Keeping the boson occupation number to a much smaller value does indeed decrease the number of iterations required for convergence, but I have not yet done some serious test.

I have a log file (about 5 MB) for a system with 16 bosons sites with occupation number 24 that clearly shows the convergence issues. It takes 100 iterations to lower the error from from 1e-5 to 1-6. Below a few lines from the log file.

---

Sweep=1, HS=2, Bond=15/16

Iteration: 1, Error: 0.638119

Iteration: 2, Error: 0.287186

Iteration: 3, Error: 0.130251

Iteration: 4, Error: 0.071088

Iteration: 5, Error: 0.049083

Iteration: 6, Error: 0.0423913

Iteration: 7, Error: 0.0452068

Iteration: 8, Error: 0.0538683

Iteration: 9, Error: 0.0589756

Iteration: 10, Error: 0.0676309

Iteration: 11, Error: 0.0621057

Iteration: 12, Error: 0.0512839

Iteration: 13, Error: 0.0422955

Iteration: 14, Error: 0.0355001

Iteration: 15, Error: 0.0316838

Iteration: 16, Error: 0.0273959

Iteration: 17, Error: 0.0237547

Iteration: 18, Error: 0.022184

Iteration: 19, Error: 0.0202687

Iteration: 20, Error: 0.0187334

Iteration: 21, Error: 0.0185156

Iteration: 22, Error: 0.0171161

Iteration: 23, Error: 0.015366

Iteration: 24, Error: 0.0151294

Iteration: 25, Error: 0.0138789

Iteration: 26, Error: 0.0128832

Iteration: 27, Error: 0.0115974

Iteration: 28, Error: 0.00991369

Iteration: 29, Error: 0.00899013

Iteration: 30, Error: 0.00786299

Iteration: 31, Error: 0.00725331

Iteration: 32, Error: 0.00701716

Iteration: 33, Error: 0.00628013

Iteration: 34, Error: 0.00590094

Iteration: 35, Error: 0.0052219

Iteration: 36, Error: 0.00482777

Iteration: 37, Error: 0.00446068

Iteration: 38, Error: 0.0039519

Iteration: 39, Error: 0.00379703

Iteration: 40, Error: 0.00347708

Iteration: 41, Error: 0.00329166

Iteration: 42, Error: 0.00301498

Iteration: 43, Error: 0.00277684

Iteration: 44, Error: 0.00255457

Iteration: 45, Error: 0.00233283

Iteration: 46, Error: 0.00207878

Iteration: 47, Error: 0.00192199

Iteration: 48, Error: 0.00169962

Iteration: 49, Error: 0.00161412

Iteration: 50, Error: 0.00152527

Iteration: 51, Error: 0.00139379

Iteration: 52, Error: 0.00130557

Iteration: 53, Error: 0.00124559

Iteration: 54, Error: 0.00119817

Iteration: 55, Error: 0.00104333

Iteration: 56, Error: 0.000955515

Iteration: 57, Error: 0.000859409

Iteration: 58, Error: 0.000774391

Iteration: 59, Error: 0.000753224

Iteration: 60, Error: 0.000715607

Iteration: 61, Error: 0.000663465

Iteration: 62, Error: 0.000581495

Iteration: 63, Error: 0.000548726

Iteration: 64, Error: 0.000509549

Iteration: 65, Error: 0.000480556

Iteration: 66, Error: 0.000476432

Iteration: 67, Error: 0.000426619

Iteration: 68, Error: 0.000412285

Iteration: 69, Error: 0.000372208

Iteration: 70, Error: 0.000334442

Iteration: 71, Error: 0.000312243

Iteration: 72, Error: 0.000284354

Iteration: 73, Error: 0.000273403

Iteration: 74, Error: 0.000240112

Iteration: 75, Error: 0.00023832

Iteration: 76, Error: 0.00023475

Iteration: 77, Error: 0.000235279

Iteration: 78, Error: 0.000210067

Iteration: 79, Error: 0.000207372

Iteration: 80, Error: 0.000181347

Iteration: 81, Error: 0.000170289

Iteration: 82, Error: 0.000148436

Iteration: 83, Error: 0.000145014

Iteration: 84, Error: 0.000150516

Iteration: 85, Error: 0.000138971

Iteration: 86, Error: 0.00013238

Iteration: 87, Error: 0.000124886

Iteration: 88, Error: 0.000114711

Iteration: 89, Error: 0.000113345

Iteration: 90, Error: 0.00011269

Iteration: 91, Error: 0.000109958

Iteration: 92, Error: 9.76829e-05

Iteration: 93, Error: 8.65131e-05

Iteration: 94, Error: 8.43918e-05

Iteration: 95, Error: 8.40385e-05

Iteration: 96, Error: 8.23291e-05

Iteration: 97, Error: 7.99522e-05

Iteration: 98, Error: 7.42379e-05

Iteration: 99, Error: 6.70692e-05

Iteration: 100, Error: 6.20688e-05

Iteration: 101, Error: 6.16791e-05

Iteration: 102, Error: 6.0274e-05

Iteration: 103, Error: 5.99569e-05

Iteration: 104, Error: 5.8609e-05

Iteration: 105, Error: 5.7213e-05

Iteration: 106, Error: 4.73714e-05

Iteration: 107, Error: 4.73477e-05

Iteration: 108, Error: 4.57683e-05

Iteration: 109, Error: 4.27954e-05

Iteration: 110, Error: 4.33137e-05

Iteration: 111, Error: 4.52173e-05

Iteration: 112, Error: 4.24098e-05

Iteration: 113, Error: 3.57563e-05

Iteration: 114, Error: 3.95354e-05

Iteration: 115, Error: 3.7504e-05

Iteration: 116, Error: 3.39426e-05

Iteration: 117, Error: 3.32528e-05

Iteration: 118, Error: 3.24908e-05

Iteration: 119, Error: 3.40345e-05

Iteration: 120, Error: 3.50016e-05

Iteration: 121, Error: 3.08532e-05

Iteration: 122, Error: 2.88498e-05

Iteration: 123, Error: 3.12128e-05

Iteration: 124, Error: 3.10717e-05

Iteration: 125, Error: 3.06152e-05

Iteration: 126, Error: 2.72405e-05

Iteration: 127, Error: 2.66073e-05

Iteration: 128, Error: 2.61065e-05

Iteration: 129, Error: 2.9085e-05

Iteration: 130, Error: 2.59396e-05

Iteration: 131, Error: 2.48724e-05

Iteration: 132, Error: 2.35326e-05

Iteration: 133, Error: 2.42675e-05

Iteration: 134, Error: 2.40615e-05

Iteration: 135, Error: 2.31259e-05

Iteration: 136, Error: 2.14988e-05

Iteration: 137, Error: 2.08507e-05

Iteration: 138, Error: 2.17281e-05

Iteration: 139, Error: 2.03236e-05

Iteration: 140, Error: 1.86188e-05

Iteration: 141, Error: 2.00066e-05

Iteration: 142, Error: 1.96718e-05

Iteration: 143, Error: 1.74585e-05

Iteration: 144, Error: 1.90512e-05

Iteration: 145, Error: 2.0851e-05

Iteration: 146, Error: 2.0051e-05

Iteration: 147, Error: 1.76715e-05

Iteration: 148, Error: 1.87925e-05

Iteration: 149, Error: 1.87155e-05

Iteration: 150, Error: 1.69574e-05

Iteration: 151, Error: 1.66414e-05

Iteration: 152, Error: 1.79171e-05

Iteration: 153, Error: 1.89355e-05

Iteration: 154, Error: 1.7597e-05

Iteration: 155, Error: 1.65225e-05

Iteration: 156, Error: 1.63052e-05

Iteration: 157, Error: 1.73545e-05

Iteration: 158, Error: 1.60184e-05

Iteration: 159, Error: 1.51521e-05

Iteration: 160, Error: 1.73576e-05

Iteration: 161, Error: 1.6333e-05

Iteration: 162, Error: 1.38076e-05

Iteration: 163, Error: 1.47765e-05

Iteration: 164, Error: 1.33878e-05

Iteration: 165, Error: 1.42886e-05

Iteration: 166, Error: 1.62694e-05

Iteration: 167, Error: 1.41469e-05

Iteration: 168, Error: 1.42415e-05

Iteration: 169, Error: 1.52288e-05

Iteration: 170, Error: 1.21468e-05

Iteration: 171, Error: 1.13911e-05

Iteration: 172, Error: 1.32988e-05

Iteration: 173, Error: 1.35119e-05

Iteration: 174, Error: 1.2796e-05

Iteration: 175, Error: 1.29884e-05

Iteration: 176, Error: 1.30855e-05

Iteration: 177, Error: 1.31864e-05

Iteration: 178, Error: 1.14494e-05

Iteration: 179, Error: 1.19393e-05

Iteration: 180, Error: 1.33965e-05

Iteration: 181, Error: 1.23386e-05

Iteration: 182, Error: 1.11296e-05

Iteration: 183, Error: 1.11898e-05

Iteration: 184, Error: 1.05088e-05

Iteration: 185, Error: 1.12205e-05

Iteration: 186, Error: 1.0402e-05

Iteration: 187, Error: 1.03346e-05

Iteration: 188, Error: 8.68706e-06

Iteration: 189, Error: 1.02391e-05

Iteration: 190, Error: 1.10672e-05

Iteration: 191, Error: 1.04691e-05

Iteration: 192, Error: 8.89482e-06

Iteration: 193, Error: 9.40873e-06

Iteration: 194, Error: 8.57953e-06

Iteration: 195, Error: 9.7164e-06

Iteration: 196, Error: 1.00126e-05

Iteration: 197, Error: 9.38924e-06

Iteration: 198, Error: 1.0108e-05

Iteration: 199, Error: 8.33536e-06

Iteration: 200, Error: 8.88882e-06

Iteration: 201, Error: 8.21131e-06

Iteration: 202, Error: 8.15833e-06

Iteration: 203, Error: 9.35119e-06

Iteration: 204, Error: 9.5519e-06

Iteration: 205, Error: 7.9187e-06

Iteration: 206, Error: 8.08857e-06

Iteration: 207, Error: 7.64561e-06

Iteration: 208, Error: 6.85986e-06

Iteration: 209, Error: 8.53052e-06

Iteration: 210, Error: 7.86043e-06

Iteration: 211, Error: 7.33537e-06

Iteration: 212, Error: 6.39248e-06

Iteration: 213, Error: 6.38474e-06

Iteration: 214, Error: 7.22072e-06

Iteration: 215, Error: 7.07952e-06

Iteration: 216, Error: 6.80428e-06

Iteration: 217, Error: 7.034e-06

Iteration: 218, Error: 5.75385e-06

Iteration: 219, Error: 6.39325e-06

Iteration: 220, Error: 6.33908e-06

Iteration: 221, Error: 7.01694e-06

Iteration: 222, Error: 6.37219e-06

Iteration: 223, Error: 6.16033e-06

Iteration: 224, Error: 6.26016e-06

Iteration: 225, Error: 5.63829e-06

Iteration: 226, Error: 6.48061e-06

Iteration: 227, Error: 6.11072e-06

Iteration: 228, Error: 5.99218e-06

Iteration: 229, Error: 5.69966e-06

Iteration: 230, Error: 5.3489e-06

Iteration: 231, Error: 5.31105e-06

Iteration: 232, Error: 5.24717e-06

Iteration: 233, Error: 5.53838e-06

Iteration: 234, Error: 6.0289e-06

Iteration: 235, Error: 5.83203e-06

Iteration: 236, Error: 5.86855e-06

Iteration: 237, Error: 4.92979e-06

Iteration: 238, Error: 4.71234e-06

Iteration: 239, Error: 3.87016e-06

Iteration: 240, Error: 3.89903e-06

Iteration: 241, Error: 4.06568e-06

Iteration: 242, Error: 4.6644e-06

Iteration: 243, Error: 5.3939e-06

Iteration: 244, Error: 5.91335e-06

Iteration: 245, Error: 6.57035e-06

Iteration: 246, Error: 6.82027e-06

Iteration: 247, Error: 6.39711e-06

Iteration: 248, Error: 5.6575e-06

Iteration: 249, Error: 5.34638e-06

warning: applyExp not converged in 250 steps

In applyExp, number of iterations: 249

In applyExp, number of matrix-vector multiplies: 250

---