2025-08-12 09:12:52,477[DEBUG] use davidson, HC hops: 58
2025-08-12 09:12:52,478[DEBUG] energy: -13.774582804126698
2025-08-12 09:12:52,484[DEBUG] optimize site: [26, 27]
2025-08-12 09:12:52,563[DEBUG] use davidson, HC hops: 47
2025-08-12 09:12:52,566[DEBUG] energy: -13.996832655813119
2025-08-12 09:12:52,568[DEBUG] optimize site: [27, 28]
2025-08-12 09:12:52,573[DEBUG] use direct eigensolver
2025-08-12 09:12:52,835[DEBUG] energy: -13.996832655534053
2025-08-12 09:12:52,838[DEBUG] optimize site: [28, 29]
2025-08-12 09:12:52,844[DEBUG] use direct eigensolver
2025-08-12 09:12:52,921[DEBUG] energy: -13.996832655534046
2025-08-12 09:12:52,924[DEBUG] optimize site: [29, 30]
2025-08-12 09:12:52,929[DEBUG] use direct eigensolver
2025-08-12 09:12:52,939[DEBUG] energy: -13.996832655534043
2025-08-12 09:12:52,942[DEBUG] optimize site: [30, 31]
2025-08-12 09:12:52,946[DEBUG] use direct eigensolver
2025-08-12 09:12:52,951[DEBUG] energy: -13.99683265553406
2025-08-12 09:12:52,954[DEBUG] 1 sweeps are finished, lowest energy = -13.996832655813119
2025-08-12 09:12:52,958[DEBUG] isweep: 1
2025-08-12 09:12:52,959[DEBUG] compress config in current loop: 30, percent: 0
2025-08-12 09:12:52,960[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]
2025-08-12 09:12:52,963[DEBUG] optimize site: [30, 31]
2025-08-12 09:12:52,964[DEBUG] use direct eigensolver
2025-08-12 09:12:52,968[DEBUG] energy: -13.99683265553406
2025-08-12 09:12:52,971[DEBUG] optimize site: [29, 30]
2025-08-12 09:12:52,973[DEBUG] use direct eigensolver
2025-08-12 09:12:52,978[DEBUG] energy: -13.99683265553406
2025-08-12 09:12:52,983[DEBUG] optimize site: [28, 29]
2025-08-12 09:12:52,983[DEBUG] use direct eigensolver
2025-08-12 09:12:53,056[DEBUG] energy: -13.99683265553405
2025-08-12 09:12:53,058[DEBUG] optimize site: [27, 28]
2025-08-12 09:12:53,063[DEBUG] use direct eigensolver
2025-08-12 09:12:53,322[DEBUG] energy: -13.996832655534051
2025-08-12 09:12:53,326[DEBUG] optimize site: [26, 27]
2025-08-12 09:12:53,336[DEBUG] use davidson, HC hops: 4
2025-08-12 09:12:53,339[DEBUG] energy: -13.996832655813677
2025-08-12 09:12:53,342[DEBUG] optimize site: [25, 26]
2025-08-12 09:12:53,395[DEBUG] use davidson, HC hops: 22
2025-08-12 09:12:53,397[DEBUG] energy: -13.996844945038404
2025-08-12 09:12:53,402[DEBUG] optimize site: [24, 25]
2025-08-12 09:12:53,459[DEBUG] use davidson, HC hops: 28
2025-08-12 09:12:53,461[DEBUG] energy: -13.997067101658807
2025-08-12 09:12:53,466[DEBUG] optimize site: [23, 24]
2025-08-12 09:12:53,519[DEBUG] use davidson, HC hops: 25
2025-08-12 09:12:53,521[DEBUG] energy: -13.997101684717586
2025-08-12 09:12:53,526[DEBUG] optimize site: [22, 23]
2025-08-12 09:12:53,576[DEBUG] use davidson, HC hops: 23
2025-08-12 09:12:53,578[DEBUG] energy: -13.997106608213805
2025-08-12 09:12:53,583[DEBUG] optimize site: [21, 22]
2025-08-12 09:12:53,632[DEBUG] use davidson, HC hops: 23
2025-08-12 09:12:53,635[DEBUG] energy: -13.997113698271237
2025-08-12 09:12:53,639[DEBUG] optimize site: [20, 21]
2025-08-12 09:12:53,695[DEBUG] use davidson, HC hops: 26
2025-08-12 09:12:53,696[DEBUG] energy: -13.997162638323656
2025-08-12 09:12:53,702[DEBUG] optimize site: [19, 20]
2025-08-12 09:12:53,751[DEBUG] use davidson, HC hops: 23
2025-08-12 09:12:53,752[DEBUG] energy: -13.997170144965654
2025-08-12 09:12:53,758[DEBUG] optimize site: [18, 19]
2025-08-12 09:12:53,812[DEBUG] use davidson, HC hops: 26
2025-08-12 09:12:53,814[DEBUG] energy: -13.997199975427524
2025-08-12 09:12:53,820[DEBUG] optimize site: [17, 18]
2025-08-12 09:12:53,867[DEBUG] use davidson, HC hops: 22
2025-08-12 09:12:53,869[DEBUG] energy: -13.997204392621713
2025-08-12 09:12:53,875[DEBUG] optimize site: [16, 17]
2025-08-12 09:12:53,928[DEBUG] use davidson, HC hops: 25
2025-08-12 09:12:53,931[DEBUG] energy: -13.997225037523883
2025-08-12 09:12:53,936[DEBUG] optimize site: [15, 16]
2025-08-12 09:12:53,993[DEBUG] use davidson, HC hops: 26
2025-08-12 09:12:53,995[DEBUG] energy: -13.997284918121249
2025-08-12 09:12:54,001[DEBUG] optimize site: [14, 15]
2025-08-12 09:12:54,050[DEBUG] use davidson, HC hops: 22
2025-08-12 09:12:54,054[DEBUG] energy: -13.997290859971327
2025-08-12 09:12:54,060[DEBUG] optimize site: [13, 14]
2025-08-12 09:12:54,105[DEBUG] use davidson, HC hops: 20
2025-08-12 09:12:54,108[DEBUG] energy: -13.99729325765387
2025-08-12 09:12:54,113[DEBUG] optimize site: [12, 13]
2025-08-12 09:12:54,164[DEBUG] use davidson, HC hops: 23
2025-08-12 09:12:54,166[DEBUG] energy: -13.997306225086737
2025-08-12 09:12:54,173[DEBUG] optimize site: [11, 12]
2025-08-12 09:12:54,221[DEBUG] use davidson, HC hops: 21
2025-08-12 09:12:54,223[DEBUG] energy: -13.997311145595692
2025-08-12 09:12:54,229[DEBUG] optimize site: [10, 11]
2025-08-12 09:12:54,272[DEBUG] use davidson, HC hops: 20
2025-08-12 09:12:54,274[DEBUG] energy: -13.997313132707575
2025-08-12 09:12:54,279[DEBUG] optimize site: [9, 10]
2025-08-12 09:12:54,322[DEBUG] use davidson, HC hops: 17
2025-08-12 09:12:54,323[DEBUG] energy: -13.997314428626446
2025-08-12 09:12:54,329[DEBUG] optimize site: [8, 9]
2025-08-12 09:12:54,354[DEBUG] use davidson, HC hops: 11
2025-08-12 09:12:54,356[DEBUG] energy: -13.997314715468745
2025-08-12 09:12:54,360[DEBUG] optimize site: [7, 8]
2025-08-12 09:12:54,378[DEBUG] use davidson, HC hops: 7
2025-08-12 09:12:54,379[DEBUG] energy: -13.99731471266984
2025-08-12 09:12:54,384[DEBUG] optimize site: [6, 7]
2025-08-12 09:12:54,412[DEBUG] use davidson, HC hops: 12
2025-08-12 09:12:54,413[DEBUG] energy: -13.997314999750078
2025-08-12 09:12:54,417[DEBUG] optimize site: [5, 6]
2025-08-12 09:12:54,435[DEBUG] use davidson, HC hops: 7
2025-08-12 09:12:54,436[DEBUG] energy: -13.997315003811531
2025-08-12 09:12:54,440[DEBUG] optimize site: [4, 5]
2025-08-12 09:12:54,452[DEBUG] use davidson, HC hops: 5
2025-08-12 09:12:54,454[DEBUG] energy: -13.997315004767854
2025-08-12 09:12:54,456[DEBUG] optimize site: [3, 4]
2025-08-12 09:12:54,459[DEBUG] use direct eigensolver
2025-08-12 09:12:54,727[DEBUG] energy: -13.997315004467163
2025-08-12 09:12:54,729[DEBUG] optimize site: [2, 3]
2025-08-12 09:12:54,731[DEBUG] use direct eigensolver
2025-08-12 09:12:54,808[DEBUG] energy: -13.997315004467143
2025-08-12 09:12:54,811[DEBUG] optimize site: [1, 2]
2025-08-12 09:12:54,814[DEBUG] use direct eigensolver
2025-08-12 09:12:54,823[DEBUG] energy: -13.997315004467133
2025-08-12 09:12:54,824[DEBUG] optimize site: [0, 1]
2025-08-12 09:12:54,827[DEBUG] use direct eigensolver
2025-08-12 09:12:54,830[DEBUG] energy: -13.99731500446714
2025-08-12 09:12:54,832[DEBUG] 2 sweeps are finished, lowest energy = -13.997315004767854
2025-08-12 09:12:54,834[DEBUG] isweep: 2
2025-08-12 09:12:54,835[DEBUG] compress config in current loop: 30, percent: 0
2025-08-12 09:12:54,837[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]
2025-08-12 09:12:54,838[DEBUG] optimize site: [0, 1]
2025-08-12 09:12:54,839[DEBUG] use direct eigensolver
2025-08-12 09:12:54,843[DEBUG] energy: -13.99731500446714
2025-08-12 09:12:54,844[DEBUG] optimize site: [1, 2]
2025-08-12 09:12:54,846[DEBUG] use direct eigensolver
2025-08-12 09:12:54,850[DEBUG] energy: -13.997315004467143
2025-08-12 09:12:54,851[DEBUG] optimize site: [2, 3]
2025-08-12 09:12:54,853[DEBUG] use direct eigensolver
2025-08-12 09:12:54,925[DEBUG] energy: -13.997315004467143
2025-08-12 09:12:54,927[DEBUG] optimize site: [3, 4]
2025-08-12 09:12:54,932[DEBUG] use direct eigensolver
2025-08-12 09:12:55,195[DEBUG] energy: -13.997315004467163
2025-08-12 09:12:55,197[DEBUG] optimize site: [4, 5]
2025-08-12 09:12:55,209[DEBUG] use davidson, HC hops: 4
2025-08-12 09:12:55,210[DEBUG] energy: -13.997315004767929
2025-08-12 09:12:55,218[DEBUG] optimize site: [5, 6]
2025-08-12 09:12:55,231[DEBUG] use davidson, HC hops: 4
2025-08-12 09:12:55,232[DEBUG] energy: -13.99731500466783
2025-08-12 09:12:55,236[DEBUG] optimize site: [6, 7]
2025-08-12 09:12:55,253[DEBUG] use davidson, HC hops: 6
2025-08-12 09:12:55,254[DEBUG] energy: -13.997315012470711
2025-08-12 09:12:55,259[DEBUG] optimize site: [7, 8]
2025-08-12 09:12:55,273[DEBUG] use davidson, HC hops: 5
2025-08-12 09:12:55,275[DEBUG] energy: -13.99731500606673
2025-08-12 09:12:55,279[DEBUG] optimize site: [8, 9]
2025-08-12 09:12:55,297[DEBUG] use davidson, HC hops: 7
2025-08-12 09:12:55,299[DEBUG] energy: -13.997315033374592
2025-08-12 09:12:55,304[DEBUG] optimize site: [9, 10]
2025-08-12 09:12:55,319[DEBUG] use davidson, HC hops: 6
2025-08-12 09:12:55,320[DEBUG] energy: -13.997315010122026
2025-08-12 09:12:55,325[DEBUG] optimize site: [10, 11]
2025-08-12 09:12:55,346[DEBUG] use davidson, HC hops: 8
2025-08-12 09:12:55,347[DEBUG] energy: -13.997315055776962
2025-08-12 09:12:55,352[DEBUG] optimize site: [11, 12]
2025-08-12 09:12:55,369[DEBUG] use davidson, HC hops: 7
2025-08-12 09:12:55,370[DEBUG] energy: -13.997315015890555
2025-08-12 09:12:55,374[DEBUG] optimize site: [12, 13]
2025-08-12 09:12:55,386[DEBUG] use davidson, HC hops: 8
2025-08-12 09:12:55,386[DEBUG] energy: -13.997315076759467
2025-08-12 09:12:55,391[DEBUG] optimize site: [13, 14]
2025-08-12 09:12:55,401[DEBUG] use davidson, HC hops: 7
2025-08-12 09:12:55,402[DEBUG] energy: -13.997315021063859
2025-08-12 09:12:55,406[DEBUG] optimize site: [14, 15]
2025-08-12 09:12:55,417[DEBUG] use davidson, HC hops: 8
2025-08-12 09:12:55,419[DEBUG] energy: -13.997315089163566
2025-08-12 09:12:55,423[DEBUG] optimize site: [15, 16]
2025-08-12 09:12:55,435[DEBUG] use davidson, HC hops: 8
2025-08-12 09:12:55,437[DEBUG] energy: -13.997315023237807
2025-08-12 09:12:55,440[DEBUG] optimize site: [16, 17]
2025-08-12 09:12:55,457[DEBUG] use davidson, HC hops: 9
2025-08-12 09:12:55,459[DEBUG] energy: -13.997315090211718
2025-08-12 09:12:55,465[DEBUG] optimize site: [17, 18]
2025-08-12 09:12:55,486[DEBUG] use davidson, HC hops: 8
2025-08-12 09:12:55,487[DEBUG] energy: -13.997315022014341
2025-08-12 09:12:55,494[DEBUG] optimize site: [18, 19]
2025-08-12 09:12:55,515[DEBUG] use davidson, HC hops: 8
2025-08-12 09:12:55,518[DEBUG] energy: -13.997315079212626
2025-08-12 09:12:55,523[DEBUG] optimize site: [19, 20]
2025-08-12 09:12:55,541[DEBUG] use davidson, HC hops: 7
2025-08-12 09:12:55,544[DEBUG] energy: -13.99731501838978
2025-08-12 09:12:55,549[DEBUG] optimize site: [20, 21]
2025-08-12 09:12:55,570[DEBUG] use davidson, HC hops: 8
2025-08-12 09:12:55,572[DEBUG] energy: -13.997315060471667
2025-08-12 09:12:55,576[DEBUG] optimize site: [21, 22]
2025-08-12 09:12:55,586[DEBUG] use davidson, HC hops: 6
2025-08-12 09:12:55,589[DEBUG] energy: -13.99731501422307
2025-08-12 09:12:55,592[DEBUG] optimize site: [22, 23]
2025-08-12 09:12:55,605[DEBUG] use davidson, HC hops: 8
2025-08-12 09:12:55,607[DEBUG] energy: -13.997315036380842
2025-08-12 09:12:55,612[DEBUG] optimize site: [23, 24]
2025-08-12 09:12:55,629[DEBUG] use davidson, HC hops: 6
2025-08-12 09:12:55,631[DEBUG] energy: -13.997315009063412
2025-08-12 09:12:55,636[DEBUG] optimize site: [24, 25]
2025-08-12 09:12:55,652[DEBUG] use davidson, HC hops: 6
2025-08-12 09:12:55,653[DEBUG] energy: -13.99731501543188
2025-08-12 09:12:55,659[DEBUG] optimize site: [25, 26]
2025-08-12 09:12:55,673[DEBUG] use davidson, HC hops: 5
2025-08-12 09:12:55,676[DEBUG] energy: -13.997315007630561
2025-08-12 09:12:55,681[DEBUG] optimize site: [26, 27]
2025-08-12 09:12:55,692[DEBUG] use davidson, HC hops: 4
2025-08-12 09:12:55,694[DEBUG] energy: -13.997315007727543
2025-08-12 09:12:55,695[DEBUG] optimize site: [27, 28]
2025-08-12 09:12:55,699[DEBUG] use direct eigensolver
2025-08-12 09:12:55,961[DEBUG] energy: -13.997315007427511
2025-08-12 09:12:55,963[DEBUG] optimize site: [28, 29]
2025-08-12 09:12:55,965[DEBUG] use direct eigensolver
2025-08-12 09:12:56,029[DEBUG] energy: -13.997315007427506
2025-08-12 09:12:56,033[DEBUG] optimize site: [29, 30]
2025-08-12 09:12:56,034[DEBUG] use direct eigensolver
2025-08-12 09:12:56,040[DEBUG] energy: -13.997315007427517
2025-08-12 09:12:56,042[DEBUG] optimize site: [30, 31]
2025-08-12 09:12:56,044[DEBUG] use direct eigensolver
2025-08-12 09:12:56,047[DEBUG] energy: -13.997315007427506
2025-08-12 09:12:56,049[DEBUG] 3 sweeps are finished, lowest energy = -13.997315090211718
2025-08-12 09:12:56,051[INFO] DMRG has converged!
2025-08-12 09:12:56,086[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: -13.997315090211718

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