Update "Code Formulas" for V3

[mtfishman]

Code Formulas (http://www.itensor.org/docs.cgi?vers=cppv3&page=formulas) updates for V3:

NOTE:

• Extract the Storage of a Dense ITensor
• Evaluate a Function on Each Element of a Tensor

are linked twice, update for V2 docs as well.

• Evaluate a Function on Each Element of a Tensor (http://www.itensor.org/docs.cgi?vers=cppv3&page=formulas/visit):

• [ ] randomize(T) -> T.randomize()

• Extract the Storage of a Dense ITensor (http://www.itensor.org/docs.cgi?vers=cppv3&page=formulas):

• [ ] Update Index constructors

• [ ] randomize(T) -> T.randomize()

• Create a set of Site indices to use as a lattice (http://www.itensor.org/docs.cgi?vers=cppv3&page=formulas/index_sites):

• [ ] nameint("site_",7) -> format("site_%d",7) (nameint was removed since there is no name anymore)

• [ ] Change Index constructors

• [ ] Change IndexVal constructors from e.g. i(1) -> i=1

• Make a single-site operator (no quantum numbers) (http://www.itensor.org/docs.cgi?vers=cppv3&page=formulas/itensor_single_site_op):

• [ ] Change Index constructors

• [ ] s(1) -> s=1

• Exactly Compute the Ground State of a Small Hamiltonian (http://www.itensor.org/docs.cgi?vers=cppv3&page=formulas/simple_ed)

• [ ] Code is not found, make sure it is updated for V3

• Replace an ITensor Index with Another Index (http://www.itensor.org/docs.cgi?vers=cppv3&page=formulas/itensor_replace_index):

• [ ] It would be good to show x = sim(b), I think we should advertise it's use more as a way to make temporary indices as an alternative to tags and prime levels. Also, we should add a constructor x = sim(b,"...") as a way to assign new tags and prime levels to the similar index.

• [ ] Is the description of the delta correct here? I thought it didn't simply replace the Index of the ITensor, but actually did a sparse diagonal multiplication. Does it act differently for delta with more than two indices?

• Perform a basic DMRG calculation (http://www.itensor.org/docs.cgi?vers=cppv3&page=formulas/basic_dmrg):

• [ ] MPO -> toMPO

• [ ] maxm -> maxDim

• [ ] Add {"ConserveQNs=",false} arg

• Make a Ladder Hamiltonian for DMRG (http://www.itensor.org/docs.cgi?vers=cppv3&page=formulas/ladder):

• [ ] MPO -> toMPO

• [ ] Add {"ConserveQNs=",false} arg

• [ ] maxm -> maxDim

• Make a 2D Hamiltonian for DMRG (http://www.itensor.org/docs.cgi?vers=cppv3&page=formulas):

• [ ] IQMPO -> toMPO

• [ ] IQMPS -> MPS

• [ ] maxm -> maxDim

• Compute excited states using DMRG (http://www.itensor.org/docs.cgi?vers=cppv3&page=formulas/excited_dmrg)

• [ ] Add {"ConserveQNs=",false} arg

• [ ] maxm -> maxDim

• [ ] MPO -> toMPO

Measure local properties of an MPS wavefunction (http://www.itensor.org/docs.cgi?vers=cppv3&page=formulas/measure_mps):

• [ ] Change psi.A(j) -> psi(j)
• [ ] Site -> "Site"
• [ ] T.real() -> elt(T)
• [ ] sites.op(...) -> op(sites,...)

Measure two-point correlator from an MPS wavefunction (http://www.itensor.org/docs.cgi?vers=cppv3&page=formulas/correlator_mps):

• [ ] IQMPS -> MPS
• [ ] sites.op("Op1",i) - > op(sites,"Op1",i), etc.
• [ ] Link -> "Link", etc.
• [ ] psi.A(i) -> psi(i), etc.
• [ ] commonIndex(psi.A(i),psi.A(i+1),Link) -> linkInd(psi,i)
• [ ] psi.A(i)*op_i*dag(prime(psi.A(i),Site,ir)) -> prime(psi(i),linkInd(psi,i-1))*op_i*dag(prime(psi(i)))
• [ ] C *= psi.A(k); -> auto sk = siteInd(psi,k); C *= prime(psi(k),sk);
• [ ] C *= dag(prime(psi.A(k),Link)); -> C *= dag(prime(psi(k)));
• [ ] C *= psi.A(j); -> auto lj = linkInd(psi,j); C *= prime(psi(j),lj);
• [ ] C *= dag(prime(psi.A(j),jl,Site)); -> C *= dag(prime(psi(j)));
• [ ] C.real() -> elt(C)

Compute entanglement entropy (http://www.itensor.org/docs.cgi?vers=cppv3&page=formulas/entanglement_mps):

• [ ] psi.A(b) -> psi(b)
• [ ] commonIndex(psi.A(i),psi.A(i+1),Link) -> linkInd(psi,i)

Measure spinless fermion two-point correlator (http://www.itensor.org/docs.cgi?vers=cppv3&page=formulas/spinless_correlator_mps):

• [ ] Changes similar to "Measure two-point correlator from an MPS wavefunction" page

Compute a two-site reduced density matrix from an MPS (http://www.itensor.org/docs.cgi?vers=cppv3&page=formulas/mps_two_rdm):

• [ ] Changes similar to "Measure two-point correlator from an MPS wavefunction" page

Operator matrix elements involving two MPS (http://www.itensor.org/docs.cgi?vers=cppv3&page=formulas/two_mps):

• [ ] Changes similar to "Measure two-point correlator from an MPS wavefunction" page

Time-evolving an MPS with Trotter Gates (http://www.itensor.org/docs.cgi?vers=cppv3&page=formulas/tevol_trotter):

• [ ] BondGate<ITensor> -> BondGate
• [ ] sites.op(...) -> op(sites,...)?

Time-evolving an MPS with an MPO (matrix product operator) (http://www.itensor.org/docs.cgi?vers=cppv3&page=formulas/tevol_mps_mpo):

• [ ] psi.A(3) -> psi(3)
• [ ] noprime -> noPrime
• [ ] toExpH<ITensor> -> toExpH
• [ ] exactApplyMPO(...) -> applyMPO(...,{"Method=","DensityMatrix"}), fitApplyMPO(...) -> ..., ect.
• [ ] normalize(psi) -> psi.normalize()

Applying a two-site 'gate' to an MPS (http://www.itensor.org/docs.cgi?vers=cppv3&page=formulas/gate):

• [ ] psi.A(3) -> psi(3)
• [ ] noprime -> noPrime
• [ ] psi.setA(3,U) -> psi.set(3,U)

[mtfishman]

To good approximation all of these have been completed.