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

2025-03-31 01:33:56,541[INFO] Use NumPy as backend
2025-03-31 01:33:56,542[INFO] numpy random seed is 9012
2025-03-31 01:33:56,543[INFO] random seed is 1092
2025-03-31 01:33:56,551[INFO] Git Commit Hash: bca9354a44d9e425271d4ba7b6dd2315d1969503
2025-03-31 01:33:56,553[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}")

2025-03-31 01:33:56,649[DEBUG] # of operator terms: 93
2025-03-31 01:33:56,650[DEBUG] Input operator terms: 93
2025-03-31 01:33:56,651[DEBUG] After combination of the same terms: 93
2025-03-31 01:33:56,652[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))

2025-03-31 01:33:56,723[INFO] optimization method: 2site
2025-03-31 01:33:56,724[INFO] e_rtol: 1e-06
2025-03-31 01:33:56,725[INFO] e_atol: 1e-08
2025-03-31 01:33:56,726[INFO] procedure: [[30, 0.2], [30, 0], [30, 0], [30, 0], [30, 0]]
2025-03-31 01:33:56,759[DEBUG] isweep: 0
2025-03-31 01:33:56,762[DEBUG] compress config in current loop: 30, percent: 0.2
2025-03-31 01:33:56,762[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]
2025-03-31 01:33:56,765[DEBUG] optimize site: [0, 1]
2025-03-31 01:33:56,766[DEBUG] use direct eigensolver
2025-03-31 01:33:56,771[DEBUG] energy: -0.9279990226898324
2025-03-31 01:33:56,773[DEBUG] optimize site: [1, 2]
2025-03-31 01:33:56,775[DEBUG] use direct eigensolver
2025-03-31 01:33:56,781[DEBUG] energy: -1.2840895734105349
2025-03-31 01:33:56,783[DEBUG] optimize site: [2, 3]
2025-03-31 01:33:56,785[DEBUG] use direct eigensolver
2025-03-31 01:33:56,808[DEBUG] energy: -2.0857452647499213
2025-03-31 01:33:56,811[DEBUG] optimize site: [3, 4]
2025-03-31 01:33:56,813[DEBUG] use direct eigensolver
2025-03-31 01:33:57,067[DEBUG] energy: -2.8158895272374123
2025-03-31 01:33:57,069[DEBUG] optimize site: [4, 5]
2025-03-31 01:33:57,127[DEBUG] use davidson, HC hops: 34
2025-03-31 01:33:57,129[DEBUG] energy: -3.293367315585801
2025-03-31 01:33:57,131[DEBUG] optimize site: [5, 6]
2025-03-31 01:33:57,223[DEBUG] use davidson, HC hops: 42
2025-03-31 01:33:57,225[DEBUG] energy: -3.7449867503071985
2025-03-31 01:33:57,229[DEBUG] optimize site: [6, 7]
2025-03-31 01:33:57,317[DEBUG] use davidson, HC hops: 42
2025-03-31 01:33:57,318[DEBUG] energy: -4.17638557549649
2025-03-31 01:33:57,323[DEBUG] optimize site: [7, 8]
2025-03-31 01:33:57,417[DEBUG] use davidson, HC hops: 44
2025-03-31 01:33:57,418[DEBUG] energy: -4.583593477927385
2025-03-31 01:33:57,423[DEBUG] optimize site: [8, 9]
2025-03-31 01:33:57,556[DEBUG] use davidson, HC hops: 55
2025-03-31 01:33:57,557[DEBUG] energy: -4.968031845671203
2025-03-31 01:33:57,561[DEBUG] optimize site: [9, 10]
2025-03-31 01:33:57,674[DEBUG] use davidson, HC hops: 68
2025-03-31 01:33:57,675[DEBUG] energy: -5.414706360833986
2025-03-31 01:33:57,679[DEBUG] optimize site: [10, 11]
2025-03-31 01:33:57,827[DEBUG] use davidson, HC hops: 72
2025-03-31 01:33:57,828[DEBUG] energy: -5.856529754520469
2025-03-31 01:33:57,833[DEBUG] optimize site: [11, 12]
2025-03-31 01:33:57,967[DEBUG] use davidson, HC hops: 100
2025-03-31 01:33:57,968[DEBUG] energy: -6.279022467295806
2025-03-31 01:33:57,972[DEBUG] optimize site: [12, 13]
2025-03-31 01:33:58,079[DEBUG] use davidson, HC hops: 52
2025-03-31 01:33:58,080[DEBUG] energy: -6.857389012204752
2025-03-31 01:33:58,086[DEBUG] optimize site: [13, 14]
2025-03-31 01:33:58,257[DEBUG] use davidson, HC hops: 100
2025-03-31 01:33:58,258[DEBUG] energy: -7.114588022005764
2025-03-31 01:33:58,264[DEBUG] optimize site: [14, 15]
2025-03-31 01:33:58,352[DEBUG] use davidson, HC hops: 47
2025-03-31 01:33:58,352[DEBUG] energy: -7.641631783835402
2025-03-31 01:33:58,355[DEBUG] optimize site: [15, 16]
2025-03-31 01:33:58,442[DEBUG] use davidson, HC hops: 51
2025-03-31 01:33:58,443[DEBUG] energy: -8.118395338420036
2025-03-31 01:33:58,448[DEBUG] optimize site: [16, 17]
2025-03-31 01:33:58,565[DEBUG] use davidson, HC hops: 57
2025-03-31 01:33:58,565[DEBUG] energy: -8.579533430762844
2025-03-31 01:33:58,570[DEBUG] optimize site: [17, 18]
2025-03-31 01:33:58,698[DEBUG] use davidson, HC hops: 66
2025-03-31 01:33:58,699[DEBUG] energy: -8.983113190158441
2025-03-31 01:33:58,701[DEBUG] optimize site: [18, 19]
2025-03-31 01:33:58,774[DEBUG] use davidson, HC hops: 62
2025-03-31 01:33:58,774[DEBUG] energy: -9.422205404607642
2025-03-31 01:33:58,777[DEBUG] optimize site: [19, 20]
2025-03-31 01:33:58,907[DEBUG] use davidson, HC hops: 62
2025-03-31 01:33:58,909[DEBUG] energy: -9.903693680914376
2025-03-31 01:33:58,912[DEBUG] optimize site: [20, 21]
2025-03-31 01:33:59,075[DEBUG] use davidson, HC hops: 81
2025-03-31 01:33:59,076[DEBUG] energy: -10.39853061169795
2025-03-31 01:33:59,081[DEBUG] optimize site: [21, 22]
2025-03-31 01:33:59,201[DEBUG] use davidson, HC hops: 76
2025-03-31 01:33:59,203[DEBUG] energy: -10.834489434421664
2025-03-31 01:33:59,207[DEBUG] optimize site: [22, 23]
2025-03-31 01:33:59,306[DEBUG] use davidson, HC hops: 58
2025-03-31 01:33:59,307[DEBUG] energy: -11.415128707126813
2025-03-31 01:33:59,310[DEBUG] optimize site: [23, 24]
2025-03-31 01:33:59,409[DEBUG] use davidson, HC hops: 52
2025-03-31 01:33:59,411[DEBUG] energy: -12.122795879745063
2025-03-31 01:33:59,415[DEBUG] optimize site: [24, 25]
2025-03-31 01:33:59,559[DEBUG] use davidson, HC hops: 71
2025-03-31 01:33:59,560[DEBUG] energy: -12.812234874023495
2025-03-31 01:33:59,565[DEBUG] optimize site: [25, 26]
2025-03-31 01:33:59,667[DEBUG] use davidson, HC hops: 58
2025-03-31 01:33:59,668[DEBUG] energy: -13.774582804126695
2025-03-31 01:33:59,672[DEBUG] optimize site: [26, 27]
2025-03-31 01:33:59,748[DEBUG] use davidson, HC hops: 47
2025-03-31 01:33:59,749[DEBUG] energy: -13.996832655813106
2025-03-31 01:33:59,751[DEBUG] optimize site: [27, 28]
2025-03-31 01:33:59,753[DEBUG] use direct eigensolver
2025-03-31 01:34:00,011[DEBUG] energy: -13.996832655534028
2025-03-31 01:34:00,013[DEBUG] optimize site: [28, 29]
2025-03-31 01:34:00,015[DEBUG] use direct eigensolver
2025-03-31 01:34:00,066[DEBUG] energy: -13.996832655534028
2025-03-31 01:34:00,069[DEBUG] optimize site: [29, 30]
2025-03-31 01:34:00,070[DEBUG] use direct eigensolver
2025-03-31 01:34:00,075[DEBUG] energy: -13.996832655534039
2025-03-31 01:34:00,076[DEBUG] optimize site: [30, 31]
2025-03-31 01:34:00,078[DEBUG] use direct eigensolver
2025-03-31 01:34:00,081[DEBUG] energy: -13.996832655534039
2025-03-31 01:34:00,082[DEBUG] 1 sweeps are finished, lowest energy = -13.996832655813106
2025-03-31 01:34:00,083[DEBUG] isweep: 1
2025-03-31 01:34:00,083[DEBUG] compress config in current loop: 30, percent: 0
2025-03-31 01:34:00,084[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]
2025-03-31 01:34:00,085[DEBUG] optimize site: [30, 31]
2025-03-31 01:34:00,086[DEBUG] use direct eigensolver
2025-03-31 01:34:00,088[DEBUG] energy: -13.996832655534039
2025-03-31 01:34:00,089[DEBUG] optimize site: [29, 30]
2025-03-31 01:34:00,090[DEBUG] use direct eigensolver
2025-03-31 01:34:00,096[DEBUG] energy: -13.996832655534037
2025-03-31 01:34:00,098[DEBUG] optimize site: [28, 29]
2025-03-31 01:34:00,099[DEBUG] use direct eigensolver
2025-03-31 01:34:00,142[DEBUG] energy: -13.996832655534018
2025-03-31 01:34:00,144[DEBUG] optimize site: [27, 28]
2025-03-31 01:34:00,146[DEBUG] use direct eigensolver
2025-03-31 01:34:00,404[DEBUG] energy: -13.996832655534039
2025-03-31 01:34:00,406[DEBUG] optimize site: [26, 27]
2025-03-31 01:34:00,416[DEBUG] use davidson, HC hops: 4
2025-03-31 01:34:00,417[DEBUG] energy: -13.996832655813659
2025-03-31 01:34:00,424[DEBUG] optimize site: [25, 26]
2025-03-31 01:34:00,464[DEBUG] use davidson, HC hops: 22
2025-03-31 01:34:00,465[DEBUG] energy: -13.996844945038394
2025-03-31 01:34:00,467[DEBUG] optimize site: [24, 25]
2025-03-31 01:34:00,500[DEBUG] use davidson, HC hops: 28
2025-03-31 01:34:00,501[DEBUG] energy: -13.997067101658786
2025-03-31 01:34:00,505[DEBUG] optimize site: [23, 24]
2025-03-31 01:34:00,536[DEBUG] use davidson, HC hops: 25
2025-03-31 01:34:00,537[DEBUG] energy: -13.997101684717542
2025-03-31 01:34:00,541[DEBUG] optimize site: [22, 23]
2025-03-31 01:34:00,570[DEBUG] use davidson, HC hops: 23
2025-03-31 01:34:00,571[DEBUG] energy: -13.997106608213747
2025-03-31 01:34:00,575[DEBUG] optimize site: [21, 22]
2025-03-31 01:34:00,604[DEBUG] use davidson, HC hops: 23
2025-03-31 01:34:00,606[DEBUG] energy: -13.997113698271155
2025-03-31 01:34:00,609[DEBUG] optimize site: [20, 21]
2025-03-31 01:34:00,642[DEBUG] use davidson, HC hops: 26
2025-03-31 01:34:00,643[DEBUG] energy: -13.997162638323537
2025-03-31 01:34:00,647[DEBUG] optimize site: [19, 20]
2025-03-31 01:34:00,685[DEBUG] use davidson, HC hops: 23
2025-03-31 01:34:00,687[DEBUG] energy: -13.997170144965533
2025-03-31 01:34:00,692[DEBUG] optimize site: [18, 19]
2025-03-31 01:34:00,748[DEBUG] use davidson, HC hops: 26
2025-03-31 01:34:00,751[DEBUG] energy: -13.997199975427378
2025-03-31 01:34:00,755[DEBUG] optimize site: [17, 18]
2025-03-31 01:34:00,804[DEBUG] use davidson, HC hops: 22
2025-03-31 01:34:00,806[DEBUG] energy: -13.997204392621578
2025-03-31 01:34:00,811[DEBUG] optimize site: [16, 17]
2025-03-31 01:34:00,850[DEBUG] use davidson, HC hops: 25
2025-03-31 01:34:00,850[DEBUG] energy: -13.997225037523778
2025-03-31 01:34:00,855[DEBUG] optimize site: [15, 16]
2025-03-31 01:34:00,887[DEBUG] use davidson, HC hops: 26
2025-03-31 01:34:00,887[DEBUG] energy: -13.997284918121142
2025-03-31 01:34:00,892[DEBUG] optimize site: [14, 15]
2025-03-31 01:34:00,919[DEBUG] use davidson, HC hops: 22
2025-03-31 01:34:00,920[DEBUG] energy: -13.997290859971216
2025-03-31 01:34:00,924[DEBUG] optimize site: [13, 14]
2025-03-31 01:34:00,955[DEBUG] use davidson, HC hops: 20
2025-03-31 01:34:00,957[DEBUG] energy: -13.997293257653748
2025-03-31 01:34:00,961[DEBUG] optimize site: [12, 13]
2025-03-31 01:34:01,012[DEBUG] use davidson, HC hops: 23
2025-03-31 01:34:01,014[DEBUG] energy: -13.997306225086637
2025-03-31 01:34:01,018[DEBUG] optimize site: [11, 12]
2025-03-31 01:34:01,078[DEBUG] use davidson, HC hops: 21
2025-03-31 01:34:01,079[DEBUG] energy: -13.997311145595573
2025-03-31 01:34:01,085[DEBUG] optimize site: [10, 11]
2025-03-31 01:34:01,139[DEBUG] use davidson, HC hops: 20
2025-03-31 01:34:01,140[DEBUG] energy: -13.997313132707447
2025-03-31 01:34:01,146[DEBUG] optimize site: [9, 10]
2025-03-31 01:34:01,168[DEBUG] use davidson, HC hops: 17
2025-03-31 01:34:01,169[DEBUG] energy: -13.997314428626334
2025-03-31 01:34:01,173[DEBUG] optimize site: [8, 9]
2025-03-31 01:34:01,189[DEBUG] use davidson, HC hops: 11
2025-03-31 01:34:01,190[DEBUG] energy: -13.997314715468647
2025-03-31 01:34:01,194[DEBUG] optimize site: [7, 8]
2025-03-31 01:34:01,210[DEBUG] use davidson, HC hops: 7
2025-03-31 01:34:01,212[DEBUG] energy: -13.997314712669745
2025-03-31 01:34:01,217[DEBUG] optimize site: [6, 7]
2025-03-31 01:34:01,246[DEBUG] use davidson, HC hops: 12
2025-03-31 01:34:01,249[DEBUG] energy: -13.997314999750003
2025-03-31 01:34:01,253[DEBUG] optimize site: [5, 6]
2025-03-31 01:34:01,274[DEBUG] use davidson, HC hops: 7
2025-03-31 01:34:01,275[DEBUG] energy: -13.997315003811433
2025-03-31 01:34:01,279[DEBUG] optimize site: [4, 5]
2025-03-31 01:34:01,291[DEBUG] use davidson, HC hops: 5
2025-03-31 01:34:01,293[DEBUG] energy: -13.997315004767765
2025-03-31 01:34:01,294[DEBUG] optimize site: [3, 4]
2025-03-31 01:34:01,298[DEBUG] use direct eigensolver
2025-03-31 01:34:01,567[DEBUG] energy: -13.99731500446707
2025-03-31 01:34:01,569[DEBUG] optimize site: [2, 3]
2025-03-31 01:34:01,572[DEBUG] use direct eigensolver
2025-03-31 01:34:01,620[DEBUG] energy: -13.997315004467065
2025-03-31 01:34:01,621[DEBUG] optimize site: [1, 2]
2025-03-31 01:34:01,623[DEBUG] use direct eigensolver
2025-03-31 01:34:01,628[DEBUG] energy: -13.99731500446705
2025-03-31 01:34:01,629[DEBUG] optimize site: [0, 1]
2025-03-31 01:34:01,630[DEBUG] use direct eigensolver
2025-03-31 01:34:01,635[DEBUG] energy: -13.997315004467058
2025-03-31 01:34:01,636[DEBUG] 2 sweeps are finished, lowest energy = -13.997315004767765
2025-03-31 01:34:01,640[DEBUG] isweep: 2
2025-03-31 01:34:01,640[DEBUG] compress config in current loop: 30, percent: 0
2025-03-31 01:34:01,641[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]
2025-03-31 01:34:01,641[DEBUG] optimize site: [0, 1]
2025-03-31 01:34:01,644[DEBUG] use direct eigensolver
2025-03-31 01:34:01,646[DEBUG] energy: -13.997315004467058
2025-03-31 01:34:01,647[DEBUG] optimize site: [1, 2]
2025-03-31 01:34:01,649[DEBUG] use direct eigensolver
2025-03-31 01:34:01,655[DEBUG] energy: -13.997315004467048
2025-03-31 01:34:01,656[DEBUG] optimize site: [2, 3]
2025-03-31 01:34:01,657[DEBUG] use direct eigensolver
2025-03-31 01:34:01,705[DEBUG] energy: -13.997315004467064
2025-03-31 01:34:01,706[DEBUG] optimize site: [3, 4]
2025-03-31 01:34:01,707[DEBUG] use direct eigensolver
2025-03-31 01:34:01,963[DEBUG] energy: -13.997315004467078
2025-03-31 01:34:01,965[DEBUG] optimize site: [4, 5]
2025-03-31 01:34:01,973[DEBUG] use davidson, HC hops: 4
2025-03-31 01:34:01,974[DEBUG] energy: -13.99731500476784
2025-03-31 01:34:01,980[DEBUG] optimize site: [5, 6]
2025-03-31 01:34:01,994[DEBUG] use davidson, HC hops: 4
2025-03-31 01:34:01,995[DEBUG] energy: -13.997315004667737
2025-03-31 01:34:01,999[DEBUG] optimize site: [6, 7]
2025-03-31 01:34:02,015[DEBUG] use davidson, HC hops: 6
2025-03-31 01:34:02,016[DEBUG] energy: -13.99731501247064
2025-03-31 01:34:02,021[DEBUG] optimize site: [7, 8]
2025-03-31 01:34:02,034[DEBUG] use davidson, HC hops: 5
2025-03-31 01:34:02,036[DEBUG] energy: -13.997315006066634
2025-03-31 01:34:02,040[DEBUG] optimize site: [8, 9]
2025-03-31 01:34:02,059[DEBUG] use davidson, HC hops: 7
2025-03-31 01:34:02,060[DEBUG] energy: -13.997315033374514
2025-03-31 01:34:02,064[DEBUG] optimize site: [9, 10]
2025-03-31 01:34:02,080[DEBUG] use davidson, HC hops: 6
2025-03-31 01:34:02,081[DEBUG] energy: -13.997315010121964
2025-03-31 01:34:02,085[DEBUG] optimize site: [10, 11]
2025-03-31 01:34:02,106[DEBUG] use davidson, HC hops: 8
2025-03-31 01:34:02,108[DEBUG] energy: -13.997315055776888
2025-03-31 01:34:02,113[DEBUG] optimize site: [11, 12]
2025-03-31 01:34:02,132[DEBUG] use davidson, HC hops: 7
2025-03-31 01:34:02,133[DEBUG] energy: -13.99731501589049
2025-03-31 01:34:02,136[DEBUG] optimize site: [12, 13]
2025-03-31 01:34:02,148[DEBUG] use davidson, HC hops: 8
2025-03-31 01:34:02,148[DEBUG] energy: -13.997315076759413
2025-03-31 01:34:02,151[DEBUG] optimize site: [13, 14]
2025-03-31 01:34:02,161[DEBUG] use davidson, HC hops: 7
2025-03-31 01:34:02,162[DEBUG] energy: -13.997315021063784
2025-03-31 01:34:02,165[DEBUG] optimize site: [14, 15]
2025-03-31 01:34:02,176[DEBUG] use davidson, HC hops: 8
2025-03-31 01:34:02,177[DEBUG] energy: -13.997315089163504
2025-03-31 01:34:02,180[DEBUG] optimize site: [15, 16]
2025-03-31 01:34:02,192[DEBUG] use davidson, HC hops: 8
2025-03-31 01:34:02,192[DEBUG] energy: -13.997315023237768
2025-03-31 01:34:02,195[DEBUG] optimize site: [16, 17]
2025-03-31 01:34:02,208[DEBUG] use davidson, HC hops: 9
2025-03-31 01:34:02,209[DEBUG] energy: -13.99731509021169
2025-03-31 01:34:02,211[DEBUG] optimize site: [17, 18]
2025-03-31 01:34:02,224[DEBUG] use davidson, HC hops: 8
2025-03-31 01:34:02,225[DEBUG] energy: -13.997315022014295
2025-03-31 01:34:02,227[DEBUG] optimize site: [18, 19]
2025-03-31 01:34:02,244[DEBUG] use davidson, HC hops: 8
2025-03-31 01:34:02,245[DEBUG] energy: -13.997315079212589
2025-03-31 01:34:02,249[DEBUG] optimize site: [19, 20]
2025-03-31 01:34:02,267[DEBUG] use davidson, HC hops: 7
2025-03-31 01:34:02,268[DEBUG] energy: -13.99731501838971
2025-03-31 01:34:02,272[DEBUG] optimize site: [20, 21]
2025-03-31 01:34:02,292[DEBUG] use davidson, HC hops: 8
2025-03-31 01:34:02,293[DEBUG] energy: -13.99731506047161
2025-03-31 01:34:02,297[DEBUG] optimize site: [21, 22]
2025-03-31 01:34:02,314[DEBUG] use davidson, HC hops: 6
2025-03-31 01:34:02,315[DEBUG] energy: -13.997315014223034
2025-03-31 01:34:02,319[DEBUG] optimize site: [22, 23]
2025-03-31 01:34:02,340[DEBUG] use davidson, HC hops: 8
2025-03-31 01:34:02,341[DEBUG] energy: -13.997315036380805
2025-03-31 01:34:02,345[DEBUG] optimize site: [23, 24]
2025-03-31 01:34:02,360[DEBUG] use davidson, HC hops: 6
2025-03-31 01:34:02,361[DEBUG] energy: -13.997315009063385
2025-03-31 01:34:02,363[DEBUG] optimize site: [24, 25]
2025-03-31 01:34:02,373[DEBUG] use davidson, HC hops: 6
2025-03-31 01:34:02,373[DEBUG] energy: -13.997315015431878
2025-03-31 01:34:02,378[DEBUG] optimize site: [25, 26]
2025-03-31 01:34:02,386[DEBUG] use davidson, HC hops: 5
2025-03-31 01:34:02,388[DEBUG] energy: -13.99731500763058
2025-03-31 01:34:02,391[DEBUG] optimize site: [26, 27]
2025-03-31 01:34:02,397[DEBUG] use davidson, HC hops: 4
2025-03-31 01:34:02,399[DEBUG] energy: -13.997315007727554
2025-03-31 01:34:02,402[DEBUG] optimize site: [27, 28]
2025-03-31 01:34:02,404[DEBUG] use direct eigensolver
2025-03-31 01:34:02,667[DEBUG] energy: -13.997315007427515
2025-03-31 01:34:02,671[DEBUG] optimize site: [28, 29]
2025-03-31 01:34:02,673[DEBUG] use direct eigensolver
2025-03-31 01:34:02,721[DEBUG] energy: -13.997315007427504
2025-03-31 01:34:02,723[DEBUG] optimize site: [29, 30]
2025-03-31 01:34:02,725[DEBUG] use direct eigensolver
2025-03-31 01:34:02,731[DEBUG] energy: -13.997315007427506
2025-03-31 01:34:02,734[DEBUG] optimize site: [30, 31]
2025-03-31 01:34:02,735[DEBUG] use direct eigensolver
2025-03-31 01:34:02,738[DEBUG] energy: -13.997315007427504
2025-03-31 01:34:02,740[DEBUG] 3 sweeps are finished, lowest energy = -13.99731509021169
2025-03-31 01:34:02,742[INFO] DMRG has converged!
2025-03-31 01:34:02,778[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: -13.99731509021169

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