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

2025-05-13 23:55:52,330[INFO] Use NumPy as backend
2025-05-13 23:55:52,331[INFO] numpy random seed is 9012
2025-05-13 23:55:52,332[INFO] random seed is 1092
2025-05-13 23:55:52,341[INFO] Git Commit Hash: c7642c8c4a7ac79dfcc3457812be9d846ab9e2a8
2025-05-13 23:55:52,342[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}")

2025-05-13 23:55:52,440[DEBUG] # of operator terms: 93
2025-05-13 23:55:52,440[DEBUG] Input operator terms: 93
2025-05-13 23:55:52,442[DEBUG] After combination of the same terms: 93
2025-05-13 23:55:52,443[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
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))

2025-05-13 23:55:52,514[INFO] optimization method: 2site
2025-05-13 23:55:52,515[INFO] e_rtol: 1e-06
2025-05-13 23:55:52,517[INFO] e_atol: 1e-08
2025-05-13 23:55:52,518[INFO] procedure: [[30, 0.2], [30, 0], [30, 0], [30, 0], [30, 0]]
2025-05-13 23:55:52,545[DEBUG] isweep: 0
2025-05-13 23:55:52,547[DEBUG] compress config in current loop: 30, percent: 0.2
2025-05-13 23:55:52,549[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]
2025-05-13 23:55:52,550[DEBUG] optimize site: [0, 1]
2025-05-13 23:55:52,551[DEBUG] use direct eigensolver
2025-05-13 23:55:52,554[DEBUG] energy: -0.927999022689833
2025-05-13 23:55:52,557[DEBUG] optimize site: [1, 2]
2025-05-13 23:55:52,560[DEBUG] use direct eigensolver
2025-05-13 23:55:52,563[DEBUG] energy: -1.284089573410534
2025-05-13 23:55:52,564[DEBUG] optimize site: [2, 3]
2025-05-13 23:55:52,567[DEBUG] use direct eigensolver
2025-05-13 23:55:52,583[DEBUG] energy: -2.08574526474992
2025-05-13 23:55:52,585[DEBUG] optimize site: [3, 4]
2025-05-13 23:55:52,587[DEBUG] use direct eigensolver
2025-05-13 23:55:52,826[DEBUG] energy: -2.815889527237408
2025-05-13 23:55:52,830[DEBUG] optimize site: [4, 5]
2025-05-13 23:55:52,861[DEBUG] use davidson, HC hops: 34
2025-05-13 23:55:52,862[DEBUG] energy: -3.293367315585799
2025-05-13 23:55:52,865[DEBUG] optimize site: [5, 6]
2025-05-13 23:55:52,917[DEBUG] use davidson, HC hops: 42
2025-05-13 23:55:52,919[DEBUG] energy: -3.7449867503072003
2025-05-13 23:55:52,924[DEBUG] optimize site: [6, 7]
2025-05-13 23:55:53,040[DEBUG] use davidson, HC hops: 42
2025-05-13 23:55:53,041[DEBUG] energy: -4.1763855754964885
2025-05-13 23:55:53,047[DEBUG] optimize site: [7, 8]
2025-05-13 23:55:53,155[DEBUG] use davidson, HC hops: 44
2025-05-13 23:55:53,156[DEBUG] energy: -4.583593477927385
2025-05-13 23:55:53,160[DEBUG] optimize site: [8, 9]
2025-05-13 23:55:53,273[DEBUG] use davidson, HC hops: 55
2025-05-13 23:55:53,275[DEBUG] energy: -4.968031845671196
2025-05-13 23:55:53,279[DEBUG] optimize site: [9, 10]
2025-05-13 23:55:53,419[DEBUG] use davidson, HC hops: 68
2025-05-13 23:55:53,420[DEBUG] energy: -5.41470636083398
2025-05-13 23:55:53,425[DEBUG] optimize site: [10, 11]
2025-05-13 23:55:53,565[DEBUG] use davidson, HC hops: 72
2025-05-13 23:55:53,566[DEBUG] energy: -5.856529754520466
2025-05-13 23:55:53,571[DEBUG] optimize site: [11, 12]
2025-05-13 23:55:53,791[DEBUG] use davidson, HC hops: 100
2025-05-13 23:55:53,793[DEBUG] energy: -6.2790224672958
2025-05-13 23:55:53,798[DEBUG] optimize site: [12, 13]
2025-05-13 23:55:53,901[DEBUG] use davidson, HC hops: 52
2025-05-13 23:55:53,903[DEBUG] energy: -6.857389012204761
2025-05-13 23:55:53,909[DEBUG] optimize site: [13, 14]
2025-05-13 23:55:54,110[DEBUG] use davidson, HC hops: 100
2025-05-13 23:55:54,112[DEBUG] energy: -7.114588022005771
2025-05-13 23:55:54,119[DEBUG] optimize site: [14, 15]
2025-05-13 23:55:54,217[DEBUG] use davidson, HC hops: 47
2025-05-13 23:55:54,218[DEBUG] energy: -7.641631783835409
2025-05-13 23:55:54,224[DEBUG] optimize site: [15, 16]
2025-05-13 23:55:54,333[DEBUG] use davidson, HC hops: 51
2025-05-13 23:55:54,335[DEBUG] energy: -8.11839533842004
2025-05-13 23:55:54,340[DEBUG] optimize site: [16, 17]
2025-05-13 23:55:54,458[DEBUG] use davidson, HC hops: 57
2025-05-13 23:55:54,459[DEBUG] energy: -8.579533430762847
2025-05-13 23:55:54,463[DEBUG] optimize site: [17, 18]
2025-05-13 23:55:54,601[DEBUG] use davidson, HC hops: 66
2025-05-13 23:55:54,602[DEBUG] energy: -8.983113190158459
2025-05-13 23:55:54,608[DEBUG] optimize site: [18, 19]
2025-05-13 23:55:54,736[DEBUG] use davidson, HC hops: 62
2025-05-13 23:55:54,737[DEBUG] energy: -9.422205404607647
2025-05-13 23:55:54,742[DEBUG] optimize site: [19, 20]
2025-05-13 23:55:54,871[DEBUG] use davidson, HC hops: 62
2025-05-13 23:55:54,872[DEBUG] energy: -9.903693680914389
2025-05-13 23:55:54,878[DEBUG] optimize site: [20, 21]
2025-05-13 23:55:55,042[DEBUG] use davidson, HC hops: 81
2025-05-13 23:55:55,043[DEBUG] energy: -10.398530611697973
2025-05-13 23:55:55,047[DEBUG] optimize site: [21, 22]
2025-05-13 23:55:55,202[DEBUG] use davidson, HC hops: 76
2025-05-13 23:55:55,204[DEBUG] energy: -10.834489434421682
2025-05-13 23:55:55,210[DEBUG] optimize site: [22, 23]
2025-05-13 23:55:55,328[DEBUG] use davidson, HC hops: 58
2025-05-13 23:55:55,329[DEBUG] energy: -11.4151287071268
2025-05-13 23:55:55,335[DEBUG] optimize site: [23, 24]
2025-05-13 23:55:55,439[DEBUG] use davidson, HC hops: 52
2025-05-13 23:55:55,441[DEBUG] energy: -12.122795879745048
2025-05-13 23:55:55,445[DEBUG] optimize site: [24, 25]
2025-05-13 23:55:55,591[DEBUG] use davidson, HC hops: 71
2025-05-13 23:55:55,593[DEBUG] energy: -12.812234874023506
2025-05-13 23:55:55,597[DEBUG] optimize site: [25, 26]
2025-05-13 23:55:55,715[DEBUG] use davidson, HC hops: 58
2025-05-13 23:55:55,716[DEBUG] energy: -13.774582804126702
2025-05-13 23:55:55,720[DEBUG] optimize site: [26, 27]
2025-05-13 23:55:55,795[DEBUG] use davidson, HC hops: 47
2025-05-13 23:55:55,796[DEBUG] energy: -13.996832655813115
2025-05-13 23:55:55,798[DEBUG] optimize site: [27, 28]
2025-05-13 23:55:55,801[DEBUG] use direct eigensolver
2025-05-13 23:55:56,067[DEBUG] energy: -13.996832655534062
2025-05-13 23:55:56,069[DEBUG] optimize site: [28, 29]
2025-05-13 23:55:56,072[DEBUG] use direct eigensolver
2025-05-13 23:55:56,122[DEBUG] energy: -13.996832655534039
2025-05-13 23:55:56,125[DEBUG] optimize site: [29, 30]
2025-05-13 23:55:56,126[DEBUG] use direct eigensolver
2025-05-13 23:55:56,131[DEBUG] energy: -13.996832655534046
2025-05-13 23:55:56,132[DEBUG] optimize site: [30, 31]
2025-05-13 23:55:56,134[DEBUG] use direct eigensolver
2025-05-13 23:55:56,136[DEBUG] energy: -13.996832655534046
2025-05-13 23:55:56,137[DEBUG] 1 sweeps are finished, lowest energy = -13.996832655813115
2025-05-13 23:55:56,137[DEBUG] isweep: 1
2025-05-13 23:55:56,138[DEBUG] compress config in current loop: 30, percent: 0
2025-05-13 23:55:56,139[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]
2025-05-13 23:55:56,140[DEBUG] optimize site: [30, 31]
2025-05-13 23:55:56,141[DEBUG] use direct eigensolver
2025-05-13 23:55:56,143[DEBUG] energy: -13.996832655534046
2025-05-13 23:55:56,144[DEBUG] optimize site: [29, 30]
2025-05-13 23:55:56,145[DEBUG] use direct eigensolver
2025-05-13 23:55:56,157[DEBUG] energy: -13.99683265553405
2025-05-13 23:55:56,159[DEBUG] optimize site: [28, 29]
2025-05-13 23:55:56,161[DEBUG] use direct eigensolver
2025-05-13 23:55:56,211[DEBUG] energy: -13.996832655534053
2025-05-13 23:55:56,213[DEBUG] optimize site: [27, 28]
2025-05-13 23:55:56,214[DEBUG] use direct eigensolver
2025-05-13 23:55:56,460[DEBUG] energy: -13.996832655534055
2025-05-13 23:55:56,462[DEBUG] optimize site: [26, 27]
2025-05-13 23:55:56,471[DEBUG] use davidson, HC hops: 4
2025-05-13 23:55:56,472[DEBUG] energy: -13.996832655813687
2025-05-13 23:55:56,479[DEBUG] optimize site: [25, 26]
2025-05-13 23:55:56,527[DEBUG] use davidson, HC hops: 22
2025-05-13 23:55:56,528[DEBUG] energy: -13.996844945038404
2025-05-13 23:55:56,531[DEBUG] optimize site: [24, 25]
2025-05-13 23:55:56,563[DEBUG] use davidson, HC hops: 28
2025-05-13 23:55:56,565[DEBUG] energy: -13.99706710165879
2025-05-13 23:55:56,568[DEBUG] optimize site: [23, 24]
2025-05-13 23:55:56,604[DEBUG] use davidson, HC hops: 25
2025-05-13 23:55:56,605[DEBUG] energy: -13.997101684717524
2025-05-13 23:55:56,611[DEBUG] optimize site: [22, 23]
2025-05-13 23:55:56,659[DEBUG] use davidson, HC hops: 23
2025-05-13 23:55:56,660[DEBUG] energy: -13.997106608213704
2025-05-13 23:55:56,666[DEBUG] optimize site: [21, 22]
2025-05-13 23:55:56,715[DEBUG] use davidson, HC hops: 23
2025-05-13 23:55:56,717[DEBUG] energy: -13.997113698271145
2025-05-13 23:55:56,720[DEBUG] optimize site: [20, 21]
2025-05-13 23:55:56,751[DEBUG] use davidson, HC hops: 26
2025-05-13 23:55:56,753[DEBUG] energy: -13.997162638323559
2025-05-13 23:55:56,756[DEBUG] optimize site: [19, 20]
2025-05-13 23:55:56,788[DEBUG] use davidson, HC hops: 23
2025-05-13 23:55:56,790[DEBUG] energy: -13.997170144965558
2025-05-13 23:55:56,795[DEBUG] optimize site: [18, 19]
2025-05-13 23:55:56,849[DEBUG] use davidson, HC hops: 26
2025-05-13 23:55:56,851[DEBUG] energy: -13.997199975427414
2025-05-13 23:55:56,856[DEBUG] optimize site: [17, 18]
2025-05-13 23:55:56,903[DEBUG] use davidson, HC hops: 22
2025-05-13 23:55:56,905[DEBUG] energy: -13.997204392621619
2025-05-13 23:55:56,908[DEBUG] optimize site: [16, 17]
2025-05-13 23:55:56,938[DEBUG] use davidson, HC hops: 25
2025-05-13 23:55:56,938[DEBUG] energy: -13.997225037523808
2025-05-13 23:55:56,943[DEBUG] optimize site: [15, 16]
2025-05-13 23:55:56,981[DEBUG] use davidson, HC hops: 26
2025-05-13 23:55:56,983[DEBUG] energy: -13.997284918121153
2025-05-13 23:55:56,987[DEBUG] optimize site: [14, 15]
2025-05-13 23:55:57,034[DEBUG] use davidson, HC hops: 22
2025-05-13 23:55:57,036[DEBUG] energy: -13.99729085997124
2025-05-13 23:55:57,041[DEBUG] optimize site: [13, 14]
2025-05-13 23:55:57,083[DEBUG] use davidson, HC hops: 20
2025-05-13 23:55:57,084[DEBUG] energy: -13.997293257653777
2025-05-13 23:55:57,089[DEBUG] optimize site: [12, 13]
2025-05-13 23:55:57,118[DEBUG] use davidson, HC hops: 23
2025-05-13 23:55:57,118[DEBUG] energy: -13.99730622508664
2025-05-13 23:55:57,123[DEBUG] optimize site: [11, 12]
2025-05-13 23:55:57,148[DEBUG] use davidson, HC hops: 21
2025-05-13 23:55:57,149[DEBUG] energy: -13.99731114559556
2025-05-13 23:55:57,153[DEBUG] optimize site: [10, 11]
2025-05-13 23:55:57,177[DEBUG] use davidson, HC hops: 20
2025-05-13 23:55:57,179[DEBUG] energy: -13.99731313270745
2025-05-13 23:55:57,182[DEBUG] optimize site: [9, 10]
2025-05-13 23:55:57,203[DEBUG] use davidson, HC hops: 17
2025-05-13 23:55:57,203[DEBUG] energy: -13.997314428626325
2025-05-13 23:55:57,207[DEBUG] optimize site: [8, 9]
2025-05-13 23:55:57,222[DEBUG] use davidson, HC hops: 11
2025-05-13 23:55:57,224[DEBUG] energy: -13.997314715468633
2025-05-13 23:55:57,227[DEBUG] optimize site: [7, 8]
2025-05-13 23:55:57,237[DEBUG] use davidson, HC hops: 7
2025-05-13 23:55:57,238[DEBUG] energy: -13.99731471266975
2025-05-13 23:55:57,242[DEBUG] optimize site: [6, 7]
2025-05-13 23:55:57,258[DEBUG] use davidson, HC hops: 12
2025-05-13 23:55:57,260[DEBUG] energy: -13.997314999749996
2025-05-13 23:55:57,263[DEBUG] optimize site: [5, 6]
2025-05-13 23:55:57,274[DEBUG] use davidson, HC hops: 7
2025-05-13 23:55:57,275[DEBUG] energy: -13.997315003811432
2025-05-13 23:55:57,279[DEBUG] optimize site: [4, 5]
2025-05-13 23:55:57,286[DEBUG] use davidson, HC hops: 5
2025-05-13 23:55:57,288[DEBUG] energy: -13.997315004767755
2025-05-13 23:55:57,289[DEBUG] optimize site: [3, 4]
2025-05-13 23:55:57,291[DEBUG] use direct eigensolver
2025-05-13 23:55:57,552[DEBUG] energy: -13.997315004467058
2025-05-13 23:55:57,554[DEBUG] optimize site: [2, 3]
2025-05-13 23:55:57,557[DEBUG] use direct eigensolver
2025-05-13 23:55:57,605[DEBUG] energy: -13.997315004467055
2025-05-13 23:55:57,608[DEBUG] optimize site: [1, 2]
2025-05-13 23:55:57,610[DEBUG] use direct eigensolver
2025-05-13 23:55:57,616[DEBUG] energy: -13.99731500446705
2025-05-13 23:55:57,618[DEBUG] optimize site: [0, 1]
2025-05-13 23:55:57,620[DEBUG] use direct eigensolver
2025-05-13 23:55:57,623[DEBUG] energy: -13.99731500446704
2025-05-13 23:55:57,625[DEBUG] 2 sweeps are finished, lowest energy = -13.997315004767755
2025-05-13 23:55:57,626[DEBUG] isweep: 2
2025-05-13 23:55:57,628[DEBUG] compress config in current loop: 30, percent: 0
2025-05-13 23:55:57,629[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]
2025-05-13 23:55:57,631[DEBUG] optimize site: [0, 1]
2025-05-13 23:55:57,633[DEBUG] use direct eigensolver
2025-05-13 23:55:57,636[DEBUG] energy: -13.99731500446704
2025-05-13 23:55:57,638[DEBUG] optimize site: [1, 2]
2025-05-13 23:55:57,640[DEBUG] use direct eigensolver
2025-05-13 23:55:57,645[DEBUG] energy: -13.997315004467044
2025-05-13 23:55:57,648[DEBUG] optimize site: [2, 3]
2025-05-13 23:55:57,649[DEBUG] use direct eigensolver
2025-05-13 23:55:57,695[DEBUG] energy: -13.997315004467051
2025-05-13 23:55:57,697[DEBUG] optimize site: [3, 4]
2025-05-13 23:55:57,700[DEBUG] use direct eigensolver
2025-05-13 23:55:57,953[DEBUG] energy: -13.997315004467069
2025-05-13 23:55:57,955[DEBUG] optimize site: [4, 5]
2025-05-13 23:55:57,963[DEBUG] use davidson, HC hops: 4
2025-05-13 23:55:57,963[DEBUG] energy: -13.997315004767824
2025-05-13 23:55:57,967[DEBUG] optimize site: [5, 6]
2025-05-13 23:55:57,976[DEBUG] use davidson, HC hops: 4
2025-05-13 23:55:57,978[DEBUG] energy: -13.997315004667728
2025-05-13 23:55:57,981[DEBUG] optimize site: [6, 7]
2025-05-13 23:55:57,990[DEBUG] use davidson, HC hops: 6
2025-05-13 23:55:57,992[DEBUG] energy: -13.997315012470608
2025-05-13 23:55:57,995[DEBUG] optimize site: [7, 8]
2025-05-13 23:55:58,003[DEBUG] use davidson, HC hops: 5
2025-05-13 23:55:58,004[DEBUG] energy: -13.997315006066612
2025-05-13 23:55:58,008[DEBUG] optimize site: [8, 9]
2025-05-13 23:55:58,018[DEBUG] use davidson, HC hops: 7
2025-05-13 23:55:58,020[DEBUG] energy: -13.997315033374491
2025-05-13 23:55:58,024[DEBUG] optimize site: [9, 10]
2025-05-13 23:55:58,033[DEBUG] use davidson, HC hops: 6
2025-05-13 23:55:58,034[DEBUG] energy: -13.997315010121925
2025-05-13 23:55:58,038[DEBUG] optimize site: [10, 11]
2025-05-13 23:55:58,050[DEBUG] use davidson, HC hops: 8
2025-05-13 23:55:58,050[DEBUG] energy: -13.997315055776864
2025-05-13 23:55:58,055[DEBUG] optimize site: [11, 12]
2025-05-13 23:55:58,065[DEBUG] use davidson, HC hops: 7
2025-05-13 23:55:58,065[DEBUG] energy: -13.997315015890447
2025-05-13 23:55:58,070[DEBUG] optimize site: [12, 13]
2025-05-13 23:55:58,081[DEBUG] use davidson, HC hops: 8
2025-05-13 23:55:58,082[DEBUG] energy: -13.997315076759376
2025-05-13 23:55:58,086[DEBUG] optimize site: [13, 14]
2025-05-13 23:55:58,096[DEBUG] use davidson, HC hops: 7
2025-05-13 23:55:58,097[DEBUG] energy: -13.997315021063756
2025-05-13 23:55:58,101[DEBUG] optimize site: [14, 15]
2025-05-13 23:55:58,112[DEBUG] use davidson, HC hops: 8
2025-05-13 23:55:58,114[DEBUG] energy: -13.997315089163472
2025-05-13 23:55:58,117[DEBUG] optimize site: [15, 16]
2025-05-13 23:55:58,129[DEBUG] use davidson, HC hops: 8
2025-05-13 23:55:58,130[DEBUG] energy: -13.997315023237729
2025-05-13 23:55:58,134[DEBUG] optimize site: [16, 17]
2025-05-13 23:55:58,146[DEBUG] use davidson, HC hops: 9
2025-05-13 23:55:58,147[DEBUG] energy: -13.997315090211643
2025-05-13 23:55:58,151[DEBUG] optimize site: [17, 18]
2025-05-13 23:55:58,163[DEBUG] use davidson, HC hops: 8
2025-05-13 23:55:58,164[DEBUG] energy: -13.99731502201425
2025-05-13 23:55:58,168[DEBUG] optimize site: [18, 19]
2025-05-13 23:55:58,179[DEBUG] use davidson, HC hops: 8
2025-05-13 23:55:58,181[DEBUG] energy: -13.997315079212553
2025-05-13 23:55:58,184[DEBUG] optimize site: [19, 20]
2025-05-13 23:55:58,194[DEBUG] use davidson, HC hops: 7
2025-05-13 23:55:58,195[DEBUG] energy: -13.997315018389685
2025-05-13 23:55:58,199[DEBUG] optimize site: [20, 21]
2025-05-13 23:55:58,211[DEBUG] use davidson, HC hops: 8
2025-05-13 23:55:58,212[DEBUG] energy: -13.99731506047156
2025-05-13 23:55:58,216[DEBUG] optimize site: [21, 22]
2025-05-13 23:55:58,225[DEBUG] use davidson, HC hops: 6
2025-05-13 23:55:58,227[DEBUG] energy: -13.997315014222977
2025-05-13 23:55:58,230[DEBUG] optimize site: [22, 23]
2025-05-13 23:55:58,242[DEBUG] use davidson, HC hops: 8
2025-05-13 23:55:58,243[DEBUG] energy: -13.99731503638075
2025-05-13 23:55:58,247[DEBUG] optimize site: [23, 24]
2025-05-13 23:55:58,256[DEBUG] use davidson, HC hops: 6
2025-05-13 23:55:58,256[DEBUG] energy: -13.99731500906334
2025-05-13 23:55:58,261[DEBUG] optimize site: [24, 25]
2025-05-13 23:55:58,270[DEBUG] use davidson, HC hops: 6
2025-05-13 23:55:58,271[DEBUG] energy: -13.997315015431855
2025-05-13 23:55:58,275[DEBUG] optimize site: [25, 26]
2025-05-13 23:55:58,283[DEBUG] use davidson, HC hops: 5
2025-05-13 23:55:58,285[DEBUG] energy: -13.997315007630533
2025-05-13 23:55:58,288[DEBUG] optimize site: [26, 27]
2025-05-13 23:55:58,295[DEBUG] use davidson, HC hops: 4
2025-05-13 23:55:58,295[DEBUG] energy: -13.997315007727522
2025-05-13 23:55:58,299[DEBUG] optimize site: [27, 28]
2025-05-13 23:55:58,301[DEBUG] use direct eigensolver
2025-05-13 23:55:58,549[DEBUG] energy: -13.99731500742747
2025-05-13 23:55:58,553[DEBUG] optimize site: [28, 29]
2025-05-13 23:55:58,555[DEBUG] use direct eigensolver
2025-05-13 23:55:58,603[DEBUG] energy: -13.997315007427467
2025-05-13 23:55:58,606[DEBUG] optimize site: [29, 30]
2025-05-13 23:55:58,608[DEBUG] use direct eigensolver
2025-05-13 23:55:58,614[DEBUG] energy: -13.997315007427446
2025-05-13 23:55:58,616[DEBUG] optimize site: [30, 31]
2025-05-13 23:55:58,617[DEBUG] use direct eigensolver
2025-05-13 23:55:58,620[DEBUG] energy: -13.997315007427453
2025-05-13 23:55:58,622[DEBUG] 3 sweeps are finished, lowest energy = -13.997315090211643
2025-05-13 23:55:58,624[INFO] DMRG has converged!
2025-05-13 23:55:58,660[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: -13.997315090211643

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