The interest in understanding the dynamics of strongly correlated systems beyond the linear response regime has grown tremendously in recent years. As a result, there is mounting evidence that quantum matter far from equilibrium possesses interesting and unanticipated properties. On the one hand, the recent interest in non-equilibrium properties of quantum matter is fueled by advances in creating such states in a controlled fashion through.

Nonequilibrium quantum dynamics, e.g. can be studied  in adiabatically isolated optical traps  and well characterized non-equilibrium states in open systems are frequently investigated in nano-structured systems. On the other hand, a growing number of spectroscopic investigations are based on pump-probe or time-resolved techniques.

For  quantum critical systems with their scale-invariant spectrum, i.e. in the absence of any intrinsic scale, any perturbation may probe the system in the nonlinear regime beyond the validity of the fluctuation-dissipation theorem. Understanding non-equilibrium response is thus of practical importance. Yet, there is at present no generally accepted theory to organize  the quantum critical dynamics far from equilibrium in terms of universality classes.

The quest for a unified understanding of different classes of quantum materials has led to the notion of quantum critical points as an economic and powerful way of describing the phase diagram of quantum matter.

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Highlights

“Mixed-order symmetry-breaking quantum phase transition far from equilibrium”

T. O. Puel, S. Chesi, S. Kirchner, and P. Ribeiro 
accepted in Phys. Rev. Lett. and arXiv:1809.07219 (2018)

We study the current-carrying steady-state of a transverse field Ising chain coupled to magnetic thermal reservoirs and obtain the non-equilibrium phase diagram as a function of the magnetization potential of the reservoirs. Upon increasing the magnetization bias we observe a discontinuous jump of the magnetic order parameter that coincides with a divergence of the correlation length. For steady-states with a non-vanishing conductance, the entanglement entropy at zero temperature displays a bias dependent logarithmic correction that violates the area law and differs from the well-known equilibrium case. Our findings show that out-of-equilibrium conditions allow for novel critical phenomena not possible at equilibrium.

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“The renormalized superperturbation theory (rSPT) approach to the Anderson model in and out of equilibrium”

Enrique Muñoz, Farzaneh Zamani, Lukas Merker, Theo A. Costi, and Stefan Kirchner
J. Phys.: Conf. Ser. 807, 092001 (2017)

The properties of current-carrying steady states of strongly correlated systems away from the linear-response regime are of topical interest. In this article, we review the renormalized perturbation theory (rSPT), or renormalized SPT of reference [1] for the Anderson model. We present an extension to higher orders and compare the higher-order results with NRG calculations. Finally, we elucidate the role of Ward identities in calculating out-of-equilibrium properties and address claims made in the literature.
[1] Muñoz, E. and Bolech, C. J. and Kirchner, S.  Phys. Rev. Lett. 110 016601 (2013)

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“Steady-State Dynamics and Effective Temperature for a Model of Quantum Criticality in an Open System”

P. Ribeiro, F. Zamani, and S. Kirchner
Phys. Rev. Lett. 115 220602 (2015)

We study the thermal and nonthermal steady-state scaling functions and the steady-state dynamics of a model of local quantum criticality. The model we consider, i.e., the pseudogap Kondo model, allows us to study the concept of effective temperatures near fully interacting as well as weak coupling fixed points. In the vicinity of each fixed point we establish the existence of an effective temperature—different at each fixed point—such that the equilibrium fluctuation-dissipation theorem is recovered. Most notably, steady- state scaling functions in terms of the effective temperatures coincide with the equilibrium scaling functions. This result extends to higher correlation functions as is explicitly demonstrated for the Kondo singlet strength. The nonlinear charge transport is also studied and analyzed in terms of the effective temperature.

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