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

2024-11-19 03:14:04,130[INFO] Use NumPy as backend
2024-11-19 03:14:04,131[INFO] numpy random seed is 9012
2024-11-19 03:14:04,131[INFO] random seed is 1092
2024-11-19 03:14:04,142[INFO] Git Commit Hash: 5d9832501dbae153174503f00b3479337588b7f1
2024-11-19 03:14:04,143[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}")

2024-11-19 03:14:04,240[DEBUG] # of operator terms: 93
2024-11-19 03:14:04,241[DEBUG] Input operator terms: 93
2024-11-19 03:14:04,243[DEBUG] After combination of the same terms: 93
2024-11-19 03:14:04,243[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))

2024-11-19 03:14:04,313[INFO] optimization method: 2site
2024-11-19 03:14:04,313[INFO] e_rtol: 1e-06
2024-11-19 03:14:04,314[INFO] e_atol: 1e-08
2024-11-19 03:14:04,315[INFO] procedure: [[30, 0.2], [30, 0], [30, 0], [30, 0], [30, 0]]
2024-11-19 03:14:04,347[DEBUG] isweep: 0
2024-11-19 03:14:04,347[DEBUG] compress config in current loop: 30, percent: 0.2
2024-11-19 03:14:04,348[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]
2024-11-19 03:14:04,349[DEBUG] optimize site: [0, 1]
2024-11-19 03:14:04,350[DEBUG] use direct eigensolver
2024-11-19 03:14:04,352[DEBUG] energy: -0.9279990226898331
2024-11-19 03:14:04,353[DEBUG] optimize site: [1, 2]
2024-11-19 03:14:04,354[DEBUG] use direct eigensolver
2024-11-19 03:14:04,357[DEBUG] energy: -1.284089573410534
2024-11-19 03:14:04,359[DEBUG] optimize site: [2, 3]
2024-11-19 03:14:04,361[DEBUG] use direct eigensolver
2024-11-19 03:14:04,384[DEBUG] energy: -2.0857452647499213
2024-11-19 03:14:04,386[DEBUG] optimize site: [3, 4]
2024-11-19 03:14:04,387[DEBUG] use direct eigensolver
2024-11-19 03:14:04,642[DEBUG] energy: -2.8158895272374123
2024-11-19 03:14:04,645[DEBUG] optimize site: [4, 5]
2024-11-19 03:14:04,701[DEBUG] use davidson, HC hops: 34
2024-11-19 03:14:04,702[DEBUG] energy: -3.293367315585802
2024-11-19 03:14:04,704[DEBUG] optimize site: [5, 6]
2024-11-19 03:14:04,780[DEBUG] use davidson, HC hops: 42
2024-11-19 03:14:04,781[DEBUG] energy: -3.744986750307201
2024-11-19 03:14:04,791[DEBUG] optimize site: [6, 7]
2024-11-19 03:14:04,870[DEBUG] use davidson, HC hops: 42
2024-11-19 03:14:04,872[DEBUG] energy: -4.176385575496492
2024-11-19 03:14:04,877[DEBUG] optimize site: [7, 8]
2024-11-19 03:14:04,957[DEBUG] use davidson, HC hops: 44
2024-11-19 03:14:04,959[DEBUG] energy: -4.583593477927389
2024-11-19 03:14:04,970[DEBUG] optimize site: [8, 9]
2024-11-19 03:14:05,070[DEBUG] use davidson, HC hops: 55
2024-11-19 03:14:05,072[DEBUG] energy: -4.9680318456712
2024-11-19 03:14:05,077[DEBUG] optimize site: [9, 10]
2024-11-19 03:14:05,199[DEBUG] use davidson, HC hops: 68
2024-11-19 03:14:05,201[DEBUG] energy: -5.414706360833991
2024-11-19 03:14:05,212[DEBUG] optimize site: [10, 11]
2024-11-19 03:14:05,342[DEBUG] use davidson, HC hops: 72
2024-11-19 03:14:05,345[DEBUG] energy: -5.856529754520475
2024-11-19 03:14:05,356[DEBUG] optimize site: [11, 12]
2024-11-19 03:14:05,539[DEBUG] use davidson, HC hops: 100
2024-11-19 03:14:05,541[DEBUG] energy: -6.27902246729581
2024-11-19 03:14:05,546[DEBUG] optimize site: [12, 13]
2024-11-19 03:14:05,643[DEBUG] use davidson, HC hops: 52
2024-11-19 03:14:05,645[DEBUG] energy: -6.85738901220476
2024-11-19 03:14:05,649[DEBUG] optimize site: [13, 14]
2024-11-19 03:14:05,823[DEBUG] use davidson, HC hops: 100
2024-11-19 03:14:05,825[DEBUG] energy: -7.1145880220057665
2024-11-19 03:14:05,830[DEBUG] optimize site: [14, 15]
2024-11-19 03:14:05,919[DEBUG] use davidson, HC hops: 47
2024-11-19 03:14:05,921[DEBUG] energy: -7.641631783835399
2024-11-19 03:14:05,925[DEBUG] optimize site: [15, 16]
2024-11-19 03:14:06,023[DEBUG] use davidson, HC hops: 51
2024-11-19 03:14:06,026[DEBUG] energy: -8.11839533842003
2024-11-19 03:14:06,030[DEBUG] optimize site: [16, 17]
2024-11-19 03:14:06,133[DEBUG] use davidson, HC hops: 57
2024-11-19 03:14:06,135[DEBUG] energy: -8.579533430762853
2024-11-19 03:14:06,140[DEBUG] optimize site: [17, 18]
2024-11-19 03:14:06,257[DEBUG] use davidson, HC hops: 66
2024-11-19 03:14:06,259[DEBUG] energy: -8.983113190158477
2024-11-19 03:14:06,263[DEBUG] optimize site: [18, 19]
2024-11-19 03:14:06,377[DEBUG] use davidson, HC hops: 62
2024-11-19 03:14:06,379[DEBUG] energy: -9.422205404607668
2024-11-19 03:14:06,389[DEBUG] optimize site: [19, 20]
2024-11-19 03:14:06,501[DEBUG] use davidson, HC hops: 62
2024-11-19 03:14:06,503[DEBUG] energy: -9.903693680914406
2024-11-19 03:14:06,508[DEBUG] optimize site: [20, 21]
2024-11-19 03:14:06,655[DEBUG] use davidson, HC hops: 81
2024-11-19 03:14:06,657[DEBUG] energy: -10.398530611697982
2024-11-19 03:14:06,662[DEBUG] optimize site: [21, 22]
2024-11-19 03:14:06,798[DEBUG] use davidson, HC hops: 76
2024-11-19 03:14:06,800[DEBUG] energy: -10.834489434421698
2024-11-19 03:14:06,804[DEBUG] optimize site: [22, 23]
2024-11-19 03:14:06,906[DEBUG] use davidson, HC hops: 58
2024-11-19 03:14:06,908[DEBUG] energy: -11.415128707126836
2024-11-19 03:14:06,912[DEBUG] optimize site: [23, 24]
2024-11-19 03:14:07,001[DEBUG] use davidson, HC hops: 52
2024-11-19 03:14:07,002[DEBUG] energy: -12.12279587974509
2024-11-19 03:14:07,005[DEBUG] optimize site: [24, 25]
2024-11-19 03:14:07,141[DEBUG] use davidson, HC hops: 71
2024-11-19 03:14:07,142[DEBUG] energy: -12.812234874023513
2024-11-19 03:14:07,146[DEBUG] optimize site: [25, 26]
2024-11-19 03:14:07,246[DEBUG] use davidson, HC hops: 58
2024-11-19 03:14:07,248[DEBUG] energy: -13.774582804126688
2024-11-19 03:14:07,252[DEBUG] optimize site: [26, 27]
2024-11-19 03:14:07,327[DEBUG] use davidson, HC hops: 47
2024-11-19 03:14:07,328[DEBUG] energy: -13.996832655813112
2024-11-19 03:14:07,330[DEBUG] optimize site: [27, 28]
2024-11-19 03:14:07,332[DEBUG] use direct eigensolver
2024-11-19 03:14:07,648[DEBUG] energy: -13.996832655534027
2024-11-19 03:14:07,651[DEBUG] optimize site: [28, 29]
2024-11-19 03:14:07,653[DEBUG] use direct eigensolver
2024-11-19 03:14:07,700[DEBUG] energy: -13.996832655534037
2024-11-19 03:14:07,703[DEBUG] optimize site: [29, 30]
2024-11-19 03:14:07,705[DEBUG] use direct eigensolver
2024-11-19 03:14:07,710[DEBUG] energy: -13.996832655534016
2024-11-19 03:14:07,713[DEBUG] optimize site: [30, 31]
2024-11-19 03:14:07,714[DEBUG] use direct eigensolver
2024-11-19 03:14:07,717[DEBUG] energy: -13.996832655534018
2024-11-19 03:14:07,720[DEBUG] 1 sweeps are finished, lowest energy = -13.996832655813112
2024-11-19 03:14:07,721[DEBUG] isweep: 1
2024-11-19 03:14:07,723[DEBUG] compress config in current loop: 30, percent: 0
2024-11-19 03:14:07,725[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]
2024-11-19 03:14:07,726[DEBUG] optimize site: [30, 31]
2024-11-19 03:14:07,728[DEBUG] use direct eigensolver
2024-11-19 03:14:07,731[DEBUG] energy: -13.996832655534018
2024-11-19 03:14:07,733[DEBUG] optimize site: [29, 30]
2024-11-19 03:14:07,735[DEBUG] use direct eigensolver
2024-11-19 03:14:07,740[DEBUG] energy: -13.996832655534025
2024-11-19 03:14:07,743[DEBUG] optimize site: [28, 29]
2024-11-19 03:14:07,744[DEBUG] use direct eigensolver
2024-11-19 03:14:07,787[DEBUG] energy: -13.996832655534028
2024-11-19 03:14:07,790[DEBUG] optimize site: [27, 28]
2024-11-19 03:14:07,792[DEBUG] use direct eigensolver
2024-11-19 03:14:08,030[DEBUG] energy: -13.99683265553402
2024-11-19 03:14:08,033[DEBUG] optimize site: [26, 27]
2024-11-19 03:14:08,039[DEBUG] use davidson, HC hops: 4
2024-11-19 03:14:08,041[DEBUG] energy: -13.996832655813675
2024-11-19 03:14:08,046[DEBUG] optimize site: [25, 26]
2024-11-19 03:14:08,068[DEBUG] use davidson, HC hops: 22
2024-11-19 03:14:08,070[DEBUG] energy: -13.996844945038402
2024-11-19 03:14:08,073[DEBUG] optimize site: [24, 25]
2024-11-19 03:14:08,101[DEBUG] use davidson, HC hops: 28
2024-11-19 03:14:08,102[DEBUG] energy: -13.997067101658809
2024-11-19 03:14:08,106[DEBUG] optimize site: [23, 24]
2024-11-19 03:14:08,131[DEBUG] use davidson, HC hops: 25
2024-11-19 03:14:08,133[DEBUG] energy: -13.997101684717578
2024-11-19 03:14:08,136[DEBUG] optimize site: [22, 23]
2024-11-19 03:14:08,162[DEBUG] use davidson, HC hops: 23
2024-11-19 03:14:08,164[DEBUG] energy: -13.99710660821378
2024-11-19 03:14:08,168[DEBUG] optimize site: [21, 22]
2024-11-19 03:14:08,202[DEBUG] use davidson, HC hops: 23
2024-11-19 03:14:08,204[DEBUG] energy: -13.997113698271193
2024-11-19 03:14:08,210[DEBUG] optimize site: [20, 21]
2024-11-19 03:14:08,237[DEBUG] use davidson, HC hops: 26
2024-11-19 03:14:08,239[DEBUG] energy: -13.997162638323632
2024-11-19 03:14:08,242[DEBUG] optimize site: [19, 20]
2024-11-19 03:14:08,268[DEBUG] use davidson, HC hops: 23
2024-11-19 03:14:08,269[DEBUG] energy: -13.997170144965615
2024-11-19 03:14:08,273[DEBUG] optimize site: [18, 19]
2024-11-19 03:14:08,302[DEBUG] use davidson, HC hops: 26
2024-11-19 03:14:08,304[DEBUG] energy: -13.997199975427458
2024-11-19 03:14:08,309[DEBUG] optimize site: [17, 18]
2024-11-19 03:14:08,350[DEBUG] use davidson, HC hops: 22
2024-11-19 03:14:08,353[DEBUG] energy: -13.997204392621663
2024-11-19 03:14:08,358[DEBUG] optimize site: [16, 17]
2024-11-19 03:14:08,404[DEBUG] use davidson, HC hops: 25
2024-11-19 03:14:08,406[DEBUG] energy: -13.997225037523844
2024-11-19 03:14:08,411[DEBUG] optimize site: [15, 16]
2024-11-19 03:14:08,458[DEBUG] use davidson, HC hops: 26
2024-11-19 03:14:08,459[DEBUG] energy: -13.997284918121196
2024-11-19 03:14:08,462[DEBUG] optimize site: [14, 15]
2024-11-19 03:14:08,500[DEBUG] use davidson, HC hops: 22
2024-11-19 03:14:08,502[DEBUG] energy: -13.997290859971265
2024-11-19 03:14:08,505[DEBUG] optimize site: [13, 14]
2024-11-19 03:14:08,527[DEBUG] use davidson, HC hops: 20
2024-11-19 03:14:08,528[DEBUG] energy: -13.997293257653812
2024-11-19 03:14:08,532[DEBUG] optimize site: [12, 13]
2024-11-19 03:14:08,564[DEBUG] use davidson, HC hops: 23
2024-11-19 03:14:08,565[DEBUG] energy: -13.997306225086701
2024-11-19 03:14:08,569[DEBUG] optimize site: [11, 12]
2024-11-19 03:14:08,608[DEBUG] use davidson, HC hops: 21
2024-11-19 03:14:08,609[DEBUG] energy: -13.997311145595656
2024-11-19 03:14:08,613[DEBUG] optimize site: [10, 11]
2024-11-19 03:14:08,649[DEBUG] use davidson, HC hops: 20
2024-11-19 03:14:08,650[DEBUG] energy: -13.997313132707532
2024-11-19 03:14:08,654[DEBUG] optimize site: [9, 10]
2024-11-19 03:14:08,681[DEBUG] use davidson, HC hops: 17
2024-11-19 03:14:08,683[DEBUG] energy: -13.997314428626403
2024-11-19 03:14:08,686[DEBUG] optimize site: [8, 9]
2024-11-19 03:14:08,700[DEBUG] use davidson, HC hops: 11
2024-11-19 03:14:08,702[DEBUG] energy: -13.99731471546873
2024-11-19 03:14:08,705[DEBUG] optimize site: [7, 8]
2024-11-19 03:14:08,715[DEBUG] use davidson, HC hops: 7
2024-11-19 03:14:08,716[DEBUG] energy: -13.997314712669821
2024-11-19 03:14:08,720[DEBUG] optimize site: [6, 7]
2024-11-19 03:14:08,734[DEBUG] use davidson, HC hops: 12
2024-11-19 03:14:08,736[DEBUG] energy: -13.997314999750081
2024-11-19 03:14:08,739[DEBUG] optimize site: [5, 6]
2024-11-19 03:14:08,749[DEBUG] use davidson, HC hops: 7
2024-11-19 03:14:08,750[DEBUG] energy: -13.997315003811494
2024-11-19 03:14:08,754[DEBUG] optimize site: [4, 5]
2024-11-19 03:14:08,762[DEBUG] use davidson, HC hops: 5
2024-11-19 03:14:08,764[DEBUG] energy: -13.997315004767811
2024-11-19 03:14:08,768[DEBUG] optimize site: [3, 4]
2024-11-19 03:14:08,770[DEBUG] use direct eigensolver
2024-11-19 03:14:09,027[DEBUG] energy: -13.997315004467138
2024-11-19 03:14:09,030[DEBUG] optimize site: [2, 3]
2024-11-19 03:14:09,033[DEBUG] use direct eigensolver
2024-11-19 03:14:09,079[DEBUG] energy: -13.997315004467104
2024-11-19 03:14:09,082[DEBUG] optimize site: [1, 2]
2024-11-19 03:14:09,084[DEBUG] use direct eigensolver
2024-11-19 03:14:09,089[DEBUG] energy: -13.997315004467113
2024-11-19 03:14:09,092[DEBUG] optimize site: [0, 1]
2024-11-19 03:14:09,093[DEBUG] use direct eigensolver
2024-11-19 03:14:09,097[DEBUG] energy: -13.997315004467115
2024-11-19 03:14:09,099[DEBUG] 2 sweeps are finished, lowest energy = -13.997315004767811
2024-11-19 03:14:09,102[DEBUG] isweep: 2
2024-11-19 03:14:09,103[DEBUG] compress config in current loop: 30, percent: 0
2024-11-19 03:14:09,105[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]
2024-11-19 03:14:09,107[DEBUG] optimize site: [0, 1]
2024-11-19 03:14:09,109[DEBUG] use direct eigensolver
2024-11-19 03:14:09,112[DEBUG] energy: -13.997315004467115
2024-11-19 03:14:09,115[DEBUG] optimize site: [1, 2]
2024-11-19 03:14:09,117[DEBUG] use direct eigensolver
2024-11-19 03:14:09,124[DEBUG] energy: -13.997315004467115
2024-11-19 03:14:09,126[DEBUG] optimize site: [2, 3]
2024-11-19 03:14:09,128[DEBUG] use direct eigensolver
2024-11-19 03:14:09,171[DEBUG] energy: -13.99731500446711
2024-11-19 03:14:09,174[DEBUG] optimize site: [3, 4]
2024-11-19 03:14:09,176[DEBUG] use direct eigensolver
2024-11-19 03:14:09,421[DEBUG] energy: -13.99731500446713
2024-11-19 03:14:09,425[DEBUG] optimize site: [4, 5]
2024-11-19 03:14:09,430[DEBUG] use davidson, HC hops: 4
2024-11-19 03:14:09,432[DEBUG] energy: -13.997315004767882
2024-11-19 03:14:09,436[DEBUG] optimize site: [5, 6]
2024-11-19 03:14:09,443[DEBUG] use davidson, HC hops: 4
2024-11-19 03:14:09,445[DEBUG] energy: -13.997315004667787
2024-11-19 03:14:09,448[DEBUG] optimize site: [6, 7]
2024-11-19 03:14:09,456[DEBUG] use davidson, HC hops: 6
2024-11-19 03:14:09,458[DEBUG] energy: -13.9973150124707
2024-11-19 03:14:09,461[DEBUG] optimize site: [7, 8]
2024-11-19 03:14:09,468[DEBUG] use davidson, HC hops: 5
2024-11-19 03:14:09,470[DEBUG] energy: -13.997315006066689
2024-11-19 03:14:09,473[DEBUG] optimize site: [8, 9]
2024-11-19 03:14:09,482[DEBUG] use davidson, HC hops: 7
2024-11-19 03:14:09,483[DEBUG] energy: -13.997315033374585
2024-11-19 03:14:09,488[DEBUG] optimize site: [9, 10]
2024-11-19 03:14:09,496[DEBUG] use davidson, HC hops: 6
2024-11-19 03:14:09,497[DEBUG] energy: -13.997315010122
2024-11-19 03:14:09,501[DEBUG] optimize site: [10, 11]
2024-11-19 03:14:09,511[DEBUG] use davidson, HC hops: 8
2024-11-19 03:14:09,512[DEBUG] energy: -13.997315055776903
2024-11-19 03:14:09,515[DEBUG] optimize site: [11, 12]
2024-11-19 03:14:09,524[DEBUG] use davidson, HC hops: 7
2024-11-19 03:14:09,526[DEBUG] energy: -13.997315015890504
2024-11-19 03:14:09,529[DEBUG] optimize site: [12, 13]
2024-11-19 03:14:09,539[DEBUG] use davidson, HC hops: 8
2024-11-19 03:14:09,541[DEBUG] energy: -13.99731507675942
2024-11-19 03:14:09,544[DEBUG] optimize site: [13, 14]
2024-11-19 03:14:09,553[DEBUG] use davidson, HC hops: 7
2024-11-19 03:14:09,555[DEBUG] energy: -13.99731502106376
2024-11-19 03:14:09,558[DEBUG] optimize site: [14, 15]
2024-11-19 03:14:09,568[DEBUG] use davidson, HC hops: 8
2024-11-19 03:14:09,569[DEBUG] energy: -13.997315089163486
2024-11-19 03:14:09,573[DEBUG] optimize site: [15, 16]
2024-11-19 03:14:09,583[DEBUG] use davidson, HC hops: 8
2024-11-19 03:14:09,584[DEBUG] energy: -13.997315023237704
2024-11-19 03:14:09,588[DEBUG] optimize site: [16, 17]
2024-11-19 03:14:09,599[DEBUG] use davidson, HC hops: 9
2024-11-19 03:14:09,601[DEBUG] energy: -13.997315090211625
2024-11-19 03:14:09,604[DEBUG] optimize site: [17, 18]
2024-11-19 03:14:09,614[DEBUG] use davidson, HC hops: 8
2024-11-19 03:14:09,616[DEBUG] energy: -13.99731502201422
2024-11-19 03:14:09,619[DEBUG] optimize site: [18, 19]
2024-11-19 03:14:09,630[DEBUG] use davidson, HC hops: 8
2024-11-19 03:14:09,632[DEBUG] energy: -13.997315079212509
2024-11-19 03:14:09,635[DEBUG] optimize site: [19, 20]
2024-11-19 03:14:09,645[DEBUG] use davidson, HC hops: 7
2024-11-19 03:14:09,646[DEBUG] energy: -13.997315018389646
2024-11-19 03:14:09,650[DEBUG] optimize site: [20, 21]
2024-11-19 03:14:09,660[DEBUG] use davidson, HC hops: 8
2024-11-19 03:14:09,662[DEBUG] energy: -13.99731506047155
2024-11-19 03:14:09,665[DEBUG] optimize site: [21, 22]
2024-11-19 03:14:09,674[DEBUG] use davidson, HC hops: 6
2024-11-19 03:14:09,675[DEBUG] energy: -13.997315014222966
2024-11-19 03:14:09,679[DEBUG] optimize site: [22, 23]
2024-11-19 03:14:09,689[DEBUG] use davidson, HC hops: 8
2024-11-19 03:14:09,691[DEBUG] energy: -13.997315036380716
2024-11-19 03:14:09,694[DEBUG] optimize site: [23, 24]
2024-11-19 03:14:09,703[DEBUG] use davidson, HC hops: 6
2024-11-19 03:14:09,704[DEBUG] energy: -13.997315009063305
2024-11-19 03:14:09,708[DEBUG] optimize site: [24, 25]
2024-11-19 03:14:09,716[DEBUG] use davidson, HC hops: 6
2024-11-19 03:14:09,718[DEBUG] energy: -13.997315015431775
2024-11-19 03:14:09,721[DEBUG] optimize site: [25, 26]
2024-11-19 03:14:09,729[DEBUG] use davidson, HC hops: 5
2024-11-19 03:14:09,731[DEBUG] energy: -13.997315007630451
2024-11-19 03:14:09,734[DEBUG] optimize site: [26, 27]
2024-11-19 03:14:09,740[DEBUG] use davidson, HC hops: 4
2024-11-19 03:14:09,742[DEBUG] energy: -13.997315007727407
2024-11-19 03:14:09,745[DEBUG] optimize site: [27, 28]
2024-11-19 03:14:09,747[DEBUG] use direct eigensolver
2024-11-19 03:14:09,998[DEBUG] energy: -13.99731500742737
2024-11-19 03:14:10,001[DEBUG] optimize site: [28, 29]
2024-11-19 03:14:10,010[DEBUG] use direct eigensolver
2024-11-19 03:14:10,073[DEBUG] energy: -13.99731500742737
2024-11-19 03:14:10,076[DEBUG] optimize site: [29, 30]
2024-11-19 03:14:10,078[DEBUG] use direct eigensolver
2024-11-19 03:14:10,083[DEBUG] energy: -13.997315007427366
2024-11-19 03:14:10,086[DEBUG] optimize site: [30, 31]
2024-11-19 03:14:10,088[DEBUG] use direct eigensolver
2024-11-19 03:14:10,090[DEBUG] energy: -13.997315007427368
2024-11-19 03:14:10,093[DEBUG] 3 sweeps are finished, lowest energy = -13.997315090211625
2024-11-19 03:14:10,094[INFO] DMRG has converged!
2024-11-19 03:14:10,130[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: -13.997315090211625

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