fix typos in docs

docs/source/tutorial/hubbard.ipynb

@@ -130,7 +130,7 @@
         "\n",
         "For example, ``b.add_term(\"dCc\", [1, 3, 0], 0.7)`` will add the term: $0.7 \\ a_{1\\alpha} a^\\dagger_{3\\beta} a^\\dagger_{0\\alpha}$.\n",
         "\n",
-        "Most of the time, there can be multiple terms differ only in the operator indices and coefficients. For this case, One can invoke ``add_term`` only once. So ``b.add_term(\"CD\", [1, 3, 3, 1, 2, 2, 2, 4], [0.7, 0.6, 0.5, 0.4])``\n",
+        "Most of the time, there can be multiple terms differ only in the operator indices and coefficients. For this case, one can invoke ``add_term`` only once. So ``b.add_term(\"CD\", [1, 3, 3, 1, 2, 2, 2, 4], [0.7, 0.6, 0.5, 0.4])``\n",
         "\n",
         "is equivalent to\n",
         "\n",
@@ -217,7 +217,7 @@
         "- ``bond_dim`` is the bond dimension of the initial guess MPS. The final optimized MPS may have a larger bond dimension.\n",
         "- ``nroots`` is the number of roots. If ``nroots > 1``, it will compute the ground state and ``nroots - 1`` low-energy excited states.\n",
         "\n",
-        "The DMRG algorithm consists of many \"sweeps\". The bond dimension of the MPS can increase after several sweeps. After a few tens of the sweeps, the MPS gradually converges to the ground state if ``nroots == 1``. To prevent stuck in local minima, we may add noise in most sweeps, but the last sweep will not have any noise (namely, ``noises[-1] == 0``) so that the accuracy of the final printed energy is not affected. In each sweep, the DMRG algorithm will optimize $L$ tensors in the MPS, one by one. For optimizing each tensor, an effective Hamiltonian will be created and the Davidson algorithm is used to sovle the eigenvalue problem of this effective Hamiltonian. The eigenvalue (energy) of this effective Hamiltonian is the same as the eigenvalue of the full many-body Hamiltonian (if the bond dimension of the MPS is big enough).\n",
+        "The DMRG algorithm consists of many \"sweeps\". The bond dimension of the MPS can increase after several sweeps. After a few tens of the sweeps, the MPS gradually converges to the ground state if ``nroots == 1``. To prevent from getting stuck in local minima, we may add noise in most sweeps, but the last sweep will not have any noise (namely, ``noises[-1] == 0``) so that the accuracy of the final printed energy is not affected. In each sweep, the DMRG algorithm will optimize $L$ tensors in the MPS, one by one. For optimizing each tensor, an effective Hamiltonian will be created and the Davidson algorithm is used to solve the eigenvalue problem of this effective Hamiltonian. The eigenvalue (energy) of this effective Hamiltonian is the same as the eigenvalue of the full many-body Hamiltonian (if the bond dimension of the MPS is big enough).\n",
         "\n",
         "Therefore, to run a DMRG calculation, we need to set up a \"sweep schedule\", namely, we need to set for each sweep: (a) the MPS bond dimension used in this sweep; (b) the noise used in this sweep; and (c) the Davidson algorithm convergence threshold for this sweep. Typically, these parameters should be changed every 4 to 5 sweeps (for Hubbard model with several hundred sites they may be changed every 30 to 50 sweeps), and the MPS bond dimension increases, while the noise and Davidson algorithm convergence decrease. The Davidson algorithm convergence cannot be set to zero.\n",
         "\n",