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

2025-03-08 11:09:42,675[INFO] Use NumPy as backend
2025-03-08 11:09:42,676[INFO] numpy random seed is 9012
2025-03-08 11:09:42,676[INFO] random seed is 1092
2025-03-08 11:09:42,686[INFO] Git Commit Hash: d553391e2b487be8866afade06e47c2377a27a9b
2025-03-08 11:09:42,687[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}")

2025-03-08 11:09:42,779[DEBUG] # of operator terms: 93
2025-03-08 11:09:42,779[DEBUG] Input operator terms: 93
2025-03-08 11:09:42,781[DEBUG] After combination of the same terms: 93
2025-03-08 11:09:42,782[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))

2025-03-08 11:09:42,851[INFO] optimization method: 2site
2025-03-08 11:09:42,851[INFO] e_rtol: 1e-06
2025-03-08 11:09:42,852[INFO] e_atol: 1e-08
2025-03-08 11:09:42,852[INFO] procedure: [[30, 0.2], [30, 0], [30, 0], [30, 0], [30, 0]]
2025-03-08 11:09:42,884[DEBUG] isweep: 0
2025-03-08 11:09:42,886[DEBUG] compress config in current loop: 30, percent: 0.2
2025-03-08 11:09:42,887[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]
2025-03-08 11:09:42,888[DEBUG] optimize site: [0, 1]
2025-03-08 11:09:42,889[DEBUG] use direct eigensolver
2025-03-08 11:09:42,892[DEBUG] energy: -0.9279990226898331
2025-03-08 11:09:42,894[DEBUG] optimize site: [1, 2]
2025-03-08 11:09:42,896[DEBUG] use direct eigensolver
2025-03-08 11:09:42,901[DEBUG] energy: -1.284089573410534
2025-03-08 11:09:42,903[DEBUG] optimize site: [2, 3]
2025-03-08 11:09:42,905[DEBUG] use direct eigensolver
2025-03-08 11:09:42,928[DEBUG] energy: -2.0857452647499213
2025-03-08 11:09:42,930[DEBUG] optimize site: [3, 4]
2025-03-08 11:09:42,933[DEBUG] use direct eigensolver
2025-03-08 11:09:43,189[DEBUG] energy: -2.8158895272374123
2025-03-08 11:09:43,191[DEBUG] optimize site: [4, 5]
2025-03-08 11:09:43,241[DEBUG] use davidson, HC hops: 34
2025-03-08 11:09:43,242[DEBUG] energy: -3.293367315585801
2025-03-08 11:09:43,244[DEBUG] optimize site: [5, 6]
2025-03-08 11:09:43,319[DEBUG] use davidson, HC hops: 42
2025-03-08 11:09:43,320[DEBUG] energy: -3.7449867503071976
2025-03-08 11:09:43,325[DEBUG] optimize site: [6, 7]
2025-03-08 11:09:43,398[DEBUG] use davidson, HC hops: 42
2025-03-08 11:09:43,400[DEBUG] energy: -4.176385575496491
2025-03-08 11:09:43,404[DEBUG] optimize site: [7, 8]
2025-03-08 11:09:43,483[DEBUG] use davidson, HC hops: 44
2025-03-08 11:09:43,484[DEBUG] energy: -4.583593477927387
2025-03-08 11:09:43,488[DEBUG] optimize site: [8, 9]
2025-03-08 11:09:43,585[DEBUG] use davidson, HC hops: 55
2025-03-08 11:09:43,587[DEBUG] energy: -4.968031845671204
2025-03-08 11:09:43,590[DEBUG] optimize site: [9, 10]
2025-03-08 11:09:43,710[DEBUG] use davidson, HC hops: 68
2025-03-08 11:09:43,712[DEBUG] energy: -5.414706360833986
2025-03-08 11:09:43,716[DEBUG] optimize site: [10, 11]
2025-03-08 11:09:43,842[DEBUG] use davidson, HC hops: 72
2025-03-08 11:09:43,844[DEBUG] energy: -5.856529754520472
2025-03-08 11:09:43,847[DEBUG] optimize site: [11, 12]
2025-03-08 11:09:44,017[DEBUG] use davidson, HC hops: 100
2025-03-08 11:09:44,017[DEBUG] energy: -6.279022467295808
2025-03-08 11:09:44,020[DEBUG] optimize site: [12, 13]
2025-03-08 11:09:44,071[DEBUG] use davidson, HC hops: 52
2025-03-08 11:09:44,072[DEBUG] energy: -6.857389012204745
2025-03-08 11:09:44,076[DEBUG] optimize site: [13, 14]
2025-03-08 11:09:44,201[DEBUG] use davidson, HC hops: 100
2025-03-08 11:09:44,203[DEBUG] energy: -7.114588022005752
2025-03-08 11:09:44,208[DEBUG] optimize site: [14, 15]
2025-03-08 11:09:44,278[DEBUG] use davidson, HC hops: 47
2025-03-08 11:09:44,279[DEBUG] energy: -7.641631783835396
2025-03-08 11:09:44,283[DEBUG] optimize site: [15, 16]
2025-03-08 11:09:44,342[DEBUG] use davidson, HC hops: 51
2025-03-08 11:09:44,343[DEBUG] energy: -8.118395338420026
2025-03-08 11:09:44,349[DEBUG] optimize site: [16, 17]
2025-03-08 11:09:44,444[DEBUG] use davidson, HC hops: 57
2025-03-08 11:09:44,445[DEBUG] energy: -8.579533430762845
2025-03-08 11:09:44,449[DEBUG] optimize site: [17, 18]
2025-03-08 11:09:44,559[DEBUG] use davidson, HC hops: 66
2025-03-08 11:09:44,560[DEBUG] energy: -8.983113190158456
2025-03-08 11:09:44,564[DEBUG] optimize site: [18, 19]
2025-03-08 11:09:44,669[DEBUG] use davidson, HC hops: 62
2025-03-08 11:09:44,669[DEBUG] energy: -9.42220540460764
2025-03-08 11:09:44,673[DEBUG] optimize site: [19, 20]
2025-03-08 11:09:44,772[DEBUG] use davidson, HC hops: 62
2025-03-08 11:09:44,773[DEBUG] energy: -9.90369368091438
2025-03-08 11:09:44,776[DEBUG] optimize site: [20, 21]
2025-03-08 11:09:44,858[DEBUG] use davidson, HC hops: 81
2025-03-08 11:09:44,859[DEBUG] energy: -10.398530611697952
2025-03-08 11:09:44,863[DEBUG] optimize site: [21, 22]
2025-03-08 11:09:44,989[DEBUG] use davidson, HC hops: 76
2025-03-08 11:09:44,990[DEBUG] energy: -10.834489434421672
2025-03-08 11:09:44,995[DEBUG] optimize site: [22, 23]
2025-03-08 11:09:45,092[DEBUG] use davidson, HC hops: 58
2025-03-08 11:09:45,094[DEBUG] energy: -11.415128707126794
2025-03-08 11:09:45,098[DEBUG] optimize site: [23, 24]
2025-03-08 11:09:45,186[DEBUG] use davidson, HC hops: 52
2025-03-08 11:09:45,188[DEBUG] energy: -12.122795879745034
2025-03-08 11:09:45,193[DEBUG] optimize site: [24, 25]
2025-03-08 11:09:45,270[DEBUG] use davidson, HC hops: 71
2025-03-08 11:09:45,272[DEBUG] energy: -12.812234874023474
2025-03-08 11:09:45,276[DEBUG] optimize site: [25, 26]
2025-03-08 11:09:45,373[DEBUG] use davidson, HC hops: 58
2025-03-08 11:09:45,374[DEBUG] energy: -13.774582804126663
2025-03-08 11:09:45,379[DEBUG] optimize site: [26, 27]
2025-03-08 11:09:45,452[DEBUG] use davidson, HC hops: 47
2025-03-08 11:09:45,454[DEBUG] energy: -13.996832655813071
2025-03-08 11:09:45,456[DEBUG] optimize site: [27, 28]
2025-03-08 11:09:45,459[DEBUG] use direct eigensolver
2025-03-08 11:09:45,724[DEBUG] energy: -13.99683265553401
2025-03-08 11:09:45,727[DEBUG] optimize site: [28, 29]
2025-03-08 11:09:45,729[DEBUG] use direct eigensolver
2025-03-08 11:09:45,801[DEBUG] energy: -13.99683265553399
2025-03-08 11:09:45,804[DEBUG] optimize site: [29, 30]
2025-03-08 11:09:45,806[DEBUG] use direct eigensolver
2025-03-08 11:09:45,815[DEBUG] energy: -13.99683265553399
2025-03-08 11:09:45,816[DEBUG] optimize site: [30, 31]
2025-03-08 11:09:45,819[DEBUG] use direct eigensolver
2025-03-08 11:09:45,822[DEBUG] energy: -13.996832655534
2025-03-08 11:09:45,825[DEBUG] 1 sweeps are finished, lowest energy = -13.996832655813071
2025-03-08 11:09:45,827[DEBUG] isweep: 1
2025-03-08 11:09:45,828[DEBUG] compress config in current loop: 30, percent: 0
2025-03-08 11:09:45,829[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]
2025-03-08 11:09:45,831[DEBUG] optimize site: [30, 31]
2025-03-08 11:09:45,832[DEBUG] use direct eigensolver
2025-03-08 11:09:45,836[DEBUG] energy: -13.996832655534
2025-03-08 11:09:45,838[DEBUG] optimize site: [29, 30]
2025-03-08 11:09:45,840[DEBUG] use direct eigensolver
2025-03-08 11:09:45,845[DEBUG] energy: -13.996832655533996
2025-03-08 11:09:45,846[DEBUG] optimize site: [28, 29]
2025-03-08 11:09:45,847[DEBUG] use direct eigensolver
2025-03-08 11:09:45,917[DEBUG] energy: -13.996832655533998
2025-03-08 11:09:45,920[DEBUG] optimize site: [27, 28]
2025-03-08 11:09:45,922[DEBUG] use direct eigensolver
2025-03-08 11:09:46,178[DEBUG] energy: -13.996832655534005
2025-03-08 11:09:46,181[DEBUG] optimize site: [26, 27]
2025-03-08 11:09:46,190[DEBUG] use davidson, HC hops: 4
2025-03-08 11:09:46,192[DEBUG] energy: -13.996832655813622
2025-03-08 11:09:46,199[DEBUG] optimize site: [25, 26]
2025-03-08 11:09:46,239[DEBUG] use davidson, HC hops: 22
2025-03-08 11:09:46,240[DEBUG] energy: -13.996844945038365
2025-03-08 11:09:46,244[DEBUG] optimize site: [24, 25]
2025-03-08 11:09:46,291[DEBUG] use davidson, HC hops: 28
2025-03-08 11:09:46,291[DEBUG] energy: -13.997067101658736
2025-03-08 11:09:46,296[DEBUG] optimize site: [23, 24]
2025-03-08 11:09:46,322[DEBUG] use davidson, HC hops: 25
2025-03-08 11:09:46,323[DEBUG] energy: -13.99710168471751
2025-03-08 11:09:46,327[DEBUG] optimize site: [22, 23]
2025-03-08 11:09:46,352[DEBUG] use davidson, HC hops: 23
2025-03-08 11:09:46,353[DEBUG] energy: -13.99710660821372
2025-03-08 11:09:46,357[DEBUG] optimize site: [21, 22]
2025-03-08 11:09:46,382[DEBUG] use davidson, HC hops: 23
2025-03-08 11:09:46,384[DEBUG] energy: -13.997113698271148
2025-03-08 11:09:46,387[DEBUG] optimize site: [20, 21]
2025-03-08 11:09:46,428[DEBUG] use davidson, HC hops: 26
2025-03-08 11:09:46,430[DEBUG] energy: -13.997162638323573
2025-03-08 11:09:46,434[DEBUG] optimize site: [19, 20]
2025-03-08 11:09:46,476[DEBUG] use davidson, HC hops: 23
2025-03-08 11:09:46,477[DEBUG] energy: -13.997170144965569
2025-03-08 11:09:46,482[DEBUG] optimize site: [18, 19]
2025-03-08 11:09:46,524[DEBUG] use davidson, HC hops: 26
2025-03-08 11:09:46,526[DEBUG] energy: -13.997199975427426
2025-03-08 11:09:46,529[DEBUG] optimize site: [17, 18]
2025-03-08 11:09:46,553[DEBUG] use davidson, HC hops: 22
2025-03-08 11:09:46,554[DEBUG] energy: -13.997204392621637
2025-03-08 11:09:46,558[DEBUG] optimize site: [16, 17]
2025-03-08 11:09:46,586[DEBUG] use davidson, HC hops: 25
2025-03-08 11:09:46,586[DEBUG] energy: -13.997225037523819
2025-03-08 11:09:46,590[DEBUG] optimize site: [15, 16]
2025-03-08 11:09:46,618[DEBUG] use davidson, HC hops: 26
2025-03-08 11:09:46,619[DEBUG] energy: -13.997284918121172
2025-03-08 11:09:46,623[DEBUG] optimize site: [14, 15]
2025-03-08 11:09:46,658[DEBUG] use davidson, HC hops: 22
2025-03-08 11:09:46,660[DEBUG] energy: -13.997290859971237
2025-03-08 11:09:46,665[DEBUG] optimize site: [13, 14]
2025-03-08 11:09:46,703[DEBUG] use davidson, HC hops: 20
2025-03-08 11:09:46,705[DEBUG] energy: -13.997293257653768
2025-03-08 11:09:46,709[DEBUG] optimize site: [12, 13]
2025-03-08 11:09:46,751[DEBUG] use davidson, HC hops: 23
2025-03-08 11:09:46,753[DEBUG] energy: -13.997306225086662
2025-03-08 11:09:46,758[DEBUG] optimize site: [11, 12]
2025-03-08 11:09:46,796[DEBUG] use davidson, HC hops: 21
2025-03-08 11:09:46,797[DEBUG] energy: -13.99731114559561
2025-03-08 11:09:46,802[DEBUG] optimize site: [10, 11]
2025-03-08 11:09:46,838[DEBUG] use davidson, HC hops: 20
2025-03-08 11:09:46,839[DEBUG] energy: -13.99731313270749
2025-03-08 11:09:46,843[DEBUG] optimize site: [9, 10]
2025-03-08 11:09:46,868[DEBUG] use davidson, HC hops: 17
2025-03-08 11:09:46,869[DEBUG] energy: -13.997314428626357
2025-03-08 11:09:46,873[DEBUG] optimize site: [8, 9]
2025-03-08 11:09:46,895[DEBUG] use davidson, HC hops: 11
2025-03-08 11:09:46,897[DEBUG] energy: -13.997314715468697
2025-03-08 11:09:46,902[DEBUG] optimize site: [7, 8]
2025-03-08 11:09:46,916[DEBUG] use davidson, HC hops: 7
2025-03-08 11:09:46,917[DEBUG] energy: -13.997314712669803
2025-03-08 11:09:46,922[DEBUG] optimize site: [6, 7]
2025-03-08 11:09:46,946[DEBUG] use davidson, HC hops: 12
2025-03-08 11:09:46,947[DEBUG] energy: -13.997314999750055
2025-03-08 11:09:46,953[DEBUG] optimize site: [5, 6]
2025-03-08 11:09:46,971[DEBUG] use davidson, HC hops: 7
2025-03-08 11:09:46,973[DEBUG] energy: -13.99731500381148
2025-03-08 11:09:46,978[DEBUG] optimize site: [4, 5]
2025-03-08 11:09:46,990[DEBUG] use davidson, HC hops: 5
2025-03-08 11:09:46,992[DEBUG] energy: -13.997315004767804
2025-03-08 11:09:46,994[DEBUG] optimize site: [3, 4]
2025-03-08 11:09:46,999[DEBUG] use direct eigensolver
2025-03-08 11:09:47,264[DEBUG] energy: -13.997315004467124
2025-03-08 11:09:47,267[DEBUG] optimize site: [2, 3]
2025-03-08 11:09:47,270[DEBUG] use direct eigensolver
2025-03-08 11:09:47,318[DEBUG] energy: -13.997315004467112
2025-03-08 11:09:47,319[DEBUG] optimize site: [1, 2]
2025-03-08 11:09:47,323[DEBUG] use direct eigensolver
2025-03-08 11:09:47,328[DEBUG] energy: -13.9973150044671
2025-03-08 11:09:47,329[DEBUG] optimize site: [0, 1]
2025-03-08 11:09:47,332[DEBUG] use direct eigensolver
2025-03-08 11:09:47,335[DEBUG] energy: -13.997315004467104
2025-03-08 11:09:47,336[DEBUG] 2 sweeps are finished, lowest energy = -13.997315004767804
2025-03-08 11:09:47,339[DEBUG] isweep: 2
2025-03-08 11:09:47,339[DEBUG] compress config in current loop: 30, percent: 0
2025-03-08 11:09:47,342[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]
2025-03-08 11:09:47,344[DEBUG] optimize site: [0, 1]
2025-03-08 11:09:47,344[DEBUG] use direct eigensolver
2025-03-08 11:09:47,348[DEBUG] energy: -13.997315004467104
2025-03-08 11:09:47,349[DEBUG] optimize site: [1, 2]
2025-03-08 11:09:47,352[DEBUG] use direct eigensolver
2025-03-08 11:09:47,358[DEBUG] energy: -13.997315004467097
2025-03-08 11:09:47,360[DEBUG] optimize site: [2, 3]
2025-03-08 11:09:47,361[DEBUG] use direct eigensolver
2025-03-08 11:09:47,406[DEBUG] energy: -13.997315004467092
2025-03-08 11:09:47,407[DEBUG] optimize site: [3, 4]
2025-03-08 11:09:47,410[DEBUG] use direct eigensolver
2025-03-08 11:09:47,663[DEBUG] energy: -13.997315004467117
2025-03-08 11:09:47,667[DEBUG] optimize site: [4, 5]
2025-03-08 11:09:47,673[DEBUG] use davidson, HC hops: 4
2025-03-08 11:09:47,675[DEBUG] energy: -13.997315004767874
2025-03-08 11:09:47,679[DEBUG] optimize site: [5, 6]
2025-03-08 11:09:47,686[DEBUG] use davidson, HC hops: 4
2025-03-08 11:09:47,688[DEBUG] energy: -13.99731500466776
2025-03-08 11:09:47,691[DEBUG] optimize site: [6, 7]
2025-03-08 11:09:47,699[DEBUG] use davidson, HC hops: 6
2025-03-08 11:09:47,700[DEBUG] energy: -13.997315012470631
2025-03-08 11:09:47,704[DEBUG] optimize site: [7, 8]
2025-03-08 11:09:47,712[DEBUG] use davidson, HC hops: 5
2025-03-08 11:09:47,712[DEBUG] energy: -13.997315006066628
2025-03-08 11:09:47,717[DEBUG] optimize site: [8, 9]
2025-03-08 11:09:47,726[DEBUG] use davidson, HC hops: 7
2025-03-08 11:09:47,727[DEBUG] energy: -13.997315033374505
2025-03-08 11:09:47,731[DEBUG] optimize site: [9, 10]
2025-03-08 11:09:47,740[DEBUG] use davidson, HC hops: 6
2025-03-08 11:09:47,740[DEBUG] energy: -13.997315010121918
2025-03-08 11:09:47,745[DEBUG] optimize site: [10, 11]
2025-03-08 11:09:47,755[DEBUG] use davidson, HC hops: 8
2025-03-08 11:09:47,757[DEBUG] energy: -13.997315055776836
2025-03-08 11:09:47,760[DEBUG] optimize site: [11, 12]
2025-03-08 11:09:47,769[DEBUG] use davidson, HC hops: 7
2025-03-08 11:09:47,770[DEBUG] energy: -13.997315015890429
2025-03-08 11:09:47,774[DEBUG] optimize site: [12, 13]
2025-03-08 11:09:47,785[DEBUG] use davidson, HC hops: 8
2025-03-08 11:09:47,785[DEBUG] energy: -13.997315076759346
2025-03-08 11:09:47,789[DEBUG] optimize site: [13, 14]
2025-03-08 11:09:47,799[DEBUG] use davidson, HC hops: 7
2025-03-08 11:09:47,799[DEBUG] energy: -13.997315021063715
2025-03-08 11:09:47,804[DEBUG] optimize site: [14, 15]
2025-03-08 11:09:47,814[DEBUG] use davidson, HC hops: 8
2025-03-08 11:09:47,815[DEBUG] energy: -13.997315089163413
2025-03-08 11:09:47,819[DEBUG] optimize site: [15, 16]
2025-03-08 11:09:47,830[DEBUG] use davidson, HC hops: 8
2025-03-08 11:09:47,832[DEBUG] energy: -13.997315023237665
2025-03-08 11:09:47,835[DEBUG] optimize site: [16, 17]
2025-03-08 11:09:47,847[DEBUG] use davidson, HC hops: 9
2025-03-08 11:09:47,848[DEBUG] energy: -13.997315090211583
2025-03-08 11:09:47,851[DEBUG] optimize site: [17, 18]
2025-03-08 11:09:47,863[DEBUG] use davidson, HC hops: 8
2025-03-08 11:09:47,865[DEBUG] energy: -13.997315022014197
2025-03-08 11:09:47,868[DEBUG] optimize site: [18, 19]
2025-03-08 11:09:47,885[DEBUG] use davidson, HC hops: 8
2025-03-08 11:09:47,886[DEBUG] energy: -13.997315079212502
2025-03-08 11:09:47,891[DEBUG] optimize site: [19, 20]
2025-03-08 11:09:47,906[DEBUG] use davidson, HC hops: 7
2025-03-08 11:09:47,907[DEBUG] energy: -13.997315018389624
2025-03-08 11:09:47,912[DEBUG] optimize site: [20, 21]
2025-03-08 11:09:47,928[DEBUG] use davidson, HC hops: 8
2025-03-08 11:09:47,929[DEBUG] energy: -13.997315060471507
2025-03-08 11:09:47,934[DEBUG] optimize site: [21, 22]
2025-03-08 11:09:47,947[DEBUG] use davidson, HC hops: 6
2025-03-08 11:09:47,948[DEBUG] energy: -13.997315014222917
2025-03-08 11:09:47,953[DEBUG] optimize site: [22, 23]
2025-03-08 11:09:47,970[DEBUG] use davidson, HC hops: 8
2025-03-08 11:09:47,972[DEBUG] energy: -13.99731503638068
2025-03-08 11:09:47,976[DEBUG] optimize site: [23, 24]
2025-03-08 11:09:47,989[DEBUG] use davidson, HC hops: 6
2025-03-08 11:09:47,990[DEBUG] energy: -13.997315009063263
2025-03-08 11:09:47,995[DEBUG] optimize site: [24, 25]
2025-03-08 11:09:48,008[DEBUG] use davidson, HC hops: 6
2025-03-08 11:09:48,009[DEBUG] energy: -13.997315015431745
2025-03-08 11:09:48,014[DEBUG] optimize site: [25, 26]
2025-03-08 11:09:48,026[DEBUG] use davidson, HC hops: 5
2025-03-08 11:09:48,026[DEBUG] energy: -13.99731500763044
2025-03-08 11:09:48,031[DEBUG] optimize site: [26, 27]
2025-03-08 11:09:48,041[DEBUG] use davidson, HC hops: 4
2025-03-08 11:09:48,042[DEBUG] energy: -13.997315007727408
2025-03-08 11:09:48,044[DEBUG] optimize site: [27, 28]
2025-03-08 11:09:48,047[DEBUG] use direct eigensolver
2025-03-08 11:09:48,320[DEBUG] energy: -13.997315007427375
2025-03-08 11:09:48,323[DEBUG] optimize site: [28, 29]
2025-03-08 11:09:48,329[DEBUG] use direct eigensolver
2025-03-08 11:09:48,407[DEBUG] energy: -13.997315007427375
2025-03-08 11:09:48,410[DEBUG] optimize site: [29, 30]
2025-03-08 11:09:48,411[DEBUG] use direct eigensolver
2025-03-08 11:09:48,417[DEBUG] energy: -13.997315007427359
2025-03-08 11:09:48,418[DEBUG] optimize site: [30, 31]
2025-03-08 11:09:48,421[DEBUG] use direct eigensolver
2025-03-08 11:09:48,424[DEBUG] energy: -13.997315007427373
2025-03-08 11:09:48,426[DEBUG] 3 sweeps are finished, lowest energy = -13.997315090211583
2025-03-08 11:09:48,427[INFO] DMRG has converged!
2025-03-08 11:09:48,462[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: -13.997315090211583

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