Correlated electron systems display a wealth of interesting properties possibly relevant for future technological devices, such as ultrafast transistors or energy applications.
However, the accurate description of their phases and dynamics still poses a major theoretical challenge.
In this talk I will focus on recent progress in the theory of superconductivity and the microscopic description of unconventional charge order in the cuprate high temperature superconductors. I will review experimental evidence for incommensurate charge order in various cuprate families. Motivated by these experiments, we performed a number of complementary computations to analyze charge-neutral, spin-singlet ordering in metals on the square lattice taking into account correlation effects.
Our results are in good accordance with various recent observations although open questions remain.
I will also discuss our recent work on non-equilibrium dynamic phase transitions. We computed single and two-particle dynamics of fermions on a lattice after a fast interaction ramp close to a magnetic instability, which allowed us to analyze the interplay of thermalization processes with the growth of unstable magnetic modes.