Mastodawn

@JoshuahHeath There are a ton of great intro materials for tensor network methods, but the nitty gritty details of numerics and physics is harder. Still:
The classic (MPS and DMRG focussed, but great first intro): https://arxiv.org/abs/1008.3477
Talking a bit more about PEPS: https://arxiv.org/abs/1306.2164

Tenpy has some great educational toycode examples (and is overall great library) https://tenpy.readthedocs.io/en/latest/toycodes/a_mps.html
my phd thesis though it is probably more like a summary of all of the above: https://arxiv.org/abs/2210.11130

The density-matrix renormalization group in the age of matrix product states

The density-matrix renormalization group method (DMRG) has established itself over the last decade as the leading method for the simulation of the statics and dynamics of one-dimensional strongly correlated quantum lattice systems. In the further development of the method, the realization that DMRG operates on a highly interesting class of quantum states, so-called matrix product states (MPS), has allowed a much deeper understanding of the inner structure of the DMRG method, its further potential and its limitations. In this paper, I want to give a detailed exposition of current DMRG thinking in the MPS language in order to make the advisable implementation of the family of DMRG algorithms in exclusively MPS terms transparent. I then move on to discuss some directions of potentially fruitful further algorithmic development: while DMRG is a very mature method by now, I still see potential for further improvements, as exemplified by a number of recently introduced algorithms.

arXiv.org