I am trying to understand what a thermal state is in quantum statistical mechanics. When i search for thermal state density matrix I get a bit confused. It seems like the thermal state and hence the thermal density matrix is the same as in the canonical ensemble. Can someone explain why that is? Or if I have missed something explain what a thermal state is and how one can find the density matrix of it?
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you are right. The usually called quantum thermal state is the analogue of the canonical ensemble in quantum mechanics. You can also see people using thermal states to refer to states of other ensembles. I have seen a generalized definition which was based on the possibility of atributing a temperature (like, there is a function T with certain properties for which you can write the state(matrix) as $e^{(-\beta T+\sum ...)}$-generalized ensemble). But, anyway, you can consult Sakurai's Modern Quantum Mechanics book from page 181 to 187. There he derives the state matrix in a simple introductory way assuming it obbeys Schrodinger's equation and that it is an equilibrium state. It really resembles the way we treat ensembles in classical theory, but with subtleties in interpretation. Hope this is helpful.
