3.1. Spin-1/2 1-D Heisenberg model#

3.1.1. 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

3.1.2. Setup#

[1]:

import sys
sys.path.append("..")
from renormalizer import Model, Op, BasisHalfSpin,  Mps, Mpo, optimize_mps

2022-10-17 10:49:35,719[INFO] Use NumPy as backend
2022-10-17 10:49:35,720[INFO] use 64 bits

3.1.3. 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}")

2022-10-17 10:49:35,757[DEBUG] # of operator terms: 93
2022-10-17 10:49:35,758[DEBUG] symbolic mpo algorithm: Hopcroft-Karp
2022-10-17 10:49:35,758[DEBUG] Input operator terms: 93
2022-10-17 10:49:35,774[DEBUG] After combination of the same terms: 93

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]

3.1.4. 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))

2022-10-17 10:49:35,922[INFO] optimization method: 2site
2022-10-17 10:49:35,923[INFO] e_rtol: 1e-06
2022-10-17 10:49:35,924[INFO] e_atol: 1e-08
2022-10-17 10:49:35,925[INFO] procedure: [[30, 0.2], [30, 0], [30, 0], [30, 0], [30, 0]]
2022-10-17 10:49:35,961[DEBUG] isweep: 0
2022-10-17 10:49:35,962[DEBUG] mmax, percent: 30, 0.2
2022-10-17 10:49:35,964[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]
2022-10-17 10:49:35,965[DEBUG] optimize site: [0, 1]
2022-10-17 10:49:35,966[DEBUG] use direct eigensolver
2022-10-17 10:49:35,969[DEBUG] energy: -0.8073391840594195
2022-10-17 10:49:35,971[DEBUG] optimize site: [1, 2]
2022-10-17 10:49:35,973[DEBUG] use direct eigensolver
2022-10-17 10:49:35,978[DEBUG] energy: -1.2378438263827487
2022-10-17 10:49:35,981[DEBUG] optimize site: [2, 3]
2022-10-17 10:49:35,983[DEBUG] use direct eigensolver
2022-10-17 10:49:36,003[DEBUG] energy: -2.065586315384646
2022-10-17 10:49:36,006[DEBUG] optimize site: [3, 4]
2022-10-17 10:49:36,008[DEBUG] use direct eigensolver
2022-10-17 10:49:36,300[DEBUG] energy: -2.8035001959542845
2022-10-17 10:49:36,304[DEBUG] optimize site: [4, 5]
2022-10-17 10:49:36,383[DEBUG] use davidson, HC hops: 54
2022-10-17 10:49:36,387[DEBUG] energy: -3.2163841920427214
2022-10-17 10:49:36,390[DEBUG] optimize site: [5, 6]
2022-10-17 10:49:36,532[DEBUG] use davidson, HC hops: 69
2022-10-17 10:49:36,534[DEBUG] energy: -3.6446356972958736
2022-10-17 10:49:36,539[DEBUG] optimize site: [6, 7]
2022-10-17 10:49:36,634[DEBUG] use davidson, HC hops: 49
2022-10-17 10:49:36,636[DEBUG] energy: -4.0418414411262145
2022-10-17 10:49:36,642[DEBUG] optimize site: [7, 8]
2022-10-17 10:49:36,744[DEBUG] use davidson, HC hops: 50
2022-10-17 10:49:36,745[DEBUG] energy: -4.488923472286727
2022-10-17 10:49:36,751[DEBUG] optimize site: [8, 9]
2022-10-17 10:49:36,850[DEBUG] use davidson, HC hops: 49
2022-10-17 10:49:36,852[DEBUG] energy: -4.956935755277623
2022-10-17 10:49:36,857[DEBUG] optimize site: [9, 10]
2022-10-17 10:49:36,928[DEBUG] use davidson, HC hops: 38
2022-10-17 10:49:36,930[DEBUG] energy: -5.490054650581115
2022-10-17 10:49:36,935[DEBUG] optimize site: [10, 11]
2022-10-17 10:49:37,011[DEBUG] use davidson, HC hops: 41
2022-10-17 10:49:37,013[DEBUG] energy: -5.89675718435792
2022-10-17 10:49:37,018[DEBUG] optimize site: [11, 12]
2022-10-17 10:49:37,126[DEBUG] use davidson, HC hops: 59
2022-10-17 10:49:37,128[DEBUG] energy: -6.249633133808622
2022-10-17 10:49:37,133[DEBUG] optimize site: [12, 13]
2022-10-17 10:49:37,260[DEBUG] use davidson, HC hops: 64
2022-10-17 10:49:37,262[DEBUG] energy: -6.718638326161754
2022-10-17 10:49:37,267[DEBUG] optimize site: [13, 14]
2022-10-17 10:49:37,364[DEBUG] use davidson, HC hops: 50
2022-10-17 10:49:37,366[DEBUG] energy: -7.245304399417776
2022-10-17 10:49:37,371[DEBUG] optimize site: [14, 15]
2022-10-17 10:49:37,491[DEBUG] use davidson, HC hops: 66
2022-10-17 10:49:37,493[DEBUG] energy: -7.597349342180755
2022-10-17 10:49:37,497[DEBUG] optimize site: [15, 16]
2022-10-17 10:49:37,622[DEBUG] use davidson, HC hops: 68
2022-10-17 10:49:37,624[DEBUG] energy: -8.066896786712524
2022-10-17 10:49:37,629[DEBUG] optimize site: [16, 17]
2022-10-17 10:49:37,701[DEBUG] use davidson, HC hops: 39
2022-10-17 10:49:37,702[DEBUG] energy: -8.552335896041239
2022-10-17 10:49:37,707[DEBUG] optimize site: [17, 18]
2022-10-17 10:49:37,789[DEBUG] use davidson, HC hops: 43
2022-10-17 10:49:37,791[DEBUG] energy: -8.988939917163737
2022-10-17 10:49:37,795[DEBUG] optimize site: [18, 19]
2022-10-17 10:49:37,877[DEBUG] use davidson, HC hops: 41
2022-10-17 10:49:37,879[DEBUG] energy: -9.42398765273249
2022-10-17 10:49:37,883[DEBUG] optimize site: [19, 20]
2022-10-17 10:49:38,009[DEBUG] use davidson, HC hops: 68
2022-10-17 10:49:38,011[DEBUG] energy: -9.87626593006492
2022-10-17 10:49:38,015[DEBUG] optimize site: [20, 21]
2022-10-17 10:49:38,118[DEBUG] use davidson, HC hops: 56
2022-10-17 10:49:38,120[DEBUG] energy: -10.303355863136929
2022-10-17 10:49:38,129[DEBUG] optimize site: [21, 22]
2022-10-17 10:49:38,259[DEBUG] use davidson, HC hops: 63
2022-10-17 10:49:38,261[DEBUG] energy: -10.927013460414075
2022-10-17 10:49:38,265[DEBUG] optimize site: [22, 23]
2022-10-17 10:49:38,407[DEBUG] use davidson, HC hops: 72
2022-10-17 10:49:38,409[DEBUG] energy: -11.407675015384815
2022-10-17 10:49:38,413[DEBUG] optimize site: [23, 24]
2022-10-17 10:49:38,549[DEBUG] use davidson, HC hops: 68
2022-10-17 10:49:38,550[DEBUG] energy: -12.142976645924087
2022-10-17 10:49:38,555[DEBUG] optimize site: [24, 25]
2022-10-17 10:49:38,690[DEBUG] use davidson, HC hops: 62
2022-10-17 10:49:38,692[DEBUG] energy: -12.906387175419352
2022-10-17 10:49:38,696[DEBUG] optimize site: [25, 26]
2022-10-17 10:49:38,817[DEBUG] use davidson, HC hops: 66
2022-10-17 10:49:38,819[DEBUG] energy: -13.791205715291149
2022-10-17 10:49:38,824[DEBUG] optimize site: [26, 27]
2022-10-17 10:49:38,899[DEBUG] use davidson, HC hops: 47
2022-10-17 10:49:38,900[DEBUG] energy: -13.996857596363366
2022-10-17 10:49:38,903[DEBUG] optimize site: [27, 28]
2022-10-17 10:49:38,907[DEBUG] use direct eigensolver
2022-10-17 10:49:39,210[DEBUG] energy: -13.996857596111939
2022-10-17 10:49:39,213[DEBUG] optimize site: [28, 29]
2022-10-17 10:49:39,217[DEBUG] use direct eigensolver
2022-10-17 10:49:39,280[DEBUG] energy: -13.996857596111937
2022-10-17 10:49:39,283[DEBUG] optimize site: [29, 30]
2022-10-17 10:49:39,285[DEBUG] use direct eigensolver
2022-10-17 10:49:39,292[DEBUG] energy: -13.996857596111928
2022-10-17 10:49:39,295[DEBUG] optimize site: [30, 31]
2022-10-17 10:49:39,296[DEBUG] use direct eigensolver
2022-10-17 10:49:39,300[DEBUG] energy: -13.996857596111921
2022-10-17 10:49:39,302[DEBUG] 1 sweeps are finished, lowest energy = -13.996857596363366
2022-10-17 10:49:39,303[DEBUG] isweep: 1
2022-10-17 10:49:39,304[DEBUG] mmax, percent: 30, 0
2022-10-17 10:49:39,305[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]
2022-10-17 10:49:39,306[DEBUG] optimize site: [30, 31]
2022-10-17 10:49:39,307[DEBUG] use direct eigensolver
2022-10-17 10:49:39,314[DEBUG] energy: -13.996857596111921
2022-10-17 10:49:39,316[DEBUG] optimize site: [29, 30]
2022-10-17 10:49:39,317[DEBUG] use direct eigensolver
2022-10-17 10:49:39,324[DEBUG] energy: -13.996857596111925
2022-10-17 10:49:39,327[DEBUG] optimize site: [28, 29]
2022-10-17 10:49:39,328[DEBUG] use direct eigensolver
2022-10-17 10:49:39,387[DEBUG] energy: -13.996857596111932
2022-10-17 10:49:39,390[DEBUG] optimize site: [27, 28]
2022-10-17 10:49:39,392[DEBUG] use direct eigensolver
2022-10-17 10:49:39,691[DEBUG] energy: -13.99685759611191
2022-10-17 10:49:39,694[DEBUG] optimize site: [26, 27]
2022-10-17 10:49:39,704[DEBUG] use davidson, HC hops: 4
2022-10-17 10:49:39,709[DEBUG] energy: -13.996857596364485
2022-10-17 10:49:39,717[DEBUG] optimize site: [25, 26]
2022-10-17 10:49:39,764[DEBUG] use davidson, HC hops: 24
2022-10-17 10:49:39,765[DEBUG] energy: -13.996931300004633
2022-10-17 10:49:39,770[DEBUG] optimize site: [24, 25]
2022-10-17 10:49:39,820[DEBUG] use davidson, HC hops: 26
2022-10-17 10:49:39,821[DEBUG] energy: -13.997084885060907
2022-10-17 10:49:39,826[DEBUG] optimize site: [23, 24]
2022-10-17 10:49:39,873[DEBUG] use davidson, HC hops: 24
2022-10-17 10:49:39,875[DEBUG] energy: -13.997140925987665
2022-10-17 10:49:39,880[DEBUG] optimize site: [22, 23]
2022-10-17 10:49:39,923[DEBUG] use davidson, HC hops: 22
2022-10-17 10:49:39,925[DEBUG] energy: -13.99714684097836
2022-10-17 10:49:39,930[DEBUG] optimize site: [21, 22]
2022-10-17 10:49:39,978[DEBUG] use davidson, HC hops: 25
2022-10-17 10:49:39,980[DEBUG] energy: -13.997251484367938
2022-10-17 10:49:39,985[DEBUG] optimize site: [20, 21]
2022-10-17 10:49:40,043[DEBUG] use davidson, HC hops: 19
2022-10-17 10:49:40,045[DEBUG] energy: -13.99725421273916
2022-10-17 10:49:40,050[DEBUG] optimize site: [19, 20]
2022-10-17 10:49:40,092[DEBUG] use davidson, HC hops: 21
2022-10-17 10:49:40,094[DEBUG] energy: -13.99726162234515
2022-10-17 10:49:40,098[DEBUG] optimize site: [18, 19]
2022-10-17 10:49:40,159[DEBUG] use davidson, HC hops: 21
2022-10-17 10:49:40,161[DEBUG] energy: -13.997272638116684
2022-10-17 10:49:40,166[DEBUG] optimize site: [17, 18]
2022-10-17 10:49:40,209[DEBUG] use davidson, HC hops: 22
2022-10-17 10:49:40,211[DEBUG] energy: -13.997283940670506
2022-10-17 10:49:40,215[DEBUG] optimize site: [16, 17]
2022-10-17 10:49:40,262[DEBUG] use davidson, HC hops: 20
2022-10-17 10:49:40,264[DEBUG] energy: -13.99728858850194
2022-10-17 10:49:40,268[DEBUG] optimize site: [15, 16]
2022-10-17 10:49:40,305[DEBUG] use davidson, HC hops: 18
2022-10-17 10:49:40,306[DEBUG] energy: -13.997289651804854
2022-10-17 10:49:40,311[DEBUG] optimize site: [14, 15]
2022-10-17 10:49:40,356[DEBUG] use davidson, HC hops: 22
2022-10-17 10:49:40,358[DEBUG] energy: -13.997305007295127
2022-10-17 10:49:40,362[DEBUG] optimize site: [13, 14]
2022-10-17 10:49:40,401[DEBUG] use davidson, HC hops: 20
2022-10-17 10:49:40,402[DEBUG] energy: -13.997307678387184
2022-10-17 10:49:40,407[DEBUG] optimize site: [12, 13]
2022-10-17 10:49:40,445[DEBUG] use davidson, HC hops: 19
2022-10-17 10:49:40,446[DEBUG] energy: -13.99730959587647
2022-10-17 10:49:40,450[DEBUG] optimize site: [11, 12]
2022-10-17 10:49:40,475[DEBUG] use davidson, HC hops: 11
2022-10-17 10:49:40,477[DEBUG] energy: -13.99730984752172
2022-10-17 10:49:40,481[DEBUG] optimize site: [10, 11]
2022-10-17 10:49:40,519[DEBUG] use davidson, HC hops: 19
2022-10-17 10:49:40,520[DEBUG] energy: -13.99731260922455
2022-10-17 10:49:40,525[DEBUG] optimize site: [9, 10]
2022-10-17 10:49:40,560[DEBUG] use davidson, HC hops: 17
2022-10-17 10:49:40,561[DEBUG] energy: -13.997314296846293
2022-10-17 10:49:40,566[DEBUG] optimize site: [8, 9]
2022-10-17 10:49:40,595[DEBUG] use davidson, HC hops: 14
2022-10-17 10:49:40,597[DEBUG] energy: -13.997314812575468
2022-10-17 10:49:40,601[DEBUG] optimize site: [7, 8]
2022-10-17 10:49:40,622[DEBUG] use davidson, HC hops: 9
2022-10-17 10:49:40,623[DEBUG] energy: -13.99731485681045
2022-10-17 10:49:40,627[DEBUG] optimize site: [6, 7]
2022-10-17 10:49:40,647[DEBUG] use davidson, HC hops: 9
2022-10-17 10:49:40,648[DEBUG] energy: -13.997314972270468
2022-10-17 10:49:40,653[DEBUG] optimize site: [5, 6]
2022-10-17 10:49:40,675[DEBUG] use davidson, HC hops: 8
2022-10-17 10:49:40,677[DEBUG] energy: -13.997315001780015
2022-10-17 10:49:40,690[DEBUG] optimize site: [4, 5]
2022-10-17 10:49:40,701[DEBUG] use davidson, HC hops: 5
2022-10-17 10:49:40,703[DEBUG] energy: -13.99731500527319
2022-10-17 10:49:40,705[DEBUG] optimize site: [3, 4]
2022-10-17 10:49:40,709[DEBUG] use direct eigensolver
2022-10-17 10:49:41,019[DEBUG] energy: -13.997315004973514
2022-10-17 10:49:41,023[DEBUG] optimize site: [2, 3]
2022-10-17 10:49:41,027[DEBUG] use direct eigensolver
2022-10-17 10:49:41,088[DEBUG] energy: -13.997315004973506
2022-10-17 10:49:41,092[DEBUG] optimize site: [1, 2]
2022-10-17 10:49:41,093[DEBUG] use direct eigensolver
2022-10-17 10:49:41,101[DEBUG] energy: -13.997315004973471
2022-10-17 10:49:41,103[DEBUG] optimize site: [0, 1]
2022-10-17 10:49:41,105[DEBUG] use direct eigensolver
2022-10-17 10:49:41,108[DEBUG] energy: -13.997315004973464
2022-10-17 10:49:41,110[DEBUG] 2 sweeps are finished, lowest energy = -13.99731500527319
2022-10-17 10:49:41,111[DEBUG] isweep: 2
2022-10-17 10:49:41,112[DEBUG] mmax, percent: 30, 0
2022-10-17 10:49:41,114[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]
2022-10-17 10:49:41,115[DEBUG] optimize site: [0, 1]
2022-10-17 10:49:41,116[DEBUG] use direct eigensolver
2022-10-17 10:49:41,121[DEBUG] energy: -13.997315004973464
2022-10-17 10:49:41,123[DEBUG] optimize site: [1, 2]
2022-10-17 10:49:41,125[DEBUG] use direct eigensolver
2022-10-17 10:49:41,133[DEBUG] energy: -13.997315004973474
2022-10-17 10:49:41,136[DEBUG] optimize site: [2, 3]
2022-10-17 10:49:41,137[DEBUG] use direct eigensolver
2022-10-17 10:49:41,195[DEBUG] energy: -13.997315004973483
2022-10-17 10:49:41,198[DEBUG] optimize site: [3, 4]
2022-10-17 10:49:41,199[DEBUG] use direct eigensolver
2022-10-17 10:49:41,531[DEBUG] energy: -13.997315004973492
2022-10-17 10:49:41,535[DEBUG] optimize site: [4, 5]
2022-10-17 10:49:41,546[DEBUG] use davidson, HC hops: 4
2022-10-17 10:49:41,550[DEBUG] energy: -13.997315005273315
2022-10-17 10:49:41,559[DEBUG] optimize site: [5, 6]
2022-10-17 10:49:41,569[DEBUG] use davidson, HC hops: 4
2022-10-17 10:49:41,570[DEBUG] energy: -13.997315005173007
2022-10-17 10:49:41,575[DEBUG] optimize site: [6, 7]
2022-10-17 10:49:41,590[DEBUG] use davidson, HC hops: 6
2022-10-17 10:49:41,591[DEBUG] energy: -13.997315012977305
2022-10-17 10:49:41,596[DEBUG] optimize site: [7, 8]
2022-10-17 10:49:41,609[DEBUG] use davidson, HC hops: 5
2022-10-17 10:49:41,610[DEBUG] energy: -13.997315006591329
2022-10-17 10:49:41,615[DEBUG] optimize site: [8, 9]
2022-10-17 10:49:41,631[DEBUG] use davidson, HC hops: 7
2022-10-17 10:49:41,632[DEBUG] energy: -13.997315033903927
2022-10-17 10:49:41,637[DEBUG] optimize site: [9, 10]
2022-10-17 10:49:41,651[DEBUG] use davidson, HC hops: 6
2022-10-17 10:49:41,652[DEBUG] energy: -13.997315010652088
2022-10-17 10:49:41,657[DEBUG] optimize site: [10, 11]
2022-10-17 10:49:41,674[DEBUG] use davidson, HC hops: 8
2022-10-17 10:49:41,675[DEBUG] energy: -13.997315056387109
2022-10-17 10:49:41,680[DEBUG] optimize site: [11, 12]
2022-10-17 10:49:41,696[DEBUG] use davidson, HC hops: 7
2022-10-17 10:49:41,697[DEBUG] energy: -13.997315016514136
2022-10-17 10:49:41,702[DEBUG] optimize site: [12, 13]
2022-10-17 10:49:41,719[DEBUG] use davidson, HC hops: 8
2022-10-17 10:49:41,721[DEBUG] energy: -13.997315077230738
2022-10-17 10:49:41,725[DEBUG] optimize site: [13, 14]
2022-10-17 10:49:41,743[DEBUG] use davidson, HC hops: 7
2022-10-17 10:49:41,744[DEBUG] energy: -13.99731502162283
2022-10-17 10:49:41,749[DEBUG] optimize site: [14, 15]
2022-10-17 10:49:41,766[DEBUG] use davidson, HC hops: 8
2022-10-17 10:49:41,768[DEBUG] energy: -13.997315090022743
2022-10-17 10:49:41,772[DEBUG] optimize site: [15, 16]
2022-10-17 10:49:41,790[DEBUG] use davidson, HC hops: 8
2022-10-17 10:49:41,791[DEBUG] energy: -13.997315023830005
2022-10-17 10:49:41,796[DEBUG] optimize site: [16, 17]
2022-10-17 10:49:41,813[DEBUG] use davidson, HC hops: 8
2022-10-17 10:49:41,815[DEBUG] energy: -13.99731509007019
2022-10-17 10:49:41,819[DEBUG] optimize site: [17, 18]
2022-10-17 10:49:41,843[DEBUG] use davidson, HC hops: 7
2022-10-17 10:49:41,845[DEBUG] energy: -13.997315022157295
2022-10-17 10:49:41,850[DEBUG] optimize site: [18, 19]
2022-10-17 10:49:41,868[DEBUG] use davidson, HC hops: 8
2022-10-17 10:49:41,869[DEBUG] energy: -13.997315079298344
2022-10-17 10:49:41,873[DEBUG] optimize site: [19, 20]
2022-10-17 10:49:41,890[DEBUG] use davidson, HC hops: 7
2022-10-17 10:49:41,892[DEBUG] energy: -13.997315018182011
2022-10-17 10:49:41,896[DEBUG] optimize site: [20, 21]
2022-10-17 10:49:41,914[DEBUG] use davidson, HC hops: 8
2022-10-17 10:49:41,916[DEBUG] energy: -13.997315059814827
2022-10-17 10:49:41,922[DEBUG] optimize site: [21, 22]
2022-10-17 10:49:41,943[DEBUG] use davidson, HC hops: 6
2022-10-17 10:49:41,945[DEBUG] energy: -13.99731501354093
2022-10-17 10:49:41,949[DEBUG] optimize site: [22, 23]
2022-10-17 10:49:41,967[DEBUG] use davidson, HC hops: 8
2022-10-17 10:49:41,968[DEBUG] energy: -13.997315036297948
2022-10-17 10:49:41,972[DEBUG] optimize site: [23, 24]
2022-10-17 10:49:41,985[DEBUG] use davidson, HC hops: 5
2022-10-17 10:49:41,986[DEBUG] energy: -13.997315009008041
2022-10-17 10:49:41,991[DEBUG] optimize site: [24, 25]
2022-10-17 10:49:42,005[DEBUG] use davidson, HC hops: 6
2022-10-17 10:49:42,007[DEBUG] energy: -13.997315015408876
2022-10-17 10:49:42,011[DEBUG] optimize site: [25, 26]
2022-10-17 10:49:42,024[DEBUG] use davidson, HC hops: 5
2022-10-17 10:49:42,026[DEBUG] energy: -13.997315007616416
2022-10-17 10:49:42,030[DEBUG] optimize site: [26, 27]
2022-10-17 10:49:42,044[DEBUG] use davidson, HC hops: 4
2022-10-17 10:49:42,045[DEBUG] energy: -13.997315007714352
2022-10-17 10:49:42,048[DEBUG] optimize site: [27, 28]
2022-10-17 10:49:42,051[DEBUG] use direct eigensolver
2022-10-17 10:49:42,382[DEBUG] energy: -13.997315007414704
2022-10-17 10:49:42,387[DEBUG] optimize site: [28, 29]
2022-10-17 10:49:42,391[DEBUG] use direct eigensolver
2022-10-17 10:49:42,453[DEBUG] energy: -13.997315007414716
2022-10-17 10:49:42,456[DEBUG] optimize site: [29, 30]
2022-10-17 10:49:42,458[DEBUG] use direct eigensolver
2022-10-17 10:49:42,466[DEBUG] energy: -13.99731500741472
2022-10-17 10:49:42,468[DEBUG] optimize site: [30, 31]
2022-10-17 10:49:42,470[DEBUG] use direct eigensolver
2022-10-17 10:49:42,473[DEBUG] energy: -13.997315007414732
2022-10-17 10:49:42,475[DEBUG] 3 sweeps are finished, lowest energy = -13.99731509007019
2022-10-17 10:49:42,477[INFO] DMRG has converged!
2022-10-17 10:49:42,523[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: -13.99731509007019

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