The Nonequilibrium Dynamics In Low-dimensional Strongly Correlated Systems

In condensed matter physics,strongly correlated systems have been widely investigated because of their rich underlying physics.Time-resolved spectroscopy has been employed extensively to investigate the dynamic properties of materials with strong correlations.As a promising time-resolved spectroscopy technique,ultrafast pump-probe optical measurement is able to unravel the complicated entanglement of various degrees of freedom in a correlated system to some extent,especially in the low-dimensional systems.The time-resolved optical conductivity,as an essential dynamic quantity of charge degree of freedom,can be obtained from the reflectivity measurements.However,in theoretical calculations of time-resolved optical conductivity,there exist several related but different schemes,including the nonequilibrium generalizations of the Kubo formula,linear-response theory,or a direct calculation on dynamic current-current correlations for transient states.The underlying characters and validity of these approaches have not yet been fully addressed until recently.We first present a numerical method to calculate optical conductivity based on a pump-probe setup.By employing either a steplike or a Gaussian-like probing vector potential,it is found that the method in the narrow-probe-pulse limit can be identified with variant types of linear-response theory.Theoretical analysis combined with numerical simulations elucidate the difference and connections between these various methods to a satisfactory level.They also raise the issue of the probe-pulse dependence in nonequilibrium analysis,which has been largely ignored in previous studies.Our work can be valuable for understanding the nonequilibrium dynamics of correlated systems within the scope of linear-response theory.We then apply this numerical method to analyze photoinduced in-gap states.In Mott insulators,except for photoexcited itinerant charges,photoexcitation is also expected to induce a new excitation channel inside the Mott gap.The nature of those states has not been fully understood from a theoretical viewpoint even for 1D Mott insulators.We address the physical properties of photoinduced in-gap states and their influence on the time evolution of the system.For this purpose,we calculate the timedependent optical conductivity of a 1D extended Hubbard model driven by a transient laser pulse.In this model,by tuning the parameters for on-site and nearest site Coulomb interaction,the ground state can be either the spin-density-wave(SDW)or the chargedensity-wave(SDW).We find that photoinduced in-gap excitations appear in a different manner,depending on the nature of the initial ground state.In the SDW,a dominant in-gap excitation emerges at the low-energy region,reflecting the energy difference between the even-odd parity of photoexcited states.In the CDW,in-gap states appear in the middle of the Mott gap and their origin can be attributed to photogenerated carriers.These studies may provide useful clues for probing photoinduced in-gap states in correlated materials.We extend our study to ladder systems and we consider the dynamical properties of a two-leg ladder material.In the recent literatures,a photoirradiation suppression of Drude weight both in hole-doped metallic state and photoinduced metallic-like state was found in this material.The suppression was argued to be connected with the pairing holes along the rungs in the ladder.Through our numerical simulations,we observe that the Drude weight is generally suppressed both in the 1D chain and the two-leg ladder due to the photoinduced thermalization.We note that the enhancement of the integrated weight on the optical conductivity after the radiation found in the 1D chain is attributed to the emergence of a side peak near the Drude component in low-frequency regime.On the other hand,for the isotropic ladder,the side peak with small magnitude is quickly suppressed after the pump,accompanied by the rapid decay of the photoinduced charges.We suggest that these observations can be understood from the competition between the thermalization of mobile charges and the dynamic of photoinduced carriers.Our research can contribute to the understanding of photo-controlled metal-insulator transition on this ladder material.