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

2026-10-14 01:45:52,085[INFO] Use numpy as backend
2026-10-14 01:45:52,085[INFO] numpy random seed is 9012
2026-10-14 01:45:52,086[INFO] backend random seed is 2019
2026-10-14 01:45:52,086[INFO] random seed is 1092
2026-10-14 01:45:52,091[INFO] Git Commit Hash: 3507afde83fd6f408c1c2198aad4dfe455d88312

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}")

2026-10-14 01:45:53,040[DEBUG] # of operator terms: 93
2026-10-14 01:45:53,041[DEBUG] Input operator terms: 93
2026-10-14 01:45:53,043[DEBUG] After combination of the same terms: 93
2026-10-14 01:45:53,043[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))

2026-10-14 01:45:53,095[INFO] optimization method: 2site
2026-10-14 01:45:53,095[INFO] e_rtol: 1e-06
2026-10-14 01:45:53,096[INFO] e_atol: 1e-08
2026-10-14 01:45:53,096[INFO] procedure: [[30, 0.2], [30, 0], [30, 0], [30, 0], [30, 0]]
2026-10-14 01:45:53,109[DEBUG] isweep: 0
2026-10-14 01:45:53,110[DEBUG] compress config in current loop: 30, percent: 0.2
2026-10-14 01:45:53,110[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]
2026-10-14 01:45:53,111[DEBUG] optimize site: [0, 1]
2026-10-14 01:45:53,112[DEBUG] use direct eigensolver
2026-10-14 01:45:53,114[DEBUG] energy: -0.7419708960759466
2026-10-14 01:45:53,115[DEBUG] optimize site: [1, 2]
2026-10-14 01:45:53,115[DEBUG] use direct eigensolver
2026-10-14 01:45:53,118[DEBUG] energy: -1.1765589509187797
2026-10-14 01:45:53,119[DEBUG] optimize site: [2, 3]
2026-10-14 01:45:53,120[DEBUG] use direct eigensolver
2026-10-14 01:45:53,130[DEBUG] energy: -2.0265583076241604
2026-10-14 01:45:53,132[DEBUG] optimize site: [3, 4]
2026-10-14 01:45:53,132[DEBUG] use direct eigensolver
2026-10-14 01:45:53,407[DEBUG] energy: -2.78409298882414
2026-10-14 01:45:53,409[DEBUG] optimize site: [4, 5]
2026-10-14 01:45:53,452[DEBUG] use davidson, HC hops: 77
2026-10-14 01:45:53,453[DEBUG] energy: -3.1146514070589655
2026-10-14 01:45:53,454[DEBUG] optimize site: [5, 6]
2026-10-14 01:45:53,517[DEBUG] use davidson, HC hops: 50
2026-10-14 01:45:53,518[DEBUG] energy: -3.6072464331202507
2026-10-14 01:45:53,591[DEBUG] optimize site: [6, 7]
2026-10-14 01:45:53,657[DEBUG] use davidson, HC hops: 58
2026-10-14 01:45:53,658[DEBUG] energy: -4.057368283084417
2026-10-14 01:45:53,689[DEBUG] optimize site: [7, 8]
2026-10-14 01:45:53,751[DEBUG] use davidson, HC hops: 60
2026-10-14 01:45:53,751[DEBUG] energy: -4.5236827616409085
2026-10-14 01:45:53,753[DEBUG] optimize site: [8, 9]
2026-10-14 01:45:53,807[DEBUG] use davidson, HC hops: 70
2026-10-14 01:45:53,808[DEBUG] energy: -4.885042109147768
2026-10-14 01:45:53,844[DEBUG] optimize site: [9, 10]
2026-10-14 01:45:53,877[DEBUG] use davidson, HC hops: 47
2026-10-14 01:45:53,877[DEBUG] energy: -5.472137392733305
2026-10-14 01:45:53,914[DEBUG] optimize site: [10, 11]
2026-10-14 01:45:53,984[DEBUG] use davidson, HC hops: 53
2026-10-14 01:45:53,984[DEBUG] energy: -5.8240656001561275
2026-10-14 01:45:54,048[DEBUG] optimize site: [11, 12]
2026-10-14 01:45:54,081[DEBUG] use davidson, HC hops: 46
2026-10-14 01:45:54,082[DEBUG] energy: -6.318572420045687
2026-10-14 01:45:54,085[DEBUG] optimize site: [12, 13]
2026-10-14 01:45:54,172[DEBUG] use davidson, HC hops: 69
2026-10-14 01:45:54,173[DEBUG] energy: -6.652741256503262
2026-10-14 01:45:54,178[DEBUG] optimize site: [13, 14]
2026-10-14 01:45:54,251[DEBUG] use davidson, HC hops: 55
2026-10-14 01:45:54,252[DEBUG] energy: -7.1345335634625435
2026-10-14 01:45:54,255[DEBUG] optimize site: [14, 15]
2026-10-14 01:45:54,333[DEBUG] use davidson, HC hops: 64
2026-10-14 01:45:54,335[DEBUG] energy: -7.5615524611621145
2026-10-14 01:45:54,366[DEBUG] optimize site: [15, 16]
2026-10-14 01:45:54,416[DEBUG] use davidson, HC hops: 71
2026-10-14 01:45:54,417[DEBUG] energy: -7.950669189151139
2026-10-14 01:45:54,425[DEBUG] optimize site: [16, 17]
2026-10-14 01:45:54,490[DEBUG] use davidson, HC hops: 71
2026-10-14 01:45:54,491[DEBUG] energy: -8.441251888323036
2026-10-14 01:45:54,527[DEBUG] optimize site: [17, 18]
2026-10-14 01:45:54,578[DEBUG] use davidson, HC hops: 54
2026-10-14 01:45:54,579[DEBUG] energy: -8.88006669416675
2026-10-14 01:45:54,582[DEBUG] optimize site: [18, 19]
2026-10-14 01:45:54,618[DEBUG] use davidson, HC hops: 51
2026-10-14 01:45:54,619[DEBUG] energy: -9.30409924871295
2026-10-14 01:45:54,657[DEBUG] optimize site: [19, 20]
2026-10-14 01:45:54,752[DEBUG] use davidson, HC hops: 86
2026-10-14 01:45:54,754[DEBUG] energy: -9.781285321391415
2026-10-14 01:45:54,756[DEBUG] optimize site: [20, 21]
2026-10-14 01:45:54,809[DEBUG] use davidson, HC hops: 46
2026-10-14 01:45:54,810[DEBUG] energy: -10.367535781502296
2026-10-14 01:45:54,833[DEBUG] optimize site: [21, 22]
2026-10-14 01:45:54,910[DEBUG] use davidson, HC hops: 67
2026-10-14 01:45:54,912[DEBUG] energy: -10.841587553418124
2026-10-14 01:45:54,926[DEBUG] optimize site: [22, 23]
2026-10-14 01:45:54,977[DEBUG] use davidson, HC hops: 70
2026-10-14 01:45:54,979[DEBUG] energy: -11.370021793697031
2026-10-14 01:45:55,019[DEBUG] optimize site: [23, 24]
2026-10-14 01:45:55,068[DEBUG] use davidson, HC hops: 56
2026-10-14 01:45:55,069[DEBUG] energy: -11.969644315602897
2026-10-14 01:45:55,072[DEBUG] optimize site: [24, 25]
2026-10-14 01:45:55,133[DEBUG] use davidson, HC hops: 48
2026-10-14 01:45:55,134[DEBUG] energy: -12.940445176287557
2026-10-14 01:45:55,137[DEBUG] optimize site: [25, 26]
2026-10-14 01:45:55,182[DEBUG] use davidson, HC hops: 57
2026-10-14 01:45:55,184[DEBUG] energy: -13.951015333969082
2026-10-14 01:45:55,186[DEBUG] optimize site: [26, 27]
2026-10-14 01:45:55,210[DEBUG] use davidson, HC hops: 41
2026-10-14 01:45:55,210[DEBUG] energy: -13.997018110633658
2026-10-14 01:45:55,213[DEBUG] optimize site: [27, 28]
2026-10-14 01:45:55,215[DEBUG] use direct eigensolver
2026-10-14 01:45:55,516[DEBUG] energy: -13.997018110366577
2026-10-14 01:45:55,519[DEBUG] optimize site: [28, 29]
2026-10-14 01:45:55,519[DEBUG] use direct eigensolver
2026-10-14 01:45:55,663[DEBUG] energy: -13.997018110366568
2026-10-14 01:45:55,666[DEBUG] optimize site: [29, 30]
2026-10-14 01:45:55,667[DEBUG] use direct eigensolver
2026-10-14 01:45:55,672[DEBUG] energy: -13.997018110366561
2026-10-14 01:45:55,673[DEBUG] optimize site: [30, 31]
2026-10-14 01:45:55,675[DEBUG] use direct eigensolver
2026-10-14 01:45:55,676[DEBUG] energy: -13.997018110366602
2026-10-14 01:45:55,678[DEBUG] 1 sweeps are finished, lowest energy = -13.997018110633658
2026-10-14 01:45:55,679[DEBUG] isweep: 1
2026-10-14 01:45:55,680[DEBUG] compress config in current loop: 30, percent: 0
2026-10-14 01:45:55,681[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]
2026-10-14 01:45:55,682[DEBUG] optimize site: [30, 31]
2026-10-14 01:45:55,683[DEBUG] use direct eigensolver
2026-10-14 01:45:55,684[DEBUG] energy: -13.997018110366602
2026-10-14 01:45:55,685[DEBUG] optimize site: [29, 30]
2026-10-14 01:45:55,687[DEBUG] use direct eigensolver
2026-10-14 01:45:55,692[DEBUG] energy: -13.997018110366579
2026-10-14 01:45:55,694[DEBUG] optimize site: [28, 29]
2026-10-14 01:45:55,695[DEBUG] use direct eigensolver
2026-10-14 01:45:55,774[DEBUG] energy: -13.997018110366557
2026-10-14 01:45:55,776[DEBUG] optimize site: [27, 28]
2026-10-14 01:45:55,778[DEBUG] use direct eigensolver
2026-10-14 01:45:56,063[DEBUG] energy: -13.99701811036657
2026-10-14 01:45:56,065[DEBUG] optimize site: [26, 27]
2026-10-14 01:45:56,069[DEBUG] use davidson, HC hops: 4
2026-10-14 01:45:56,070[DEBUG] energy: -13.997018110634604
2026-10-14 01:45:56,074[DEBUG] optimize site: [25, 26]
2026-10-14 01:45:56,098[DEBUG] use davidson, HC hops: 18
2026-10-14 01:45:56,099[DEBUG] energy: -13.997019894830892
2026-10-14 01:45:56,102[DEBUG] optimize site: [24, 25]
2026-10-14 01:45:56,138[DEBUG] use davidson, HC hops: 25
2026-10-14 01:45:56,139[DEBUG] energy: -13.997050707130187
2026-10-14 01:45:56,142[DEBUG] optimize site: [23, 24]
2026-10-14 01:45:56,175[DEBUG] use davidson, HC hops: 26
2026-10-14 01:45:56,176[DEBUG] energy: -13.997150789973483
2026-10-14 01:45:56,178[DEBUG] optimize site: [22, 23]
2026-10-14 01:45:56,209[DEBUG] use davidson, HC hops: 22
2026-10-14 01:45:56,210[DEBUG] energy: -13.997156828470148
2026-10-14 01:45:56,212[DEBUG] optimize site: [21, 22]
2026-10-14 01:45:56,245[DEBUG] use davidson, HC hops: 25
2026-10-14 01:45:56,247[DEBUG] energy: -13.997176682683591
2026-10-14 01:45:56,248[DEBUG] optimize site: [20, 21]
2026-10-14 01:45:56,273[DEBUG] use davidson, HC hops: 24
2026-10-14 01:45:56,274[DEBUG] energy: -13.997196066510229
2026-10-14 01:45:56,311[DEBUG] optimize site: [19, 20]
2026-10-14 01:45:56,338[DEBUG] use davidson, HC hops: 24
2026-10-14 01:45:56,341[DEBUG] energy: -13.997208542046101
2026-10-14 01:45:56,386[DEBUG] optimize site: [18, 19]
2026-10-14 01:45:56,403[DEBUG] use davidson, HC hops: 23
2026-10-14 01:45:56,404[DEBUG] energy: -13.997218539454606
2026-10-14 01:45:56,440[DEBUG] optimize site: [17, 18]
2026-10-14 01:45:56,458[DEBUG] use davidson, HC hops: 24
2026-10-14 01:45:56,460[DEBUG] energy: -13.997232982851381
2026-10-14 01:45:56,498[DEBUG] optimize site: [16, 17]
2026-10-14 01:45:56,529[DEBUG] use davidson, HC hops: 26
2026-10-14 01:45:56,530[DEBUG] energy: -13.997286667727456
2026-10-14 01:45:56,610[DEBUG] optimize site: [15, 16]
2026-10-14 01:45:56,636[DEBUG] use davidson, HC hops: 21
2026-10-14 01:45:56,638[DEBUG] energy: -13.997289976542227
2026-10-14 01:45:56,676[DEBUG] optimize site: [14, 15]
2026-10-14 01:45:56,690[DEBUG] use davidson, HC hops: 19
2026-10-14 01:45:56,691[DEBUG] energy: -13.997290766927081
2026-10-14 01:45:56,725[DEBUG] optimize site: [13, 14]
2026-10-14 01:45:56,757[DEBUG] use davidson, HC hops: 23
2026-10-14 01:45:56,759[DEBUG] energy: -13.997301691530419
2026-10-14 01:45:56,831[DEBUG] optimize site: [12, 13]
2026-10-14 01:45:56,857[DEBUG] use davidson, HC hops: 17
2026-10-14 01:45:56,860[DEBUG] energy: -13.997302673880075
2026-10-14 01:45:56,931[DEBUG] optimize site: [11, 12]
2026-10-14 01:45:56,959[DEBUG] use davidson, HC hops: 20
2026-10-14 01:45:56,962[DEBUG] energy: -13.997305253744722
2026-10-14 01:45:56,996[DEBUG] optimize site: [10, 11]
2026-10-14 01:45:57,018[DEBUG] use davidson, HC hops: 21
2026-10-14 01:45:57,020[DEBUG] energy: -13.997309261458039
2026-10-14 01:45:57,093[DEBUG] optimize site: [9, 10]
2026-10-14 01:45:57,121[DEBUG] use davidson, HC hops: 19
2026-10-14 01:45:57,122[DEBUG] energy: -13.99731297794233
2026-10-14 01:45:57,195[DEBUG] optimize site: [8, 9]
2026-10-14 01:45:57,222[DEBUG] use davidson, HC hops: 17
2026-10-14 01:45:57,224[DEBUG] energy: -13.997314066392395
2026-10-14 01:45:57,294[DEBUG] optimize site: [7, 8]
2026-10-14 01:45:57,306[DEBUG] use davidson, HC hops: 14
2026-10-14 01:45:57,308[DEBUG] energy: -13.997314835104113
2026-10-14 01:45:57,347[DEBUG] optimize site: [6, 7]
2026-10-14 01:45:57,355[DEBUG] use davidson, HC hops: 10
2026-10-14 01:45:57,357[DEBUG] energy: -13.997315008587139
2026-10-14 01:45:57,394[DEBUG] optimize site: [5, 6]
2026-10-14 01:45:57,400[DEBUG] use davidson, HC hops: 6
2026-10-14 01:45:57,401[DEBUG] energy: -13.99731500699081
2026-10-14 01:45:57,437[DEBUG] optimize site: [4, 5]
2026-10-14 01:45:57,441[DEBUG] use davidson, HC hops: 5
2026-10-14 01:45:57,442[DEBUG] energy: -13.997315007843703
2026-10-14 01:45:57,444[DEBUG] optimize site: [3, 4]
2026-10-14 01:45:57,446[DEBUG] use direct eigensolver
2026-10-14 01:45:57,753[DEBUG] energy: -13.997315007543614
2026-10-14 01:45:57,755[DEBUG] optimize site: [2, 3]
2026-10-14 01:45:57,756[DEBUG] use direct eigensolver
2026-10-14 01:45:57,885[DEBUG] energy: -13.997315007543609
2026-10-14 01:45:57,886[DEBUG] optimize site: [1, 2]
2026-10-14 01:45:57,889[DEBUG] use direct eigensolver
2026-10-14 01:45:57,893[DEBUG] energy: -13.997315007543602
2026-10-14 01:45:57,895[DEBUG] optimize site: [0, 1]
2026-10-14 01:45:57,896[DEBUG] use direct eigensolver
2026-10-14 01:45:57,898[DEBUG] energy: -13.997315007543616
2026-10-14 01:45:57,900[DEBUG] 2 sweeps are finished, lowest energy = -13.997315008587139
2026-10-14 01:45:57,901[DEBUG] isweep: 2
2026-10-14 01:45:57,903[DEBUG] compress config in current loop: 30, percent: 0
2026-10-14 01:45:57,903[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]
2026-10-14 01:45:57,904[DEBUG] optimize site: [0, 1]
2026-10-14 01:45:57,905[DEBUG] use direct eigensolver
2026-10-14 01:45:57,907[DEBUG] energy: -13.997315007543616
2026-10-14 01:45:57,909[DEBUG] optimize site: [1, 2]
2026-10-14 01:45:57,910[DEBUG] use direct eigensolver
2026-10-14 01:45:57,914[DEBUG] energy: -13.997315007543618
2026-10-14 01:45:57,916[DEBUG] optimize site: [2, 3]
2026-10-14 01:45:57,917[DEBUG] use direct eigensolver
2026-10-14 01:45:58,063[DEBUG] energy: -13.997315007543634
2026-10-14 01:45:58,065[DEBUG] optimize site: [3, 4]
2026-10-14 01:45:58,067[DEBUG] use direct eigensolver
2026-10-14 01:45:58,368[DEBUG] energy: -13.997315007543644
2026-10-14 01:45:58,371[DEBUG] optimize site: [4, 5]
2026-10-14 01:45:58,375[DEBUG] use davidson, HC hops: 4
2026-10-14 01:45:58,376[DEBUG] energy: -13.997315007843829
2026-10-14 01:45:58,378[DEBUG] optimize site: [5, 6]
2026-10-14 01:45:58,383[DEBUG] use davidson, HC hops: 4
2026-10-14 01:45:58,384[DEBUG] energy: -13.997315007741673
2026-10-14 01:45:58,388[DEBUG] optimize site: [6, 7]
2026-10-14 01:45:58,397[DEBUG] use davidson, HC hops: 6
2026-10-14 01:45:58,398[DEBUG] energy: -13.997315015505741
2026-10-14 01:45:58,402[DEBUG] optimize site: [7, 8]
2026-10-14 01:45:58,411[DEBUG] use davidson, HC hops: 5
2026-10-14 01:45:58,411[DEBUG] energy: -13.997315009163298
2026-10-14 01:45:58,413[DEBUG] optimize site: [8, 9]
2026-10-14 01:45:58,423[DEBUG] use davidson, HC hops: 7
2026-10-14 01:45:58,423[DEBUG] energy: -13.997315036233706
2026-10-14 01:45:58,426[DEBUG] optimize site: [9, 10]
2026-10-14 01:45:58,435[DEBUG] use davidson, HC hops: 6
2026-10-14 01:45:58,436[DEBUG] energy: -13.99731501301861
2026-10-14 01:45:58,439[DEBUG] optimize site: [10, 11]
2026-10-14 01:45:58,451[DEBUG] use davidson, HC hops: 8
2026-10-14 01:45:58,452[DEBUG] energy: -13.99731505882256
2026-10-14 01:45:58,454[DEBUG] optimize site: [11, 12]
2026-10-14 01:45:58,464[DEBUG] use davidson, HC hops: 7
2026-10-14 01:45:58,465[DEBUG] energy: -13.997315018800052
2026-10-14 01:45:58,467[DEBUG] optimize site: [12, 13]
2026-10-14 01:45:58,477[DEBUG] use davidson, HC hops: 8
2026-10-14 01:45:58,477[DEBUG] energy: -13.997315079671974
2026-10-14 01:45:58,483[DEBUG] optimize site: [13, 14]
2026-10-14 01:45:58,493[DEBUG] use davidson, HC hops: 7
2026-10-14 01:45:58,495[DEBUG] energy: -13.997315023824868
2026-10-14 01:45:58,497[DEBUG] optimize site: [14, 15]
2026-10-14 01:45:58,510[DEBUG] use davidson, HC hops: 8
2026-10-14 01:45:58,511[DEBUG] energy: -13.997315092179461
2026-10-14 01:45:58,514[DEBUG] optimize site: [15, 16]
2026-10-14 01:45:58,523[DEBUG] use davidson, HC hops: 7
2026-10-14 01:45:58,523[DEBUG] energy: -13.997315025959809
2026-10-14 01:45:58,525[DEBUG] optimize site: [16, 17]
2026-10-14 01:45:58,536[DEBUG] use davidson, HC hops: 8
2026-10-14 01:45:58,536[DEBUG] energy: -13.997315092248568
2026-10-14 01:45:58,538[DEBUG] optimize site: [17, 18]
2026-10-14 01:45:58,548[DEBUG] use davidson, HC hops: 8
2026-10-14 01:45:58,549[DEBUG] energy: -13.997315024706637
2026-10-14 01:45:58,551[DEBUG] optimize site: [18, 19]
2026-10-14 01:45:58,564[DEBUG] use davidson, HC hops: 8
2026-10-14 01:45:58,565[DEBUG] energy: -13.997315081031338
2026-10-14 01:45:58,568[DEBUG] optimize site: [19, 20]
2026-10-14 01:45:58,577[DEBUG] use davidson, HC hops: 7
2026-10-14 01:45:58,579[DEBUG] energy: -13.997315020612412
2026-10-14 01:45:58,580[DEBUG] optimize site: [20, 21]
2026-10-14 01:45:58,594[DEBUG] use davidson, HC hops: 8
2026-10-14 01:45:58,595[DEBUG] energy: -13.997315061147274
2026-10-14 01:45:58,597[DEBUG] optimize site: [21, 22]
2026-10-14 01:45:58,606[DEBUG] use davidson, HC hops: 6
2026-10-14 01:45:58,607[DEBUG] energy: -13.997315015215642
2026-10-14 01:45:58,609[DEBUG] optimize site: [22, 23]
2026-10-14 01:45:58,638[DEBUG] use davidson, HC hops: 8
2026-10-14 01:45:58,640[DEBUG] energy: -13.997315036589523
2026-10-14 01:45:58,704[DEBUG] optimize site: [23, 24]
2026-10-14 01:45:58,742[DEBUG] use davidson, HC hops: 5
2026-10-14 01:45:58,742[DEBUG] energy: -13.9973150092667
2026-10-14 01:45:58,745[DEBUG] optimize site: [24, 25]
2026-10-14 01:45:58,754[DEBUG] use davidson, HC hops: 6
2026-10-14 01:45:58,755[DEBUG] energy: -13.997315015667919
2026-10-14 01:45:58,757[DEBUG] optimize site: [25, 26]
2026-10-14 01:45:58,762[DEBUG] use davidson, HC hops: 5
2026-10-14 01:45:58,763[DEBUG] energy: -13.997315007871357
2026-10-14 01:45:58,764[DEBUG] optimize site: [26, 27]
2026-10-14 01:45:58,768[DEBUG] use davidson, HC hops: 4
2026-10-14 01:45:58,768[DEBUG] energy: -13.99731500796935
2026-10-14 01:45:58,769[DEBUG] optimize site: [27, 28]
2026-10-14 01:45:58,770[DEBUG] use direct eigensolver
2026-10-14 01:45:59,077[DEBUG] energy: -13.997315007669455
2026-10-14 01:45:59,079[DEBUG] optimize site: [28, 29]
2026-10-14 01:45:59,080[DEBUG] use direct eigensolver
2026-10-14 01:45:59,208[DEBUG] energy: -13.99731500766946
2026-10-14 01:45:59,209[DEBUG] optimize site: [29, 30]
2026-10-14 01:45:59,210[DEBUG] use direct eigensolver
2026-10-14 01:45:59,213[DEBUG] energy: -13.997315007669485
2026-10-14 01:45:59,214[DEBUG] optimize site: [30, 31]
2026-10-14 01:45:59,215[DEBUG] use direct eigensolver
2026-10-14 01:45:59,216[DEBUG] energy: -13.997315007669489
2026-10-14 01:45:59,217[DEBUG] 3 sweeps are finished, lowest energy = -13.997315092248568
2026-10-14 01:45:59,218[INFO] DMRG has converged!
2026-10-14 01:45:59,242[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: -13.997315092248568

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