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Abstract

The investigation of nonequilibrium phenomena in strongly correlated systems is an intense and increasingly important field of research, both from a theoretical and from an experimental perspective. Experimental advances regarding the creation of ultrashort laser pulses and large field intensities are making it feasible to avoid the decoherences that historically have made the dynamics in driven solid state systems hard to access. However, many of the powerful analytical and numerical equilibrium methods are not applicable in a nonequilibrium setup, largely because of the increasing mixing of energy scales due to the external driving. It is therefore essential to
gain a deeper theoretical understanding of systems far from equilibrium. In particular, driven dissipative systems allow for the formation of nonequilibrium steady states and the possibility of phase transitions between them. Here, we present theoretical results on driven quantum spin systems that help to gain an understanding of the different control knobs for driving such nonequilibrium phase transitions. This is of great interest because it paves the way to optically control the properties of quantum many body states.
A numerical method that has been shown to generate reliable results for periodically driven, one dimensional systems is the time-dependent density matrix renormalization group (t-DMRG). By simulating the dynamics of a quantum chain with Luttinger liquid and charge-density wave phases under both continous and pulsed laser driving with t-DMRG calculations, we show that the drive causes a light-cone spreading of density-density correlations with a Floquet-engineered
propagation velocity through the system. At large time scales, the employed continuous, off-resonant, large frequency driving protocol leads to the formation of a Floquet steady state with negligible heating. Strikingly, the formation of a discontinuity in form of a kink at the edge of the light cone is observed. This kink shows similarities with the discontinuity that has been analytically shown to exist in quenched systems, which indicates that dynamical quantum criticality can be achieved in Floquet-driven systems. These results directly connect to the field of time-resolved spectroscopy, aiming at measuring correlations in strongly correlated materials. Emergent nonequilibrium states of matter prominently feature a high degree of many-body entanglement, which may have a significant effect on the macroscopic finite-temperature behavior of the systems in question. This makes the identification of entanglement in driven quantum systems an important area of research. A quantity that has been shown to act as an entanglement witness is the Quantum Fisher Information (QFI), which can be used to discriminate criticality at nonzero temperatures from thermal behavior. We investigate the QFI in an interaction-quenched one-dimensional XXZ quantum chain, ransitioning from from adiabatic to nonadiabatic dynamics.
In order to identify critical behavior in a driven-dissipative spin system with magnon interactions we study the nonequilibrium steady states of a two-dimensional Heisenberg antiferromagnet which is driven by a high frequency laser and coupled to a reservoir. The interplay between
interactions and the flow of energy due to to drive and dissipation is crucial to describe the resulting steady state system. We demonstrate a nonthermal transition that is characterized by a qualitative change in the magnon distribution, from subthermal at low drive to a generalized Bose-Einstein form including a nonvanishing condensate fraction at high drive and find that this transition shows static and dynamical critical scaling. An analysis of the linearized kinetic
equation and its spectrum of eigenvalues allows us to draw conclusions about the role of hydrodynamic slow modes in the critical behavior near the transition point. Understanding these
mechanisms that determine the critical behavior could help understand nonthermal pathways for controlling emergent properties of driven quantum materials.