The coin example is incorrect (that is, different from QM) if you consider correlations of measurements of entangled qubits in different bases.
If you want a more advanced attempt of building a deterministic theory underlying QM, have a look at Gerard 't Hooft book The Cellular Automaton Interpretation of Quantum Mechanics which is free now.
Einstein, Podolsky and Rosen's (local) Hidden Variable theory is the most famous deterministic attempt to explain Quantum Mechanics. You can take a look at the wiki on the explanation: https://en.wikipedia.org/wiki/Hidden-variable_theory. As proved later on by Bell, this theory was not "possible" given the theory could not account for experimental ...
I would start from this excellent intro course by Thomas Vidick and Stephanie Wehner, available in Edx. Then take a look at some classic papers:
The one that started it all: https://core.ac.uk/reader/82447194.
The one that brought a whole new approach: https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.67.661
The one that simplified it somewhat: ...
Yes, there are. I just wrote a paper about it, actually.
You need to define carefully what you mean by obtaining a Bell violation or ruling out local hidden variables. You can't demand to have a result which is impossible to explain with local hidden variables: the local bound of a Bell inequality is inherently probabilistic, so it is possible to obtain any ...
We can find a number of good articles on Hamiltonians in Adiabatic Quantum Computing. Please let me share a few prominent articles here.
Hamiltonian engineering for adiabatic quantum computation: Kazutaka Takahashi
Adiabatic Quantum Computation with a 1D projector Hamiltonian
Non-diagonal problem Hamiltonian for adiabatic quantum computation