  We extend the coupled-cluster method to correlated quantum dynamics of both
closed and open systems at finite temperatures using the thermo-field
formalism. The approach expresses the time-dependent density matrix in an
exponential ansatz and describes time-evolution along the Keldysh path contour.
A distinct advantage of the approach is exact trace-preservation as a function
of time, ensuring conservation of probability and particle number. Furthermore,
the method avoids the computation of correlated bra-states, simplifying the
computational implementation. We develop the method in a thermal quasi-particle
representation, which allows seamless connection to the projection method and
diagrammatic techniques of the traditional coupled-cluster formalism. For
comparison, we also apply the thermo-field framework to renormalization-group
methods to obtain reference results for closed and open systems at finite
temperatures. We test the singles and doubles approximation to the
density-matrix coupled-cluster method on the correlated electronic dynamics of
the single-impurity Anderson model, demonstrating that the new method
successfully captures the correlated dynamics of both closed systems at finite
temperature and driven-dissipative open systems. This encouraging performance
motivates future applications to non-equilibrium quantum many-body dynamics in
realistic systems.
