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

2025-07-18 14:19:12,628[INFO] Use NumPy as backend
2025-07-18 14:19:12,629[INFO] numpy random seed is 9012
2025-07-18 14:19:12,630[INFO] random seed is 1092
2025-07-18 14:19:12,639[INFO] Git Commit Hash: fa02d78d9c8c933a8807f0ea3cdca7812e45218a
2025-07-18 14:19:12,640[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}")

2025-07-18 14:19:12,734[DEBUG] # of operator terms: 93
2025-07-18 14:19:12,735[DEBUG] Input operator terms: 93
2025-07-18 14:19:12,737[DEBUG] After combination of the same terms: 93
2025-07-18 14:19:12,738[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))

2025-07-18 14:19:12,808[INFO] optimization method: 2site
2025-07-18 14:19:12,809[INFO] e_rtol: 1e-06
2025-07-18 14:19:12,809[INFO] e_atol: 1e-08
2025-07-18 14:19:12,810[INFO] procedure: [[30, 0.2], [30, 0], [30, 0], [30, 0], [30, 0]]
2025-07-18 14:19:12,840[DEBUG] isweep: 0
2025-07-18 14:19:12,841[DEBUG] compress config in current loop: 30, percent: 0.2
2025-07-18 14:19:12,842[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]
2025-07-18 14:19:12,844[DEBUG] optimize site: [0, 1]
2025-07-18 14:19:12,844[DEBUG] use direct eigensolver
2025-07-18 14:19:12,848[DEBUG] energy: -0.9279990226898331
2025-07-18 14:19:12,850[DEBUG] optimize site: [1, 2]
2025-07-18 14:19:12,852[DEBUG] use direct eigensolver
2025-07-18 14:19:12,857[DEBUG] energy: -1.284089573410534
2025-07-18 14:19:12,859[DEBUG] optimize site: [2, 3]
2025-07-18 14:19:12,861[DEBUG] use direct eigensolver
2025-07-18 14:19:12,884[DEBUG] energy: -2.085745264749922
2025-07-18 14:19:12,886[DEBUG] optimize site: [3, 4]
2025-07-18 14:19:12,888[DEBUG] use direct eigensolver
2025-07-18 14:19:13,143[DEBUG] energy: -2.815889527237411
2025-07-18 14:19:13,145[DEBUG] optimize site: [4, 5]
2025-07-18 14:19:13,199[DEBUG] use davidson, HC hops: 34
2025-07-18 14:19:13,200[DEBUG] energy: -3.2933673155858045
2025-07-18 14:19:13,202[DEBUG] optimize site: [5, 6]
2025-07-18 14:19:13,266[DEBUG] use davidson, HC hops: 42
2025-07-18 14:19:13,266[DEBUG] energy: -3.7449867503071985
2025-07-18 14:19:13,269[DEBUG] optimize site: [6, 7]
2025-07-18 14:19:13,321[DEBUG] use davidson, HC hops: 42
2025-07-18 14:19:13,323[DEBUG] energy: -4.1763855754964885
2025-07-18 14:19:13,327[DEBUG] optimize site: [7, 8]
2025-07-18 14:19:13,413[DEBUG] use davidson, HC hops: 44
2025-07-18 14:19:13,414[DEBUG] energy: -4.583593477927385
2025-07-18 14:19:13,418[DEBUG] optimize site: [8, 9]
2025-07-18 14:19:13,475[DEBUG] use davidson, HC hops: 55
2025-07-18 14:19:13,477[DEBUG] energy: -4.968031845671206
2025-07-18 14:19:13,480[DEBUG] optimize site: [9, 10]
2025-07-18 14:19:13,568[DEBUG] use davidson, HC hops: 68
2025-07-18 14:19:13,571[DEBUG] energy: -5.414706360833989
2025-07-18 14:19:13,575[DEBUG] optimize site: [10, 11]
2025-07-18 14:19:13,701[DEBUG] use davidson, HC hops: 72
2025-07-18 14:19:13,702[DEBUG] energy: -5.85652975452048
2025-07-18 14:19:13,708[DEBUG] optimize site: [11, 12]
2025-07-18 14:19:13,835[DEBUG] use davidson, HC hops: 100
2025-07-18 14:19:13,836[DEBUG] energy: -6.279022467295824
2025-07-18 14:19:13,838[DEBUG] optimize site: [12, 13]
2025-07-18 14:19:13,932[DEBUG] use davidson, HC hops: 52
2025-07-18 14:19:13,934[DEBUG] energy: -6.857389012204772
2025-07-18 14:19:13,938[DEBUG] optimize site: [13, 14]
2025-07-18 14:19:14,060[DEBUG] use davidson, HC hops: 100
2025-07-18 14:19:14,061[DEBUG] energy: -7.114588022005797
2025-07-18 14:19:14,066[DEBUG] optimize site: [14, 15]
2025-07-18 14:19:14,151[DEBUG] use davidson, HC hops: 47
2025-07-18 14:19:14,153[DEBUG] energy: -7.641631783835441
2025-07-18 14:19:14,158[DEBUG] optimize site: [15, 16]
2025-07-18 14:19:14,253[DEBUG] use davidson, HC hops: 51
2025-07-18 14:19:14,255[DEBUG] energy: -8.118395338420072
2025-07-18 14:19:14,260[DEBUG] optimize site: [16, 17]
2025-07-18 14:19:14,326[DEBUG] use davidson, HC hops: 57
2025-07-18 14:19:14,327[DEBUG] energy: -8.579533430762886
2025-07-18 14:19:14,331[DEBUG] optimize site: [17, 18]
2025-07-18 14:19:14,448[DEBUG] use davidson, HC hops: 66
2025-07-18 14:19:14,449[DEBUG] energy: -8.983113190158498
2025-07-18 14:19:14,453[DEBUG] optimize site: [18, 19]
2025-07-18 14:19:14,523[DEBUG] use davidson, HC hops: 62
2025-07-18 14:19:14,524[DEBUG] energy: -9.422205404607706
2025-07-18 14:19:14,528[DEBUG] optimize site: [19, 20]
2025-07-18 14:19:14,641[DEBUG] use davidson, HC hops: 62
2025-07-18 14:19:14,643[DEBUG] energy: -9.903693680914461
2025-07-18 14:19:14,647[DEBUG] optimize site: [20, 21]
2025-07-18 14:19:14,793[DEBUG] use davidson, HC hops: 81
2025-07-18 14:19:14,794[DEBUG] energy: -10.398530611698053
2025-07-18 14:19:14,798[DEBUG] optimize site: [21, 22]
2025-07-18 14:19:14,921[DEBUG] use davidson, HC hops: 76
2025-07-18 14:19:14,922[DEBUG] energy: -10.834489434421751
2025-07-18 14:19:14,926[DEBUG] optimize site: [22, 23]
2025-07-18 14:19:15,037[DEBUG] use davidson, HC hops: 58
2025-07-18 14:19:15,038[DEBUG] energy: -11.415128707126902
2025-07-18 14:19:15,042[DEBUG] optimize site: [23, 24]
2025-07-18 14:19:15,143[DEBUG] use davidson, HC hops: 52
2025-07-18 14:19:15,144[DEBUG] energy: -12.122795879745162
2025-07-18 14:19:15,150[DEBUG] optimize site: [24, 25]
2025-07-18 14:19:15,273[DEBUG] use davidson, HC hops: 71
2025-07-18 14:19:15,274[DEBUG] energy: -12.812234874023599
2025-07-18 14:19:15,279[DEBUG] optimize site: [25, 26]
2025-07-18 14:19:15,390[DEBUG] use davidson, HC hops: 58
2025-07-18 14:19:15,390[DEBUG] energy: -13.774582804126812
2025-07-18 14:19:15,393[DEBUG] optimize site: [26, 27]
2025-07-18 14:19:15,468[DEBUG] use davidson, HC hops: 47
2025-07-18 14:19:15,470[DEBUG] energy: -13.996832655813243
2025-07-18 14:19:15,474[DEBUG] optimize site: [27, 28]
2025-07-18 14:19:15,478[DEBUG] use direct eigensolver
2025-07-18 14:19:15,738[DEBUG] energy: -13.996832655534188
2025-07-18 14:19:15,741[DEBUG] optimize site: [28, 29]
2025-07-18 14:19:15,742[DEBUG] use direct eigensolver
2025-07-18 14:19:15,820[DEBUG] energy: -13.996832655534181
2025-07-18 14:19:15,823[DEBUG] optimize site: [29, 30]
2025-07-18 14:19:15,826[DEBUG] use direct eigensolver
2025-07-18 14:19:15,834[DEBUG] energy: -13.996832655534163
2025-07-18 14:19:15,836[DEBUG] optimize site: [30, 31]
2025-07-18 14:19:15,838[DEBUG] use direct eigensolver
2025-07-18 14:19:15,842[DEBUG] energy: -13.996832655534172
2025-07-18 14:19:15,845[DEBUG] 1 sweeps are finished, lowest energy = -13.996832655813243
2025-07-18 14:19:15,847[DEBUG] isweep: 1
2025-07-18 14:19:15,849[DEBUG] compress config in current loop: 30, percent: 0
2025-07-18 14:19:15,850[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]
2025-07-18 14:19:15,853[DEBUG] optimize site: [30, 31]
2025-07-18 14:19:15,855[DEBUG] use direct eigensolver
2025-07-18 14:19:15,858[DEBUG] energy: -13.996832655534172
2025-07-18 14:19:15,860[DEBUG] optimize site: [29, 30]
2025-07-18 14:19:15,862[DEBUG] use direct eigensolver
2025-07-18 14:19:15,867[DEBUG] energy: -13.996832655534167
2025-07-18 14:19:15,869[DEBUG] optimize site: [28, 29]
2025-07-18 14:19:15,871[DEBUG] use direct eigensolver
2025-07-18 14:19:15,941[DEBUG] energy: -13.996832655534181
2025-07-18 14:19:15,943[DEBUG] optimize site: [27, 28]
2025-07-18 14:19:15,947[DEBUG] use direct eigensolver
2025-07-18 14:19:16,193[DEBUG] energy: -13.996832655534162
2025-07-18 14:19:16,196[DEBUG] optimize site: [26, 27]
2025-07-18 14:19:16,206[DEBUG] use davidson, HC hops: 4
2025-07-18 14:19:16,208[DEBUG] energy: -13.996832655813787
2025-07-18 14:19:16,212[DEBUG] optimize site: [25, 26]
2025-07-18 14:19:16,259[DEBUG] use davidson, HC hops: 22
2025-07-18 14:19:16,261[DEBUG] energy: -13.996844945038506
2025-07-18 14:19:16,265[DEBUG] optimize site: [24, 25]
2025-07-18 14:19:16,297[DEBUG] use davidson, HC hops: 28
2025-07-18 14:19:16,298[DEBUG] energy: -13.997067101658896
2025-07-18 14:19:16,302[DEBUG] optimize site: [23, 24]
2025-07-18 14:19:16,329[DEBUG] use davidson, HC hops: 25
2025-07-18 14:19:16,331[DEBUG] energy: -13.997101684717657
2025-07-18 14:19:16,334[DEBUG] optimize site: [22, 23]
2025-07-18 14:19:16,359[DEBUG] use davidson, HC hops: 23
2025-07-18 14:19:16,360[DEBUG] energy: -13.997106608213844
2025-07-18 14:19:16,364[DEBUG] optimize site: [21, 22]
2025-07-18 14:19:16,389[DEBUG] use davidson, HC hops: 23
2025-07-18 14:19:16,389[DEBUG] energy: -13.997113698271265
2025-07-18 14:19:16,394[DEBUG] optimize site: [20, 21]
2025-07-18 14:19:16,423[DEBUG] use davidson, HC hops: 26
2025-07-18 14:19:16,424[DEBUG] energy: -13.997162638323692
2025-07-18 14:19:16,428[DEBUG] optimize site: [19, 20]
2025-07-18 14:19:16,454[DEBUG] use davidson, HC hops: 23
2025-07-18 14:19:16,454[DEBUG] energy: -13.997170144965677
2025-07-18 14:19:16,458[DEBUG] optimize site: [18, 19]
2025-07-18 14:19:16,487[DEBUG] use davidson, HC hops: 26
2025-07-18 14:19:16,488[DEBUG] energy: -13.997199975427511
2025-07-18 14:19:16,492[DEBUG] optimize site: [17, 18]
2025-07-18 14:19:16,516[DEBUG] use davidson, HC hops: 22
2025-07-18 14:19:16,518[DEBUG] energy: -13.997204392621697
2025-07-18 14:19:16,521[DEBUG] optimize site: [16, 17]
2025-07-18 14:19:16,570[DEBUG] use davidson, HC hops: 25
2025-07-18 14:19:16,572[DEBUG] energy: -13.997225037523876
2025-07-18 14:19:16,577[DEBUG] optimize site: [15, 16]
2025-07-18 14:19:16,628[DEBUG] use davidson, HC hops: 26
2025-07-18 14:19:16,629[DEBUG] energy: -13.997284918121231
2025-07-18 14:19:16,634[DEBUG] optimize site: [14, 15]
2025-07-18 14:19:16,675[DEBUG] use davidson, HC hops: 22
2025-07-18 14:19:16,676[DEBUG] energy: -13.997290859971294
2025-07-18 14:19:16,681[DEBUG] optimize site: [13, 14]
2025-07-18 14:19:16,719[DEBUG] use davidson, HC hops: 20
2025-07-18 14:19:16,719[DEBUG] energy: -13.99729325765383
2025-07-18 14:19:16,724[DEBUG] optimize site: [12, 13]
2025-07-18 14:19:16,767[DEBUG] use davidson, HC hops: 23
2025-07-18 14:19:16,769[DEBUG] energy: -13.997306225086696
2025-07-18 14:19:16,774[DEBUG] optimize site: [11, 12]
2025-07-18 14:19:16,816[DEBUG] use davidson, HC hops: 21
2025-07-18 14:19:16,817[DEBUG] energy: -13.997311145595644
2025-07-18 14:19:16,822[DEBUG] optimize site: [10, 11]
2025-07-18 14:19:16,861[DEBUG] use davidson, HC hops: 20
2025-07-18 14:19:16,862[DEBUG] energy: -13.997313132707509
2025-07-18 14:19:16,866[DEBUG] optimize site: [9, 10]
2025-07-18 14:19:16,900[DEBUG] use davidson, HC hops: 17
2025-07-18 14:19:16,901[DEBUG] energy: -13.997314428626384
2025-07-18 14:19:16,905[DEBUG] optimize site: [8, 9]
2025-07-18 14:19:16,928[DEBUG] use davidson, HC hops: 11
2025-07-18 14:19:16,929[DEBUG] energy: -13.99731471546868
2025-07-18 14:19:16,933[DEBUG] optimize site: [7, 8]
2025-07-18 14:19:16,943[DEBUG] use davidson, HC hops: 7
2025-07-18 14:19:16,944[DEBUG] energy: -13.997314712669787
2025-07-18 14:19:16,948[DEBUG] optimize site: [6, 7]
2025-07-18 14:19:16,963[DEBUG] use davidson, HC hops: 12
2025-07-18 14:19:16,963[DEBUG] energy: -13.99731499975005
2025-07-18 14:19:16,968[DEBUG] optimize site: [5, 6]
2025-07-18 14:19:16,977[DEBUG] use davidson, HC hops: 7
2025-07-18 14:19:16,978[DEBUG] energy: -13.997315003811462
2025-07-18 14:19:16,982[DEBUG] optimize site: [4, 5]
2025-07-18 14:19:16,989[DEBUG] use davidson, HC hops: 5
2025-07-18 14:19:16,990[DEBUG] energy: -13.9973150047678
2025-07-18 14:19:16,993[DEBUG] optimize site: [3, 4]
2025-07-18 14:19:16,996[DEBUG] use direct eigensolver
2025-07-18 14:19:17,262[DEBUG] energy: -13.997315004467106
2025-07-18 14:19:17,265[DEBUG] optimize site: [2, 3]
2025-07-18 14:19:17,269[DEBUG] use direct eigensolver
2025-07-18 14:19:17,331[DEBUG] energy: -13.99731500446709
2025-07-18 14:19:17,334[DEBUG] optimize site: [1, 2]
2025-07-18 14:19:17,336[DEBUG] use direct eigensolver
2025-07-18 14:19:17,342[DEBUG] energy: -13.997315004467067
2025-07-18 14:19:17,344[DEBUG] optimize site: [0, 1]
2025-07-18 14:19:17,346[DEBUG] use direct eigensolver
2025-07-18 14:19:17,348[DEBUG] energy: -13.99731500446708
2025-07-18 14:19:17,351[DEBUG] 2 sweeps are finished, lowest energy = -13.9973150047678
2025-07-18 14:19:17,352[DEBUG] isweep: 2
2025-07-18 14:19:17,354[DEBUG] compress config in current loop: 30, percent: 0
2025-07-18 14:19:17,355[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]
2025-07-18 14:19:17,357[DEBUG] optimize site: [0, 1]
2025-07-18 14:19:17,358[DEBUG] use direct eigensolver
2025-07-18 14:19:17,361[DEBUG] energy: -13.99731500446708
2025-07-18 14:19:17,364[DEBUG] optimize site: [1, 2]
2025-07-18 14:19:17,366[DEBUG] use direct eigensolver
2025-07-18 14:19:17,371[DEBUG] energy: -13.997315004467069
2025-07-18 14:19:17,373[DEBUG] optimize site: [2, 3]
2025-07-18 14:19:17,374[DEBUG] use direct eigensolver
2025-07-18 14:19:17,427[DEBUG] energy: -13.997315004467085
2025-07-18 14:19:17,431[DEBUG] optimize site: [3, 4]
2025-07-18 14:19:17,432[DEBUG] use direct eigensolver
2025-07-18 14:19:17,684[DEBUG] energy: -13.997315004467106
2025-07-18 14:19:17,686[DEBUG] optimize site: [4, 5]
2025-07-18 14:19:17,691[DEBUG] use davidson, HC hops: 4
2025-07-18 14:19:17,692[DEBUG] energy: -13.99731500476786
2025-07-18 14:19:17,695[DEBUG] optimize site: [5, 6]
2025-07-18 14:19:17,702[DEBUG] use davidson, HC hops: 4
2025-07-18 14:19:17,703[DEBUG] energy: -13.997315004667747
2025-07-18 14:19:17,707[DEBUG] optimize site: [6, 7]
2025-07-18 14:19:17,715[DEBUG] use davidson, HC hops: 6
2025-07-18 14:19:17,716[DEBUG] energy: -13.997315012470649
2025-07-18 14:19:17,720[DEBUG] optimize site: [7, 8]
2025-07-18 14:19:17,727[DEBUG] use davidson, HC hops: 5
2025-07-18 14:19:17,728[DEBUG] energy: -13.99731500606664
2025-07-18 14:19:17,732[DEBUG] optimize site: [8, 9]
2025-07-18 14:19:17,741[DEBUG] use davidson, HC hops: 7
2025-07-18 14:19:17,742[DEBUG] energy: -13.997315033374509
2025-07-18 14:19:17,746[DEBUG] optimize site: [9, 10]
2025-07-18 14:19:17,754[DEBUG] use davidson, HC hops: 6
2025-07-18 14:19:17,755[DEBUG] energy: -13.997315010121937
2025-07-18 14:19:17,758[DEBUG] optimize site: [10, 11]
2025-07-18 14:19:17,768[DEBUG] use davidson, HC hops: 8
2025-07-18 14:19:17,769[DEBUG] energy: -13.997315055776834
2025-07-18 14:19:17,772[DEBUG] optimize site: [11, 12]
2025-07-18 14:19:17,782[DEBUG] use davidson, HC hops: 7
2025-07-18 14:19:17,783[DEBUG] energy: -13.997315015890411
2025-07-18 14:19:17,785[DEBUG] optimize site: [12, 13]
2025-07-18 14:19:17,797[DEBUG] use davidson, HC hops: 8
2025-07-18 14:19:17,797[DEBUG] energy: -13.997315076759326
2025-07-18 14:19:17,800[DEBUG] optimize site: [13, 14]
2025-07-18 14:19:17,810[DEBUG] use davidson, HC hops: 7
2025-07-18 14:19:17,811[DEBUG] energy: -13.997315021063706
2025-07-18 14:19:17,813[DEBUG] optimize site: [14, 15]
2025-07-18 14:19:17,825[DEBUG] use davidson, HC hops: 8
2025-07-18 14:19:17,825[DEBUG] energy: -13.997315089163418
2025-07-18 14:19:17,828[DEBUG] optimize site: [15, 16]
2025-07-18 14:19:17,839[DEBUG] use davidson, HC hops: 8
2025-07-18 14:19:17,840[DEBUG] energy: -13.997315023237658
2025-07-18 14:19:17,845[DEBUG] optimize site: [16, 17]
2025-07-18 14:19:17,865[DEBUG] use davidson, HC hops: 9
2025-07-18 14:19:17,866[DEBUG] energy: -13.997315090211584
2025-07-18 14:19:17,870[DEBUG] optimize site: [17, 18]
2025-07-18 14:19:17,888[DEBUG] use davidson, HC hops: 8
2025-07-18 14:19:17,889[DEBUG] energy: -13.997315022014186
2025-07-18 14:19:17,893[DEBUG] optimize site: [18, 19]
2025-07-18 14:19:17,911[DEBUG] use davidson, HC hops: 8
2025-07-18 14:19:17,912[DEBUG] energy: -13.9973150792125
2025-07-18 14:19:17,917[DEBUG] optimize site: [19, 20]
2025-07-18 14:19:17,933[DEBUG] use davidson, HC hops: 7
2025-07-18 14:19:17,934[DEBUG] energy: -13.997315018389621
2025-07-18 14:19:17,939[DEBUG] optimize site: [20, 21]
2025-07-18 14:19:17,957[DEBUG] use davidson, HC hops: 8
2025-07-18 14:19:17,957[DEBUG] energy: -13.997315060471504
2025-07-18 14:19:17,962[DEBUG] optimize site: [21, 22]
2025-07-18 14:19:17,977[DEBUG] use davidson, HC hops: 6
2025-07-18 14:19:17,978[DEBUG] energy: -13.99731501422291
2025-07-18 14:19:17,983[DEBUG] optimize site: [22, 23]
2025-07-18 14:19:18,001[DEBUG] use davidson, HC hops: 8
2025-07-18 14:19:18,001[DEBUG] energy: -13.99731503638068
2025-07-18 14:19:18,006[DEBUG] optimize site: [23, 24]
2025-07-18 14:19:18,020[DEBUG] use davidson, HC hops: 6
2025-07-18 14:19:18,021[DEBUG] energy: -13.99731500906328
2025-07-18 14:19:18,026[DEBUG] optimize site: [24, 25]
2025-07-18 14:19:18,040[DEBUG] use davidson, HC hops: 6
2025-07-18 14:19:18,041[DEBUG] energy: -13.997315015431766
2025-07-18 14:19:18,046[DEBUG] optimize site: [25, 26]
2025-07-18 14:19:18,058[DEBUG] use davidson, HC hops: 5
2025-07-18 14:19:18,060[DEBUG] energy: -13.997315007630448
2025-07-18 14:19:18,065[DEBUG] optimize site: [26, 27]
2025-07-18 14:19:18,074[DEBUG] use davidson, HC hops: 4
2025-07-18 14:19:18,075[DEBUG] energy: -13.997315007727433
2025-07-18 14:19:18,077[DEBUG] optimize site: [27, 28]
2025-07-18 14:19:18,080[DEBUG] use direct eigensolver
2025-07-18 14:19:18,351[DEBUG] energy: -13.997315007427387
2025-07-18 14:19:18,354[DEBUG] optimize site: [28, 29]
2025-07-18 14:19:18,356[DEBUG] use direct eigensolver
2025-07-18 14:19:18,404[DEBUG] energy: -13.997315007427389
2025-07-18 14:19:18,405[DEBUG] optimize site: [29, 30]
2025-07-18 14:19:18,408[DEBUG] use direct eigensolver
2025-07-18 14:19:18,414[DEBUG] energy: -13.997315007427382
2025-07-18 14:19:18,416[DEBUG] optimize site: [30, 31]
2025-07-18 14:19:18,417[DEBUG] use direct eigensolver
2025-07-18 14:19:18,421[DEBUG] energy: -13.997315007427378
2025-07-18 14:19:18,422[DEBUG] 3 sweeps are finished, lowest energy = -13.997315090211584
2025-07-18 14:19:18,425[INFO] DMRG has converged!
2025-07-18 14:19:18,461[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: -13.997315090211584

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