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

2025-10-27 14:14:50,900[INFO] Use NumPy as backend
2025-10-27 14:14:50,901[INFO] numpy random seed is 9012
2025-10-27 14:14:50,901[INFO] random seed is 1092
2025-10-27 14:14:50,910[INFO] Git Commit Hash: 190c65bf4368526ca515f9397f0e9be7762e06c6
2025-10-27 14:14:50,911[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}")

2025-10-27 14:14:51,009[DEBUG] # of operator terms: 93
2025-10-27 14:14:51,010[DEBUG] Input operator terms: 93
2025-10-27 14:14:51,013[DEBUG] After combination of the same terms: 93
2025-10-27 14:14:51,013[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))

2025-10-27 14:14:51,081[INFO] optimization method: 2site
2025-10-27 14:14:51,082[INFO] e_rtol: 1e-06
2025-10-27 14:14:51,082[INFO] e_atol: 1e-08
2025-10-27 14:14:51,083[INFO] procedure: [[30, 0.2], [30, 0], [30, 0], [30, 0], [30, 0]]
2025-10-27 14:14:51,115[DEBUG] isweep: 0
2025-10-27 14:14:51,116[DEBUG] compress config in current loop: 30, percent: 0.2
2025-10-27 14:14:51,117[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]
2025-10-27 14:14:51,118[DEBUG] optimize site: [0, 1]
2025-10-27 14:14:51,119[DEBUG] use direct eigensolver
2025-10-27 14:14:51,123[DEBUG] energy: -0.9279990226898331
2025-10-27 14:14:51,125[DEBUG] optimize site: [1, 2]
2025-10-27 14:14:51,127[DEBUG] use direct eigensolver
2025-10-27 14:14:51,131[DEBUG] energy: -1.284089573410534
2025-10-27 14:14:51,133[DEBUG] optimize site: [2, 3]
2025-10-27 14:14:51,135[DEBUG] use direct eigensolver
2025-10-27 14:14:51,158[DEBUG] energy: -2.0857452647499213
2025-10-27 14:14:51,160[DEBUG] optimize site: [3, 4]
2025-10-27 14:14:51,162[DEBUG] use direct eigensolver
2025-10-27 14:14:51,418[DEBUG] energy: -2.8158895272374123
2025-10-27 14:14:51,420[DEBUG] optimize site: [4, 5]
2025-10-27 14:14:51,476[DEBUG] use davidson, HC hops: 34
2025-10-27 14:14:51,477[DEBUG] energy: -3.2933673155858028
2025-10-27 14:14:51,479[DEBUG] optimize site: [5, 6]
2025-10-27 14:14:51,567[DEBUG] use davidson, HC hops: 42
2025-10-27 14:14:51,568[DEBUG] energy: -3.7449867503071976
2025-10-27 14:14:51,572[DEBUG] optimize site: [6, 7]
2025-10-27 14:14:51,659[DEBUG] use davidson, HC hops: 42
2025-10-27 14:14:51,661[DEBUG] energy: -4.176385575496491
2025-10-27 14:14:51,665[DEBUG] optimize site: [7, 8]
2025-10-27 14:14:51,757[DEBUG] use davidson, HC hops: 44
2025-10-27 14:14:51,759[DEBUG] energy: -4.5835934779273835
2025-10-27 14:14:51,765[DEBUG] optimize site: [8, 9]
2025-10-27 14:14:51,878[DEBUG] use davidson, HC hops: 55
2025-10-27 14:14:51,879[DEBUG] energy: -4.9680318456712
2025-10-27 14:14:51,884[DEBUG] optimize site: [9, 10]
2025-10-27 14:14:52,021[DEBUG] use davidson, HC hops: 68
2025-10-27 14:14:52,023[DEBUG] energy: -5.41470636083398
2025-10-27 14:14:52,028[DEBUG] optimize site: [10, 11]
2025-10-27 14:14:52,176[DEBUG] use davidson, HC hops: 72
2025-10-27 14:14:52,178[DEBUG] energy: -5.856529754520472
2025-10-27 14:14:52,182[DEBUG] optimize site: [11, 12]
2025-10-27 14:14:52,372[DEBUG] use davidson, HC hops: 100
2025-10-27 14:14:52,374[DEBUG] energy: -6.279022467295805
2025-10-27 14:14:52,379[DEBUG] optimize site: [12, 13]
2025-10-27 14:14:52,485[DEBUG] use davidson, HC hops: 52
2025-10-27 14:14:52,486[DEBUG] energy: -6.857389012204758
2025-10-27 14:14:52,491[DEBUG] optimize site: [13, 14]
2025-10-27 14:14:52,682[DEBUG] use davidson, HC hops: 100
2025-10-27 14:14:52,683[DEBUG] energy: -7.11458802200578
2025-10-27 14:14:52,685[DEBUG] optimize site: [14, 15]
2025-10-27 14:14:52,756[DEBUG] use davidson, HC hops: 47
2025-10-27 14:14:52,759[DEBUG] energy: -7.641631783835418
2025-10-27 14:14:52,763[DEBUG] optimize site: [15, 16]
2025-10-27 14:14:52,869[DEBUG] use davidson, HC hops: 51
2025-10-27 14:14:52,871[DEBUG] energy: -8.118395338420065
2025-10-27 14:14:52,875[DEBUG] optimize site: [16, 17]
2025-10-27 14:14:52,989[DEBUG] use davidson, HC hops: 57
2025-10-27 14:14:52,990[DEBUG] energy: -8.579533430762865
2025-10-27 14:14:52,993[DEBUG] optimize site: [17, 18]
2025-10-27 14:14:53,117[DEBUG] use davidson, HC hops: 66
2025-10-27 14:14:53,118[DEBUG] energy: -8.983113190158472
2025-10-27 14:14:53,122[DEBUG] optimize site: [18, 19]
2025-10-27 14:14:53,241[DEBUG] use davidson, HC hops: 62
2025-10-27 14:14:53,242[DEBUG] energy: -9.422205404607663
2025-10-27 14:14:53,246[DEBUG] optimize site: [19, 20]
2025-10-27 14:14:53,365[DEBUG] use davidson, HC hops: 62
2025-10-27 14:14:53,366[DEBUG] energy: -9.903693680914413
2025-10-27 14:14:53,371[DEBUG] optimize site: [20, 21]
2025-10-27 14:14:53,509[DEBUG] use davidson, HC hops: 81
2025-10-27 14:14:53,511[DEBUG] energy: -10.398530611697987
2025-10-27 14:14:53,515[DEBUG] optimize site: [21, 22]
2025-10-27 14:14:53,648[DEBUG] use davidson, HC hops: 76
2025-10-27 14:14:53,648[DEBUG] energy: -10.834489434421673
2025-10-27 14:14:53,653[DEBUG] optimize site: [22, 23]
2025-10-27 14:14:53,769[DEBUG] use davidson, HC hops: 58
2025-10-27 14:14:53,771[DEBUG] energy: -11.415128707126808
2025-10-27 14:14:53,775[DEBUG] optimize site: [23, 24]
2025-10-27 14:14:53,882[DEBUG] use davidson, HC hops: 52
2025-10-27 14:14:53,883[DEBUG] energy: -12.122795879745055
2025-10-27 14:14:53,888[DEBUG] optimize site: [24, 25]
2025-10-27 14:14:54,015[DEBUG] use davidson, HC hops: 71
2025-10-27 14:14:54,016[DEBUG] energy: -12.812234874023488
2025-10-27 14:14:54,021[DEBUG] optimize site: [25, 26]
2025-10-27 14:14:54,135[DEBUG] use davidson, HC hops: 58
2025-10-27 14:14:54,136[DEBUG] energy: -13.774582804126666
2025-10-27 14:14:54,141[DEBUG] optimize site: [26, 27]
2025-10-27 14:14:54,220[DEBUG] use davidson, HC hops: 47
2025-10-27 14:14:54,223[DEBUG] energy: -13.996832655813094
2025-10-27 14:14:54,225[DEBUG] optimize site: [27, 28]
2025-10-27 14:14:54,229[DEBUG] use direct eigensolver
2025-10-27 14:14:54,490[DEBUG] energy: -13.996832655534016
2025-10-27 14:14:54,492[DEBUG] optimize site: [28, 29]
2025-10-27 14:14:54,494[DEBUG] use direct eigensolver
2025-10-27 14:14:54,571[DEBUG] energy: -13.996832655534023
2025-10-27 14:14:54,573[DEBUG] optimize site: [29, 30]
2025-10-27 14:14:54,576[DEBUG] use direct eigensolver
2025-10-27 14:14:54,584[DEBUG] energy: -13.996832655534023
2025-10-27 14:14:54,586[DEBUG] optimize site: [30, 31]
2025-10-27 14:14:54,588[DEBUG] use direct eigensolver
2025-10-27 14:14:54,592[DEBUG] energy: -13.996832655534034
2025-10-27 14:14:54,594[DEBUG] 1 sweeps are finished, lowest energy = -13.996832655813094
2025-10-27 14:14:54,595[DEBUG] isweep: 1
2025-10-27 14:14:54,596[DEBUG] compress config in current loop: 30, percent: 0
2025-10-27 14:14:54,598[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]
2025-10-27 14:14:54,599[DEBUG] optimize site: [30, 31]
2025-10-27 14:14:54,600[DEBUG] use direct eigensolver
2025-10-27 14:14:54,604[DEBUG] energy: -13.996832655534034
2025-10-27 14:14:54,605[DEBUG] optimize site: [29, 30]
2025-10-27 14:14:54,607[DEBUG] use direct eigensolver
2025-10-27 14:14:54,612[DEBUG] energy: -13.996832655534028
2025-10-27 14:14:54,613[DEBUG] optimize site: [28, 29]
2025-10-27 14:14:54,614[DEBUG] use direct eigensolver
2025-10-27 14:14:54,682[DEBUG] energy: -13.996832655534018
2025-10-27 14:14:54,684[DEBUG] optimize site: [27, 28]
2025-10-27 14:14:54,687[DEBUG] use direct eigensolver
2025-10-27 14:14:54,937[DEBUG] energy: -13.996832655534027
2025-10-27 14:14:54,939[DEBUG] optimize site: [26, 27]
2025-10-27 14:14:54,950[DEBUG] use davidson, HC hops: 4
2025-10-27 14:14:54,952[DEBUG] energy: -13.99683265581366
2025-10-27 14:14:54,955[DEBUG] optimize site: [25, 26]
2025-10-27 14:14:54,997[DEBUG] use davidson, HC hops: 22
2025-10-27 14:14:54,998[DEBUG] energy: -13.996844945038381
2025-10-27 14:14:55,001[DEBUG] optimize site: [24, 25]
2025-10-27 14:14:55,049[DEBUG] use davidson, HC hops: 28
2025-10-27 14:14:55,050[DEBUG] energy: -13.997067101658777
2025-10-27 14:14:55,054[DEBUG] optimize site: [23, 24]
2025-10-27 14:14:55,106[DEBUG] use davidson, HC hops: 25
2025-10-27 14:14:55,107[DEBUG] energy: -13.997101684717542
2025-10-27 14:14:55,111[DEBUG] optimize site: [22, 23]
2025-10-27 14:14:55,159[DEBUG] use davidson, HC hops: 23
2025-10-27 14:14:55,160[DEBUG] energy: -13.997106608213759
2025-10-27 14:14:55,164[DEBUG] optimize site: [21, 22]
2025-10-27 14:14:55,195[DEBUG] use davidson, HC hops: 23
2025-10-27 14:14:55,196[DEBUG] energy: -13.997113698271189
2025-10-27 14:14:55,199[DEBUG] optimize site: [20, 21]
2025-10-27 14:14:55,229[DEBUG] use davidson, HC hops: 26
2025-10-27 14:14:55,230[DEBUG] energy: -13.997162638323617
2025-10-27 14:14:55,232[DEBUG] optimize site: [19, 20]
2025-10-27 14:14:55,278[DEBUG] use davidson, HC hops: 23
2025-10-27 14:14:55,280[DEBUG] energy: -13.99717014496563
2025-10-27 14:14:55,284[DEBUG] optimize site: [18, 19]
2025-10-27 14:14:55,337[DEBUG] use davidson, HC hops: 26
2025-10-27 14:14:55,339[DEBUG] energy: -13.997199975427494
2025-10-27 14:14:55,342[DEBUG] optimize site: [17, 18]
2025-10-27 14:14:55,377[DEBUG] use davidson, HC hops: 22
2025-10-27 14:14:55,378[DEBUG] energy: -13.9972043926217
2025-10-27 14:14:55,382[DEBUG] optimize site: [16, 17]
2025-10-27 14:14:55,412[DEBUG] use davidson, HC hops: 25
2025-10-27 14:14:55,414[DEBUG] energy: -13.997225037523886
2025-10-27 14:14:55,417[DEBUG] optimize site: [15, 16]
2025-10-27 14:14:55,448[DEBUG] use davidson, HC hops: 26
2025-10-27 14:14:55,449[DEBUG] energy: -13.99728491812126
2025-10-27 14:14:55,453[DEBUG] optimize site: [14, 15]
2025-10-27 14:14:55,499[DEBUG] use davidson, HC hops: 22
2025-10-27 14:14:55,500[DEBUG] energy: -13.997290859971308
2025-10-27 14:14:55,506[DEBUG] optimize site: [13, 14]
2025-10-27 14:14:55,548[DEBUG] use davidson, HC hops: 20
2025-10-27 14:14:55,549[DEBUG] energy: -13.99729325765386
2025-10-27 14:14:55,555[DEBUG] optimize site: [12, 13]
2025-10-27 14:14:55,603[DEBUG] use davidson, HC hops: 23
2025-10-27 14:14:55,605[DEBUG] energy: -13.997306225086724
2025-10-27 14:14:55,610[DEBUG] optimize site: [11, 12]
2025-10-27 14:14:55,637[DEBUG] use davidson, HC hops: 21
2025-10-27 14:14:55,638[DEBUG] energy: -13.99731114559566
2025-10-27 14:14:55,642[DEBUG] optimize site: [10, 11]
2025-10-27 14:14:55,668[DEBUG] use davidson, HC hops: 20
2025-10-27 14:14:55,670[DEBUG] energy: -13.997313132707536
2025-10-27 14:14:55,675[DEBUG] optimize site: [9, 10]
2025-10-27 14:14:55,696[DEBUG] use davidson, HC hops: 17
2025-10-27 14:14:55,698[DEBUG] energy: -13.9973144286264
2025-10-27 14:14:55,701[DEBUG] optimize site: [8, 9]
2025-10-27 14:14:55,716[DEBUG] use davidson, HC hops: 11
2025-10-27 14:14:55,717[DEBUG] energy: -13.997314715468704
2025-10-27 14:14:55,721[DEBUG] optimize site: [7, 8]
2025-10-27 14:14:55,731[DEBUG] use davidson, HC hops: 7
2025-10-27 14:14:55,732[DEBUG] energy: -13.997314712669834
2025-10-27 14:14:55,736[DEBUG] optimize site: [6, 7]
2025-10-27 14:14:55,752[DEBUG] use davidson, HC hops: 12
2025-10-27 14:14:55,753[DEBUG] energy: -13.997314999750078
2025-10-27 14:14:55,757[DEBUG] optimize site: [5, 6]
2025-10-27 14:14:55,768[DEBUG] use davidson, HC hops: 7
2025-10-27 14:14:55,769[DEBUG] energy: -13.997315003811515
2025-10-27 14:14:55,773[DEBUG] optimize site: [4, 5]
2025-10-27 14:14:55,780[DEBUG] use davidson, HC hops: 5
2025-10-27 14:14:55,780[DEBUG] energy: -13.99731500476785
2025-10-27 14:14:55,784[DEBUG] optimize site: [3, 4]
2025-10-27 14:14:55,786[DEBUG] use direct eigensolver
2025-10-27 14:14:56,043[DEBUG] energy: -13.997315004467179
2025-10-27 14:14:56,046[DEBUG] optimize site: [2, 3]
2025-10-27 14:14:56,049[DEBUG] use direct eigensolver
2025-10-27 14:14:56,097[DEBUG] energy: -13.997315004467154
2025-10-27 14:14:56,099[DEBUG] optimize site: [1, 2]
2025-10-27 14:14:56,101[DEBUG] use direct eigensolver
2025-10-27 14:14:56,107[DEBUG] energy: -13.99731500446715
2025-10-27 14:14:56,109[DEBUG] optimize site: [0, 1]
2025-10-27 14:14:56,111[DEBUG] use direct eigensolver
2025-10-27 14:14:56,113[DEBUG] energy: -13.99731500446715
2025-10-27 14:14:56,114[DEBUG] 2 sweeps are finished, lowest energy = -13.99731500476785
2025-10-27 14:14:56,117[DEBUG] isweep: 2
2025-10-27 14:14:56,117[DEBUG] compress config in current loop: 30, percent: 0
2025-10-27 14:14:56,119[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]
2025-10-27 14:14:56,121[DEBUG] optimize site: [0, 1]
2025-10-27 14:14:56,123[DEBUG] use direct eigensolver
2025-10-27 14:14:56,126[DEBUG] energy: -13.99731500446715
2025-10-27 14:14:56,127[DEBUG] optimize site: [1, 2]
2025-10-27 14:14:56,130[DEBUG] use direct eigensolver
2025-10-27 14:14:56,135[DEBUG] energy: -13.997315004467161
2025-10-27 14:14:56,138[DEBUG] optimize site: [2, 3]
2025-10-27 14:14:56,140[DEBUG] use direct eigensolver
2025-10-27 14:14:56,183[DEBUG] energy: -13.99731500446716
2025-10-27 14:14:56,186[DEBUG] optimize site: [3, 4]
2025-10-27 14:14:56,187[DEBUG] use direct eigensolver
2025-10-27 14:14:56,439[DEBUG] energy: -13.997315004467177
2025-10-27 14:14:56,442[DEBUG] optimize site: [4, 5]
2025-10-27 14:14:56,448[DEBUG] use davidson, HC hops: 4
2025-10-27 14:14:56,450[DEBUG] energy: -13.997315004767923
2025-10-27 14:14:56,454[DEBUG] optimize site: [5, 6]
2025-10-27 14:14:56,462[DEBUG] use davidson, HC hops: 4
2025-10-27 14:14:56,464[DEBUG] energy: -13.997315004667826
2025-10-27 14:14:56,467[DEBUG] optimize site: [6, 7]
2025-10-27 14:14:56,476[DEBUG] use davidson, HC hops: 6
2025-10-27 14:14:56,477[DEBUG] energy: -13.9973150124707
2025-10-27 14:14:56,481[DEBUG] optimize site: [7, 8]
2025-10-27 14:14:56,489[DEBUG] use davidson, HC hops: 5
2025-10-27 14:14:56,490[DEBUG] energy: -13.997315006066701
2025-10-27 14:14:56,494[DEBUG] optimize site: [8, 9]
2025-10-27 14:14:56,504[DEBUG] use davidson, HC hops: 7
2025-10-27 14:14:56,505[DEBUG] energy: -13.997315033374585
2025-10-27 14:14:56,509[DEBUG] optimize site: [9, 10]
2025-10-27 14:14:56,518[DEBUG] use davidson, HC hops: 6
2025-10-27 14:14:56,520[DEBUG] energy: -13.997315010122023
2025-10-27 14:14:56,523[DEBUG] optimize site: [10, 11]
2025-10-27 14:14:56,535[DEBUG] use davidson, HC hops: 8
2025-10-27 14:14:56,536[DEBUG] energy: -13.997315055776946
2025-10-27 14:14:56,540[DEBUG] optimize site: [11, 12]
2025-10-27 14:14:56,550[DEBUG] use davidson, HC hops: 7
2025-10-27 14:14:56,552[DEBUG] energy: -13.997315015890518
2025-10-27 14:14:56,555[DEBUG] optimize site: [12, 13]
2025-10-27 14:14:56,566[DEBUG] use davidson, HC hops: 8
2025-10-27 14:14:56,568[DEBUG] energy: -13.997315076759442
2025-10-27 14:14:56,571[DEBUG] optimize site: [13, 14]
2025-10-27 14:14:56,582[DEBUG] use davidson, HC hops: 7
2025-10-27 14:14:56,583[DEBUG] energy: -13.997315021063807
2025-10-27 14:14:56,587[DEBUG] optimize site: [14, 15]
2025-10-27 14:14:56,598[DEBUG] use davidson, HC hops: 8
2025-10-27 14:14:56,600[DEBUG] energy: -13.997315089163518
2025-10-27 14:14:56,603[DEBUG] optimize site: [15, 16]
2025-10-27 14:14:56,614[DEBUG] use davidson, HC hops: 8
2025-10-27 14:14:56,616[DEBUG] energy: -13.997315023237757
2025-10-27 14:14:56,619[DEBUG] optimize site: [16, 17]
2025-10-27 14:14:56,632[DEBUG] use davidson, HC hops: 9
2025-10-27 14:14:56,632[DEBUG] energy: -13.997315090211666
2025-10-27 14:14:56,637[DEBUG] optimize site: [17, 18]
2025-10-27 14:14:56,648[DEBUG] use davidson, HC hops: 8
2025-10-27 14:14:56,650[DEBUG] energy: -13.997315022014265
2025-10-27 14:14:56,653[DEBUG] optimize site: [18, 19]
2025-10-27 14:14:56,665[DEBUG] use davidson, HC hops: 8
2025-10-27 14:14:56,666[DEBUG] energy: -13.997315079212553
2025-10-27 14:14:56,670[DEBUG] optimize site: [19, 20]
2025-10-27 14:14:56,680[DEBUG] use davidson, HC hops: 7
2025-10-27 14:14:56,681[DEBUG] energy: -13.997315018389678
2025-10-27 14:14:56,685[DEBUG] optimize site: [20, 21]
2025-10-27 14:14:56,697[DEBUG] use davidson, HC hops: 8
2025-10-27 14:14:56,698[DEBUG] energy: -13.99731506047155
2025-10-27 14:14:56,702[DEBUG] optimize site: [21, 22]
2025-10-27 14:14:56,711[DEBUG] use davidson, HC hops: 6
2025-10-27 14:14:56,713[DEBUG] energy: -13.997315014222988
2025-10-27 14:14:56,716[DEBUG] optimize site: [22, 23]
2025-10-27 14:14:56,727[DEBUG] use davidson, HC hops: 8
2025-10-27 14:14:56,729[DEBUG] energy: -13.997315036380751
2025-10-27 14:14:56,732[DEBUG] optimize site: [23, 24]
2025-10-27 14:14:56,743[DEBUG] use davidson, HC hops: 6
2025-10-27 14:14:56,745[DEBUG] energy: -13.997315009063325
2025-10-27 14:14:56,750[DEBUG] optimize site: [24, 25]
2025-10-27 14:14:56,765[DEBUG] use davidson, HC hops: 6
2025-10-27 14:14:56,767[DEBUG] energy: -13.99731501543182
2025-10-27 14:14:56,772[DEBUG] optimize site: [25, 26]
2025-10-27 14:14:56,785[DEBUG] use davidson, HC hops: 5
2025-10-27 14:14:56,786[DEBUG] energy: -13.997315007630494
2025-10-27 14:14:56,790[DEBUG] optimize site: [26, 27]
2025-10-27 14:14:56,801[DEBUG] use davidson, HC hops: 4
2025-10-27 14:14:56,802[DEBUG] energy: -13.997315007727455
2025-10-27 14:14:56,804[DEBUG] optimize site: [27, 28]
2025-10-27 14:14:56,807[DEBUG] use direct eigensolver
2025-10-27 14:14:57,083[DEBUG] energy: -13.99731500742741
2025-10-27 14:14:57,085[DEBUG] optimize site: [28, 29]
2025-10-27 14:14:57,087[DEBUG] use direct eigensolver
2025-10-27 14:14:57,165[DEBUG] energy: -13.99731500742741
2025-10-27 14:14:57,167[DEBUG] optimize site: [29, 30]
2025-10-27 14:14:57,169[DEBUG] use direct eigensolver
2025-10-27 14:14:57,178[DEBUG] energy: -13.997315007427424
2025-10-27 14:14:57,180[DEBUG] optimize site: [30, 31]
2025-10-27 14:14:57,183[DEBUG] use direct eigensolver
2025-10-27 14:14:57,186[DEBUG] energy: -13.997315007427414
2025-10-27 14:14:57,188[DEBUG] 3 sweeps are finished, lowest energy = -13.997315090211666
2025-10-27 14:14:57,190[INFO] DMRG has converged!
2025-10-27 14:14:57,223[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: -13.997315090211666

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