Strongly correlated systems exhibit intriguing phenomena that emerge from intertwined spin, charge, and lattice degrees of freedom. Understanding these emergent behaviors and their nonequilibrium dynamics represents the most challenging theoretical problem in condensed matter physics. Here, I will first discuss a Mott-Peierls system with competing charge and spin density waves. It is shown by exact diagonalization that a sub-dominant d-wave superconducting instability at equilibrium can become dominant at nonequilibrium, when the original system resides near a quantum phase boundary . I will next discuss the theory of time-resolved Raman scattering , which provides the platform to explore different ultrafast processes such as thermalization and Floquet physics. It is shown on the single-band Hubbard model that time-resolved Raman scattering also can be useful for ultrafast engineering of effective spin interaction. These studies demonstrate promising new approaches for designing material properties out of equilibrium.
*C.-C.C. is supported by the National Science Foundation (NSF) Award No. 1738698.
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 Y. Wang, T. P. Devereaux, and C.-C. Chen, Phys. Rev. B 98, 245106 (2018).