Time-dependent DMRG studies of strongly correlated systems out of equilibrium

The recent development of time-dependent density-matrix renormalization group (tDMRG) has opened the door for studying several interesting problems that involve the nonequilibrium real-time dynamics of strongly interacting 1D lattice models [1]. We describe briefly one tDMRG approach, the Suzuki-Trotter algorithm. Then we discuss applying tDMRG to study the conductance of strongly correlated nanostructures [2] and describe a method to mitigate finite-size effects which may arise in such studies [3]. We present a few examples including quantum dots in the Kondo regime, and dielectric breakdown of a Mott insulator. Another class of problems involves the time-evolution of excitations in cold atoms and strongly interacting electronic materials. We present the results of a tDMRG study of an electron-hole pair in a 1D Mott insulator [4]. We finally present other possible applications and future directions. \\[4pt] [1] S. R. White and A. E. Feiguin, Phys. Rev. Lett. 93, 076401 (2004).\\[0pt] [2] K. A. Al-Hassanieh et al., Phys. Rev. B 73, 195304 (2006).\\[0pt] [3] Luis G. G. V. Dias da Silva et al., Phys. Rev. B 78 195317 (2008).\\[0pt] [4] K. A. Al-Hassanieh et al., Phys. Rev. Lett. 100 166403 (2008).