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

2024-12-04 10:30:14,233[INFO] Use NumPy as backend
2024-12-04 10:30:14,234[INFO] numpy random seed is 9012
2024-12-04 10:30:14,235[INFO] random seed is 1092
2024-12-04 10:30:14,246[INFO] Git Commit Hash: b882466cb690e4399b35e0772555500df69bb298
2024-12-04 10:30:14,248[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}")

2024-12-04 10:30:14,346[DEBUG] # of operator terms: 93
2024-12-04 10:30:14,347[DEBUG] Input operator terms: 93
2024-12-04 10:30:14,349[DEBUG] After combination of the same terms: 93
2024-12-04 10:30:14,350[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))

2024-12-04 10:30:14,422[INFO] optimization method: 2site
2024-12-04 10:30:14,425[INFO] e_rtol: 1e-06
2024-12-04 10:30:14,426[INFO] e_atol: 1e-08
2024-12-04 10:30:14,428[INFO] procedure: [[30, 0.2], [30, 0], [30, 0], [30, 0], [30, 0]]
2024-12-04 10:30:14,460[DEBUG] isweep: 0
2024-12-04 10:30:14,463[DEBUG] compress config in current loop: 30, percent: 0.2
2024-12-04 10:30:14,465[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]
2024-12-04 10:30:14,467[DEBUG] optimize site: [0, 1]
2024-12-04 10:30:14,469[DEBUG] use direct eigensolver
2024-12-04 10:30:14,473[DEBUG] energy: -0.9279990226898324
2024-12-04 10:30:14,476[DEBUG] optimize site: [1, 2]
2024-12-04 10:30:14,479[DEBUG] use direct eigensolver
2024-12-04 10:30:14,484[DEBUG] energy: -1.2840895734105349
2024-12-04 10:30:14,488[DEBUG] optimize site: [2, 3]
2024-12-04 10:30:14,490[DEBUG] use direct eigensolver
2024-12-04 10:30:14,515[DEBUG] energy: -2.0857452647499213
2024-12-04 10:30:14,519[DEBUG] optimize site: [3, 4]
2024-12-04 10:30:14,523[DEBUG] use direct eigensolver
2024-12-04 10:30:14,746[DEBUG] energy: -2.8158895272374123
2024-12-04 10:30:14,749[DEBUG] optimize site: [4, 5]
2024-12-04 10:30:14,777[DEBUG] use davidson, HC hops: 34
2024-12-04 10:30:14,779[DEBUG] energy: -3.2933673155858028
2024-12-04 10:30:14,782[DEBUG] optimize site: [5, 6]
2024-12-04 10:30:14,823[DEBUG] use davidson, HC hops: 42
2024-12-04 10:30:14,825[DEBUG] energy: -3.7449867503071994
2024-12-04 10:30:14,829[DEBUG] optimize site: [6, 7]
2024-12-04 10:30:14,888[DEBUG] use davidson, HC hops: 42
2024-12-04 10:30:14,891[DEBUG] energy: -4.176385575496492
2024-12-04 10:30:14,895[DEBUG] optimize site: [7, 8]
2024-12-04 10:30:14,939[DEBUG] use davidson, HC hops: 44
2024-12-04 10:30:14,942[DEBUG] energy: -4.583593477927389
2024-12-04 10:30:14,945[DEBUG] optimize site: [8, 9]
2024-12-04 10:30:15,023[DEBUG] use davidson, HC hops: 55
2024-12-04 10:30:15,026[DEBUG] energy: -4.968031845671205
2024-12-04 10:30:15,031[DEBUG] optimize site: [9, 10]
2024-12-04 10:30:15,148[DEBUG] use davidson, HC hops: 68
2024-12-04 10:30:15,151[DEBUG] energy: -5.414706360833982
2024-12-04 10:30:15,156[DEBUG] optimize site: [10, 11]
2024-12-04 10:30:15,281[DEBUG] use davidson, HC hops: 72
2024-12-04 10:30:15,281[DEBUG] energy: -5.856529754520465
2024-12-04 10:30:15,286[DEBUG] optimize site: [11, 12]
2024-12-04 10:30:15,432[DEBUG] use davidson, HC hops: 100
2024-12-04 10:30:15,433[DEBUG] energy: -6.279022467295804
2024-12-04 10:30:15,437[DEBUG] optimize site: [12, 13]
2024-12-04 10:30:15,502[DEBUG] use davidson, HC hops: 52
2024-12-04 10:30:15,504[DEBUG] energy: -6.85738901220476
2024-12-04 10:30:15,508[DEBUG] optimize site: [13, 14]
2024-12-04 10:30:15,606[DEBUG] use davidson, HC hops: 100
2024-12-04 10:30:15,609[DEBUG] energy: -7.114588022005781
2024-12-04 10:30:15,612[DEBUG] optimize site: [14, 15]
2024-12-04 10:30:15,667[DEBUG] use davidson, HC hops: 47
2024-12-04 10:30:15,670[DEBUG] energy: -7.6416317838354235
2024-12-04 10:30:15,673[DEBUG] optimize site: [15, 16]
2024-12-04 10:30:15,731[DEBUG] use davidson, HC hops: 51
2024-12-04 10:30:15,734[DEBUG] energy: -8.118395338420058
2024-12-04 10:30:15,739[DEBUG] optimize site: [16, 17]
2024-12-04 10:30:15,836[DEBUG] use davidson, HC hops: 57
2024-12-04 10:30:15,838[DEBUG] energy: -8.579533430762854
2024-12-04 10:30:15,842[DEBUG] optimize site: [17, 18]
2024-12-04 10:30:15,908[DEBUG] use davidson, HC hops: 66
2024-12-04 10:30:15,911[DEBUG] energy: -8.983113190158448
2024-12-04 10:30:15,914[DEBUG] optimize site: [18, 19]
2024-12-04 10:30:15,996[DEBUG] use davidson, HC hops: 62
2024-12-04 10:30:15,999[DEBUG] energy: -9.422205404607668
2024-12-04 10:30:16,004[DEBUG] optimize site: [19, 20]
2024-12-04 10:30:16,098[DEBUG] use davidson, HC hops: 62
2024-12-04 10:30:16,101[DEBUG] energy: -9.903693680914383
2024-12-04 10:30:16,104[DEBUG] optimize site: [20, 21]
2024-12-04 10:30:16,185[DEBUG] use davidson, HC hops: 81
2024-12-04 10:30:16,188[DEBUG] energy: -10.398530611697964
2024-12-04 10:30:16,191[DEBUG] optimize site: [21, 22]
2024-12-04 10:30:16,281[DEBUG] use davidson, HC hops: 76
2024-12-04 10:30:16,284[DEBUG] energy: -10.834489434421666
2024-12-04 10:30:16,289[DEBUG] optimize site: [22, 23]
2024-12-04 10:30:16,389[DEBUG] use davidson, HC hops: 58
2024-12-04 10:30:16,390[DEBUG] energy: -11.41512870712682
2024-12-04 10:30:16,394[DEBUG] optimize site: [23, 24]
2024-12-04 10:30:16,482[DEBUG] use davidson, HC hops: 52
2024-12-04 10:30:16,483[DEBUG] energy: -12.122795879745059
2024-12-04 10:30:16,487[DEBUG] optimize site: [24, 25]
2024-12-04 10:30:16,608[DEBUG] use davidson, HC hops: 71
2024-12-04 10:30:16,611[DEBUG] energy: -12.812234874023488
2024-12-04 10:30:16,616[DEBUG] optimize site: [25, 26]
2024-12-04 10:30:16,721[DEBUG] use davidson, HC hops: 58
2024-12-04 10:30:16,722[DEBUG] energy: -13.77458280412668
2024-12-04 10:30:16,725[DEBUG] optimize site: [26, 27]
2024-12-04 10:30:16,798[DEBUG] use davidson, HC hops: 47
2024-12-04 10:30:16,801[DEBUG] energy: -13.996832655813105
2024-12-04 10:30:16,804[DEBUG] optimize site: [27, 28]
2024-12-04 10:30:16,808[DEBUG] use direct eigensolver
2024-12-04 10:30:17,068[DEBUG] energy: -13.996832655534023
2024-12-04 10:30:17,070[DEBUG] optimize site: [28, 29]
2024-12-04 10:30:17,072[DEBUG] use direct eigensolver
2024-12-04 10:30:17,117[DEBUG] energy: -13.99683265553401
2024-12-04 10:30:17,119[DEBUG] optimize site: [29, 30]
2024-12-04 10:30:17,121[DEBUG] use direct eigensolver
2024-12-04 10:30:17,126[DEBUG] energy: -13.996832655534012
2024-12-04 10:30:17,127[DEBUG] optimize site: [30, 31]
2024-12-04 10:30:17,129[DEBUG] use direct eigensolver
2024-12-04 10:30:17,131[DEBUG] energy: -13.996832655533995
2024-12-04 10:30:17,133[DEBUG] 1 sweeps are finished, lowest energy = -13.996832655813105
2024-12-04 10:30:17,133[DEBUG] isweep: 1
2024-12-04 10:30:17,134[DEBUG] compress config in current loop: 30, percent: 0
2024-12-04 10:30:17,135[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]
2024-12-04 10:30:17,136[DEBUG] optimize site: [30, 31]
2024-12-04 10:30:17,137[DEBUG] use direct eigensolver
2024-12-04 10:30:17,139[DEBUG] energy: -13.996832655533995
2024-12-04 10:30:17,141[DEBUG] optimize site: [29, 30]
2024-12-04 10:30:17,142[DEBUG] use direct eigensolver
2024-12-04 10:30:17,147[DEBUG] energy: -13.996832655534021
2024-12-04 10:30:17,149[DEBUG] optimize site: [28, 29]
2024-12-04 10:30:17,150[DEBUG] use direct eigensolver
2024-12-04 10:30:17,218[DEBUG] energy: -13.996832655534014
2024-12-04 10:30:17,222[DEBUG] optimize site: [27, 28]
2024-12-04 10:30:17,224[DEBUG] use direct eigensolver
2024-12-04 10:30:17,468[DEBUG] energy: -13.99683265553401
2024-12-04 10:30:17,471[DEBUG] optimize site: [26, 27]
2024-12-04 10:30:17,477[DEBUG] use davidson, HC hops: 4
2024-12-04 10:30:17,479[DEBUG] energy: -13.996832655813652
2024-12-04 10:30:17,484[DEBUG] optimize site: [25, 26]
2024-12-04 10:30:17,506[DEBUG] use davidson, HC hops: 22
2024-12-04 10:30:17,509[DEBUG] energy: -13.996844945038399
2024-12-04 10:30:17,513[DEBUG] optimize site: [24, 25]
2024-12-04 10:30:17,541[DEBUG] use davidson, HC hops: 28
2024-12-04 10:30:17,543[DEBUG] energy: -13.9970671016588
2024-12-04 10:30:17,547[DEBUG] optimize site: [23, 24]
2024-12-04 10:30:17,573[DEBUG] use davidson, HC hops: 25
2024-12-04 10:30:17,575[DEBUG] energy: -13.99710168471755
2024-12-04 10:30:17,579[DEBUG] optimize site: [22, 23]
2024-12-04 10:30:17,616[DEBUG] use davidson, HC hops: 23
2024-12-04 10:30:17,619[DEBUG] energy: -13.997106608213755
2024-12-04 10:30:17,624[DEBUG] optimize site: [21, 22]
2024-12-04 10:30:17,669[DEBUG] use davidson, HC hops: 23
2024-12-04 10:30:17,672[DEBUG] energy: -13.997113698271178
2024-12-04 10:30:17,677[DEBUG] optimize site: [20, 21]
2024-12-04 10:30:17,717[DEBUG] use davidson, HC hops: 26
2024-12-04 10:30:17,719[DEBUG] energy: -13.997162638323594
2024-12-04 10:30:17,723[DEBUG] optimize site: [19, 20]
2024-12-04 10:30:17,749[DEBUG] use davidson, HC hops: 23
2024-12-04 10:30:17,751[DEBUG] energy: -13.99717014496559
2024-12-04 10:30:17,755[DEBUG] optimize site: [18, 19]
2024-12-04 10:30:17,798[DEBUG] use davidson, HC hops: 26
2024-12-04 10:30:17,800[DEBUG] energy: -13.997199975427481
2024-12-04 10:30:17,804[DEBUG] optimize site: [17, 18]
2024-12-04 10:30:17,844[DEBUG] use davidson, HC hops: 22
2024-12-04 10:30:17,846[DEBUG] energy: -13.997204392621665
2024-12-04 10:30:17,850[DEBUG] optimize site: [16, 17]
2024-12-04 10:30:17,896[DEBUG] use davidson, HC hops: 25
2024-12-04 10:30:17,897[DEBUG] energy: -13.997225037523867
2024-12-04 10:30:17,901[DEBUG] optimize site: [15, 16]
2024-12-04 10:30:17,944[DEBUG] use davidson, HC hops: 26
2024-12-04 10:30:17,947[DEBUG] energy: -13.997284918121238
2024-12-04 10:30:17,951[DEBUG] optimize site: [14, 15]
2024-12-04 10:30:17,974[DEBUG] use davidson, HC hops: 22
2024-12-04 10:30:17,977[DEBUG] energy: -13.997290859971317
2024-12-04 10:30:17,980[DEBUG] optimize site: [13, 14]
2024-12-04 10:30:18,008[DEBUG] use davidson, HC hops: 20
2024-12-04 10:30:18,010[DEBUG] energy: -13.99729325765385
2024-12-04 10:30:18,014[DEBUG] optimize site: [12, 13]
2024-12-04 10:30:18,048[DEBUG] use davidson, HC hops: 23
2024-12-04 10:30:18,051[DEBUG] energy: -13.997306225086716
2024-12-04 10:30:18,056[DEBUG] optimize site: [11, 12]
2024-12-04 10:30:18,097[DEBUG] use davidson, HC hops: 21
2024-12-04 10:30:18,100[DEBUG] energy: -13.997311145595647
2024-12-04 10:30:18,105[DEBUG] optimize site: [10, 11]
2024-12-04 10:30:18,144[DEBUG] use davidson, HC hops: 20
2024-12-04 10:30:18,148[DEBUG] energy: -13.997313132707516
2024-12-04 10:30:18,153[DEBUG] optimize site: [9, 10]
2024-12-04 10:30:18,190[DEBUG] use davidson, HC hops: 17
2024-12-04 10:30:18,193[DEBUG] energy: -13.997314428626407
2024-12-04 10:30:18,200[DEBUG] optimize site: [8, 9]
2024-12-04 10:30:18,225[DEBUG] use davidson, HC hops: 11
2024-12-04 10:30:18,228[DEBUG] energy: -13.997314715468722
2024-12-04 10:30:18,232[DEBUG] optimize site: [7, 8]
2024-12-04 10:30:18,249[DEBUG] use davidson, HC hops: 7
2024-12-04 10:30:18,251[DEBUG] energy: -13.997314712669825
2024-12-04 10:30:18,256[DEBUG] optimize site: [6, 7]
2024-12-04 10:30:18,282[DEBUG] use davidson, HC hops: 12
2024-12-04 10:30:18,285[DEBUG] energy: -13.99731499975007
2024-12-04 10:30:18,290[DEBUG] optimize site: [5, 6]
2024-12-04 10:30:18,307[DEBUG] use davidson, HC hops: 7
2024-12-04 10:30:18,309[DEBUG] energy: -13.997315003811492
2024-12-04 10:30:18,314[DEBUG] optimize site: [4, 5]
2024-12-04 10:30:18,326[DEBUG] use davidson, HC hops: 5
2024-12-04 10:30:18,329[DEBUG] energy: -13.997315004767831
2024-12-04 10:30:18,332[DEBUG] optimize site: [3, 4]
2024-12-04 10:30:18,336[DEBUG] use direct eigensolver
2024-12-04 10:30:18,607[DEBUG] energy: -13.997315004467152
2024-12-04 10:30:18,611[DEBUG] optimize site: [2, 3]
2024-12-04 10:30:18,619[DEBUG] use direct eigensolver
2024-12-04 10:30:18,698[DEBUG] energy: -13.997315004467152
2024-12-04 10:30:18,702[DEBUG] optimize site: [1, 2]
2024-12-04 10:30:18,706[DEBUG] use direct eigensolver
2024-12-04 10:30:18,716[DEBUG] energy: -13.99731500446714
2024-12-04 10:30:18,719[DEBUG] optimize site: [0, 1]
2024-12-04 10:30:18,722[DEBUG] use direct eigensolver
2024-12-04 10:30:18,727[DEBUG] energy: -13.99731500446715
2024-12-04 10:30:18,730[DEBUG] 2 sweeps are finished, lowest energy = -13.997315004767831
2024-12-04 10:30:18,733[DEBUG] isweep: 2
2024-12-04 10:30:18,734[DEBUG] compress config in current loop: 30, percent: 0
2024-12-04 10:30:18,736[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]
2024-12-04 10:30:18,738[DEBUG] optimize site: [0, 1]
2024-12-04 10:30:18,740[DEBUG] use direct eigensolver
2024-12-04 10:30:18,742[DEBUG] energy: -13.99731500446715
2024-12-04 10:30:18,744[DEBUG] optimize site: [1, 2]
2024-12-04 10:30:18,746[DEBUG] use direct eigensolver
2024-12-04 10:30:18,752[DEBUG] energy: -13.997315004467143
2024-12-04 10:30:18,754[DEBUG] optimize site: [2, 3]
2024-12-04 10:30:18,756[DEBUG] use direct eigensolver
2024-12-04 10:30:18,834[DEBUG] energy: -13.99731500446716
2024-12-04 10:30:18,837[DEBUG] optimize site: [3, 4]
2024-12-04 10:30:18,840[DEBUG] use direct eigensolver
2024-12-04 10:30:19,104[DEBUG] energy: -13.997315004467152
2024-12-04 10:30:19,107[DEBUG] optimize site: [4, 5]
2024-12-04 10:30:19,112[DEBUG] use davidson, HC hops: 4
2024-12-04 10:30:19,112[DEBUG] energy: -13.9973150047679
2024-12-04 10:30:19,116[DEBUG] optimize site: [5, 6]
2024-12-04 10:30:19,122[DEBUG] use davidson, HC hops: 4
2024-12-04 10:30:19,123[DEBUG] energy: -13.99731500466779
2024-12-04 10:30:19,128[DEBUG] optimize site: [6, 7]
2024-12-04 10:30:19,136[DEBUG] use davidson, HC hops: 6
2024-12-04 10:30:19,137[DEBUG] energy: -13.997315012470686
2024-12-04 10:30:19,140[DEBUG] optimize site: [7, 8]
2024-12-04 10:30:19,147[DEBUG] use davidson, HC hops: 5
2024-12-04 10:30:19,148[DEBUG] energy: -13.997315006066664
2024-12-04 10:30:19,150[DEBUG] optimize site: [8, 9]
2024-12-04 10:30:19,159[DEBUG] use davidson, HC hops: 7
2024-12-04 10:30:19,160[DEBUG] energy: -13.997315033374544
2024-12-04 10:30:19,162[DEBUG] optimize site: [9, 10]
2024-12-04 10:30:19,171[DEBUG] use davidson, HC hops: 6
2024-12-04 10:30:19,172[DEBUG] energy: -13.99731501012197
2024-12-04 10:30:19,174[DEBUG] optimize site: [10, 11]
2024-12-04 10:30:19,184[DEBUG] use davidson, HC hops: 8
2024-12-04 10:30:19,185[DEBUG] energy: -13.997315055776909
2024-12-04 10:30:19,188[DEBUG] optimize site: [11, 12]
2024-12-04 10:30:19,199[DEBUG] use davidson, HC hops: 7
2024-12-04 10:30:19,200[DEBUG] energy: -13.997315015890493
2024-12-04 10:30:19,204[DEBUG] optimize site: [12, 13]
2024-12-04 10:30:19,220[DEBUG] use davidson, HC hops: 8
2024-12-04 10:30:19,222[DEBUG] energy: -13.997315076759437
2024-12-04 10:30:19,227[DEBUG] optimize site: [13, 14]
2024-12-04 10:30:19,239[DEBUG] use davidson, HC hops: 7
2024-12-04 10:30:19,241[DEBUG] energy: -13.997315021063809
2024-12-04 10:30:19,244[DEBUG] optimize site: [14, 15]
2024-12-04 10:30:19,255[DEBUG] use davidson, HC hops: 8
2024-12-04 10:30:19,256[DEBUG] energy: -13.997315089163534
2024-12-04 10:30:19,260[DEBUG] optimize site: [15, 16]
2024-12-04 10:30:19,271[DEBUG] use davidson, HC hops: 8
2024-12-04 10:30:19,273[DEBUG] energy: -13.997315023237771
2024-12-04 10:30:19,276[DEBUG] optimize site: [16, 17]
2024-12-04 10:30:19,288[DEBUG] use davidson, HC hops: 9
2024-12-04 10:30:19,290[DEBUG] energy: -13.997315090211664
2024-12-04 10:30:19,293[DEBUG] optimize site: [17, 18]
2024-12-04 10:30:19,304[DEBUG] use davidson, HC hops: 8
2024-12-04 10:30:19,306[DEBUG] energy: -13.997315022014291
2024-12-04 10:30:19,310[DEBUG] optimize site: [18, 19]
2024-12-04 10:30:19,327[DEBUG] use davidson, HC hops: 8
2024-12-04 10:30:19,329[DEBUG] energy: -13.997315079212598
2024-12-04 10:30:19,334[DEBUG] optimize site: [19, 20]
2024-12-04 10:30:19,351[DEBUG] use davidson, HC hops: 7
2024-12-04 10:30:19,354[DEBUG] energy: -13.997315018389699
2024-12-04 10:30:19,360[DEBUG] optimize site: [20, 21]
2024-12-04 10:30:19,385[DEBUG] use davidson, HC hops: 8
2024-12-04 10:30:19,387[DEBUG] energy: -13.997315060471607
2024-12-04 10:30:19,391[DEBUG] optimize site: [21, 22]
2024-12-04 10:30:19,405[DEBUG] use davidson, HC hops: 6
2024-12-04 10:30:19,408[DEBUG] energy: -13.997315014223005
2024-12-04 10:30:19,413[DEBUG] optimize site: [22, 23]
2024-12-04 10:30:19,432[DEBUG] use davidson, HC hops: 8
2024-12-04 10:30:19,435[DEBUG] energy: -13.997315036380773
2024-12-04 10:30:19,439[DEBUG] optimize site: [23, 24]
2024-12-04 10:30:19,454[DEBUG] use davidson, HC hops: 6
2024-12-04 10:30:19,457[DEBUG] energy: -13.997315009063376
2024-12-04 10:30:19,462[DEBUG] optimize site: [24, 25]
2024-12-04 10:30:19,477[DEBUG] use davidson, HC hops: 6
2024-12-04 10:30:19,479[DEBUG] energy: -13.99731501543185
2024-12-04 10:30:19,484[DEBUG] optimize site: [25, 26]
2024-12-04 10:30:19,497[DEBUG] use davidson, HC hops: 5
2024-12-04 10:30:19,500[DEBUG] energy: -13.99731500763053
2024-12-04 10:30:19,505[DEBUG] optimize site: [26, 27]
2024-12-04 10:30:19,516[DEBUG] use davidson, HC hops: 4
2024-12-04 10:30:19,519[DEBUG] energy: -13.997315007727487
2024-12-04 10:30:19,522[DEBUG] optimize site: [27, 28]
2024-12-04 10:30:19,525[DEBUG] use direct eigensolver
2024-12-04 10:30:19,786[DEBUG] energy: -13.997315007427472
2024-12-04 10:30:19,790[DEBUG] optimize site: [28, 29]
2024-12-04 10:30:19,792[DEBUG] use direct eigensolver
2024-12-04 10:30:19,854[DEBUG] energy: -13.997315007427481
2024-12-04 10:30:19,858[DEBUG] optimize site: [29, 30]
2024-12-04 10:30:19,861[DEBUG] use direct eigensolver
2024-12-04 10:30:19,867[DEBUG] energy: -13.997315007427488
2024-12-04 10:30:19,871[DEBUG] optimize site: [30, 31]
2024-12-04 10:30:19,873[DEBUG] use direct eigensolver
2024-12-04 10:30:19,876[DEBUG] energy: -13.997315007427485
2024-12-04 10:30:19,878[DEBUG] 3 sweeps are finished, lowest energy = -13.997315090211664
2024-12-04 10:30:19,880[INFO] DMRG has converged!
2024-12-04 10:30:19,917[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: -13.997315090211664

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