Stoudenmire and White: ITensor is "[a] C++ library for creating efficient and flexible physics simulations based on tensor product wavefunctions."
PsimagLite is a light C++ library and framework that the other applications listed here depend on.
You can also use PsimagLite in your own C++ to simplify things and do complicated stuff in just a few lines of C++ code, as if you were using Mathematica or Maxima but faster and programatically! Features are:
DMRG++ is a free and open source implementation of the DMRG algorithm. Features are
Ever wanted to quickly run a code that would give you the braket <gs|ci,up c+j,up|gs> for a generic tight-binding Hamiltonian (”free system“)? Well, FreeFermions is the answer! But you can do much more! Orbitals? no problem! You need a holon-doublon operator inside the braket? We got you covered! Complicated matrix of hoppings for a difficult geometry? We have it! You need to time evolve inside the braket? We can do that too! You need to warm the braket to finite temperature? Sure. Very very few dependencies to compile. Plus an easy interface: You can almost copy your braket from paper to computer, and it will get computed.
You've got a strongly correlated model like Hubbard or t-J or Heisenberg. You want ground state correlations on a not too big lattice. Then, take a look at LanczosPlusPlus, a Hamiltonian code with a Lanczos Solver or Chebyshev solver or a full dense matrix solver. Just use a simple input file, and run it like ./lanczos -f input.inp. Large model and geometry selection. Or input your own geometry as a matrix of hoppings or exchanges. Dynamical correlations are also supported.
BetheAnsatz is a free and open source Bethe ansatz code. It supports Heisenberg and Hubbard at zero and finite temperature. It supports the t-J model at the fully symmetric point where the Bethe ansatz is possible.
QPT++ is a free and open source zero temperature quantum perturbation expansion code. It does symbolic expansion, equation simplification and also numerics. It is the newest code of this list and more features will be added in the future.