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The emergent field of cavity quantum materials bridges collective many-body phenomena in solid state platforms with strong light–matter coupling in cavity quantum electrodynamics. This brief review provides an overview of the state of the art of cavity platforms and highlights recent theoretical proposals and first experimental demonstrations of cavity control of collective phenomena in quantum materials. This encompasses light–matter coupling between electrons and cavity modes, cavity superconductivity, cavity phononics and ferroelectricity, correlated systems in a cavity, light–magnon coupling, cavity topology and the quantum Hall effect, as well as super-radiance. An outlook of potential future developments is given. [ABSTRACT FROM AUTHOR]

We introduce a method to evaluate the steady-state non-equilibrium Keldysh–Schwinger Green's functions for infinite systems subject to both an electric field and a coupling to reservoirs. The method we present exploits a physical quasi-translation invariance, where a shift by one unit cell leaves the physics invariant if all electronic energies are simultaneously shifted by the magnitude of the electric field. Our framework is straightaway applicable to diagrammatic many-body methods. We discuss two flagship applications, mean-field theories as well as a sophisticated second-order functional renormalization group approach. The latter allows us to push the renormalization-group characterization of phase transitions for lattice fermions into the out-of-equilibrium realm. We exemplify this by studying a model of spinless fermions, which in equilibrium exhibits a Berezinskii–Kosterlitz–Thouless phase transition. [ABSTRACT FROM AUTHOR]

We study the spin and thermal conductivity of spin-j ladders and chains at finite temperature, relevant for experiments with quantum magnets. Using a state-of-the-art density matrix renormalization group algorithm, we compute the current autocorrelation functions on the real-time axis and then carry out a Fourier integral to extract the frequency dependence of the corresponding conductivities. The finite-time error is analyzed carefully. We first investigate the limiting case of spin-1/2 XXZ chains, for which our analysis suggests nonzero dc conductivities in all interacting cases irrespective of the presence or absence of spin Drude weights. For ladders, we observe that all models studied are normal conductors with no ballistic contribution. Nonetheless, only the high-temperature spin conductivity of XX ladders has a simple diffusive, Drude-like form, while Heisenberg ladders exhibit a more complicated low-frequency behavior. We compute the dc spin conductivity down to temperatures of the order of T ~ 0.57, where J is the exchange coupling along the legs of the ladder. We further extract mean-free paths and discuss our results in relation to thermal conductivity measurements on quantum magnets. [ABSTRACT FROM AUTHOR]

We show that to understand the orthogonality catastrophe in the half-filled lattice model of spinless fermions with repulsive nearest-neighbor interaction and a local impurity in its Luttinger liquid phase one has to take into account (i) the impurity scaling, (ii) unusual finite-size L corrections of the form ln(L)/L, as well as (iii) the renormalization group flow of the umklapp scattering. The latter defines a length scale Lu, which becomes exceedingly large the closer the system is to its transition into the charge density wave phase. Beyond this transition umklapp scattering is relevant in the renormalization group sense. Field theory can only be employed for length scales larger than Lu. For small to intermediate two-particle interactions, for which the regime L > Lu can be accessed, and taking into account the finite-size corrections resulting from (i) and (ii) we provide strong evidence that the impurity backscattering contribution to the orthogonality exponent is asymptotically given by 1/16. While further increasing the two-particle interaction leads to a faster renormalization group flow of the impurity towards the cut chain fixed point, the increased bare amplitude of the umklapp scattering renders it virtually impossible to confirm the expected asymptotic value of 1/16 given the accessible system sizes. We employ the density matrix renormalization group. [ABSTRACT FROM AUTHOR]

We study finite-temperature transport properties of the one-dimensional Hubbard model using the density matrix renormalization group. Our aim is twofold: First, we compute both the charge- and the spin-current correlation function of the integrable model at half filling. The former decays rapidly, implying that the corresponding Drude weight is either zero or very small. Second, we calculate the optical charge conductivity σreg(ω) in the presence of small integrability-breaking next-nearest-neighbor interactions (the extended Hubbard model). The dc conductivity is finite and diverges as the temperature is decreased below the gap. Our results thus suggest that the half-filled, gapped Hubbard model is a normal charge conductor at finite temperatures. As a test bed for our numerics, we compute σreg(ω) for the integrable XXZ spin chain in its gapped phase. [ABSTRACT FROM AUTHOR]

The equilibrium physics of quantum impurities frequently involves a universal crossover from weak to strong reservoir-impurity coupling, characterized by single-parameter scaling and an energy scale TK (Kondo temperature) that breaks scale invariance. For the noninteracting resonant level model, the nonequilibrium time evolution of the Loschmidt echo after a local quantum quench was recently computed explicitly [R. Vasseur, K. Trinh, S. Haas, and H. Saleur, Phys. Rev. Lett. 110, 240601 (2013)]. It shows single-parameter scaling with variable TKt. Here, we scrutinize whether similar universal dynamics can be observed in various interacting quantum impurity systems. Using density matrix and functional renormalization group approaches, we analyze the time evolution resulting from abruptly coupling two noninteracting Fermi or interacting Luttinger liquid leads via a quantum dot or a direct link. We also consider the case of a single Luttinger liquid lead suddenly coupled to a quantum dot. We investigate whether the field-theory predictions for the universal scaling as well as for the large-time behavior successfully describe the time evolution of the Loschmidt echo and the entanglement entropy of microscopic models. Our study shows that for the considered local quench protocols the above quantum impurity models fall into a class of problems for which the nonequilibrium dynamics can largely be understood based on the knowledge of the corresponding equilibrium physics. [ABSTRACT FROM AUTHOR]

We show that the single-particle spectral properties of gapless one-dimensional Fermi systems in the Luttinger liquid state reached at intermediate times after an abrupt quench of the two-particle interaction are highly indicative of the unusual nonequilibrium nature of this state. The line shapes of the momentum-integrated and -resolved spectral functions strongly differ from their ground state as well as finite temperature equilibrium counterparts. Using an energy resolution improved version of radio-frequency spectroscopy of quasi-one-dimensional cold Fermi gases, it should be possible to experimentally identify this nonequilibrium state by its pronounced spectral signatures. [ABSTRACT FROM AUTHOR]

We present a comprehensive study of the spectral and transport properties in the Anderson–Holstein model both in and out of equilibrium using the functional renormalization group (fRG). We show how the previously established machinery of Matsubara and Keldysh fRG can be extended to include the local phonon mode. Based on the analysis of spectral properties in equilibrium we identify different regimes depending on the strength of the electron–phonon interaction and the frequency of the phonon mode. We supplement these considerations with analytical results from the Kondo model. We also calculate the nonlinear differential conductance through the Anderson–Holstein quantum dot and find clear signatures of the presence of the phonon mode. [ABSTRACT FROM AUTHOR]

We reveal several distinct regimes of the relaxation dynamics of a small quantum system coupled to an environment within the plane of the dissipation strength and the reservoir temperature. This is achieved by discriminating between coherent dynamics with damped oscillatory behavior on all time scales, partially coherent behavior being nonmonotonic at intermediate times but monotonic at large ones, and purely monotonic incoherent decay. Surprisingly, elevated temperature can render the system "more coherent" by inducing a transition from the partially coherent to the coherent regime. This provides a refined view on the relaxation dynamics of open quantum systems. [ABSTRACT FROM AUTHOR]

We study dissipation in a small quantum system coupled to an environment held in thermodynamic equilibrium. The relaxation dynamics of a system subject to an abrupt quench in the parameters of the underlying Hamiltonian is investigated using two complementary renormalization group approaches. The methods are applied to the Ohmic spin-boson model close to the coherent-to-incoherent transition. In particular, the role of non-Markovian memory for the relaxation before and after the quench of the spin-boson coupling and the Zeeman splitting of the up and down spin is investigated. [ABSTRACT FROM AUTHOR]

We study the dynamics resulting from an abrupt change of the two-particle interaction in two models of closed one-dimensional Fermi systems: (a) the field theoretical Tomonaga-Luttinger model and (b) a microscopic lattice model. Using a nonperturbative approach which is controlled for small two-particle interactions, we are able to reach large times allowing us to access the properties of the steady state of the lattice model. Comparing those to the exact solution of the full dynamics in the Tomonaga-Luttinger model, we provide evidence for universal Luttinger liquid behavior. [ABSTRACT FROM AUTHOR]

The nonequilibrium dynamics of a small quantum system coupled to a dissipative environment is studied. We show that (i) the oscillatory dynamics close to a coherent-to-incoherent transition is significantly different from the one of the classical damped harmonic oscillator and that (ii) non-Markovian memory plays a prominent role in the time evolution after a quantum quench. [ABSTRACT FROM AUTHOR]

We study the steady-state properties as well as the relaxation dynamics of the nonequilibrium interacting resonant-level model at finite temperatures. It constitutes the prototype model of a correlated charge fluctuating quantum dot. The two reservoirs are held at different chemical potentials-the difference being the bias voltage- and different temperatures; we discuss the transport through as well as the occupancy of the single level dot. First, we show analytically that in the steady state the reservoir temperatures in competition with the other energy scales act as infrared cutoffs. This is rather intuitive but, depending on the parameter regime under consideration, leads to a surprisingly rich variety of power laws in the current as a function of the temperatures and the bias voltage with different interaction dependent exponents. Next we clarify how finite reservoir temperatures affect the dynamics. They allow one to tune the interplay of the two frequencies characterizing the oscillatory part of the time evolution of the model at zero temperature. For the exponentially decaying part we disentangle the contributions of the level-lead hybridization and the temperatures to the decay rates. We identify a coherent-to-incoherent transition in the long-time dynamics as the temperature is raised. It occurs at an interaction dependent critical temperature. Finally, taking different temperatures in the reservoirs we discuss the relaxation dynamics of a temperature gradient driven current. [ABSTRACT FROM AUTHOR]

We study the relaxation dynamics of a quantum dot with local Coulomb correlations coupled to two noninteracting leads which are held in grand-canonical equilibrium. Only charge degrees of freedom are considered and the dot is described by a model which in the scaling limit becomes equivalent to the interacting resonant level model. We examine the time evolution of the current and the dot occupancy resulting from changes in the dot-lead coupling, the dots' on-site energy, or the charging energy. Abrupt and smooth parameter changes as well as setups with and without driving bias voltage are considered. For biased dots, we investigate the often studied response after turning on the dot-lead coupling but also the experimentally more relevant case in which the voltage is turned on. We identify and explain a variety of interesting many-body effects, and we clarify the role of initial correlations. [ABSTRACT FROM AUTHOR]

We introduce a real time version of the functional renormalization group, which allows us to study correlation effects on nonequilibrium transport through quantum dots. Our method is equally capable to address (i) the relaxation out of a nonequilibrium initial state into a (potentially) steady state driven by a bias voltage and (ii) the dynamics governed by an explicitly time-dependent Hamiltonian. All time regimes from transient to asymptotic can be tackled; the only approximation is the consistent truncation of the flow equations at a given order. As an application we investigate the relaxation dynamics of the interacting resonant level model, which describes a fermionic quantum dot dominated by charge fluctuations. Moreover, we study incoherence and relaxation phenomena within the ohmic spin-boson model by mapping the latter to the interacting resonant level [ABSTRACT FROM AUTHOR]

We recapitulate recent developments of the functional renormalization group (FRG) approach to the steady state of systems out of thermal equilibrium. In particular, we discuss second-order truncation schemes which account for the frequency-dependence of the two particle vertex and which incorporate inelastic processes. Our focus is on two different types of one-dimensional fermion chains: (i) infinite, open systems which feature a translation symmetry, and (ii) finite systems coupled to left and right reservoirs. In addition to giving a detailed and unified review of the technical derivation of the FRG schemes, we briefly summarize some of the key physical results. In particular, we compute the non-equilibrium phase diagram and analyze the fate of the Berezinskii–Kosterlitz–Thouless transition in the infinite, open system. [ABSTRACT FROM AUTHOR]

The field of quantum simulations in ultra-cold atomic gases has been remarkably successful. In principle it allows for an exact treatment of a variety of highly relevant lattice models and their emergent phases of matter. But so far there is a lack in the theoretical literature concerning the systematic study of the effects of the trap potential as well as the finite size of the systems, as numerical studies of such non periodic, correlated fermionic lattices models are numerically demanding beyond one dimension. We use the recently introduced real-space truncated unity functional renormalization group to study these boundary and trap effects with a focus on their impact on the superconducting phase of the 2D Hubbard model. We find that in the experiments not only lower temperatures need to be reached compared to current capabilities, but also system size and trap potential shape play a crucial role to simulate emergent phases of matter. [ABSTRACT FROM AUTHOR]

We consider a one-dimensional interacting spinless fermion model, which displays the well-known Luttinger liquid (LL) to charge density wave (CDW) transition as a function of the ratio between the strength of the interaction U and the hopping J. We subject this system to a spatially uniform drive which is ramped up over a finite time interval and becomes time periodic in the long-time limit. We show that by using a density matrix renormalization group approach formulated for infinite system sizes, we can access the large-time limit even when the drive induces finite heating. When both the initial and long-time states are in the gapless (LL) phase, the final state has power-law correlations for all ramp speeds. However, when the initial and final state are gapped (CDW phase), we find a pseudothermal state with an effective temperature that depends on the ramp rate, both for the Magnus regime in which the drive frequency is very large compared to other scales in the system and in the opposite limit where the drive frequency is less than the gap. Remarkably, quantum defects (instantons) appear when the drive tunes the system through the quantum critical point, in a realization of the Kibble-Zurek mechanism. [ABSTRACT FROM AUTHOR]

We have used a combination of ultrafast coherent phonon spectroscopy, ultrafast thermometry, and time-dependent Landau theory to study the inversion symmetry breaking phase transition at Tc=200 K in the strongly spin-orbit coupled correlated metal Cd2Re2O7. We establish that the structural distortion at Tc is a secondary effect through the absence of any softening of its associated phonon mode, which supports a purely electronically driven mechanism. However, the phonon lifetime exhibits an anomalously strong temperature dependence that decreases linearly to zero near Tc. We show that this behavior naturally explains the spurious appearance of phonon softening in previous Raman spectroscopy experiments and should be a prevalent feature of correlated electron systems with linearly coupled order parameters. [ABSTRACT FROM AUTHOR]

We use a numerical solution of the deterministic time-dependent Ginzburg-Landau (TDGL) equations to determine the response induced by a probe field in a material quenched into a superconducting state. We characterize differences in response according to whether the probe is applied before, during, or after the phase stiffness has built up to its final steady-state value. We put an emphasis on the extent to which superfluid response requires a non-negligible phase stiffness, which for the considered quench has to build up dynamically. A key finding is that the time-dependent phase stiffness controls the likelihood of phase slips as well as the magnitude of the electromagnetic response. Additionally, we address the electromagnetic response expected if the probe itself is strong enough to activate phase slip processes. If the probe is applied before phase stiffness is sufficiently built up, we find that phase slips occur so that the vector potential is compensated and no long-term supercurrent is induced, while if it is applied at sufficient phase stiffness a weak probe pulse will induce a state with a long-lived supercurrent. If the probe is strong enough to activate the phase slip process, the supercurrent state will only be metastable with a lifetime that scales logarithmically with the amplitude of fluctuations in the magnitude of the order parameter. Finally, we study the response to experimentally motivated probe fields (electric field that integrates to zero). Interestingly, depending on the relative time difference of the probe field to the buildup of superconductivity, long-lived supercurrents can be induced even though the net change in vector potential is zero. [ABSTRACT FROM AUTHOR]

A nonequilibrium theory of optical conductivity of dirty-limit superconductors and commensurate charge density wave is presented. We discuss the current response to different experimentally relevant light-field probe pulses and show that a single frequency definition of the optical conductivity σ(ω)=j(ω)/E(ω) is difficult to interpret out of the adiabatic limit. We identify characteristic time-domain signatures distinguishing between superconducting, normal-metal, and charge density wave states. We also suggest a route to directly address the instantaneous superfluid stiffness of a superconductor by shaping the probe light field. [ABSTRACT FROM AUTHOR]

We propose a route towards engineering nonthermal states of matter, which show largely unexplored physics. The main idea relies on the adiabatic passage of a thermal ensemble under slow variations of the system Hamiltonian. If the temperature of the initial thermal ensemble is either zero or infinite, the ensemble after the passage is a simple thermal one with the same vanishing or infinite temperature. However, for any finite nonzero temperature, intriguing nonthermal ensembles can be achieved. We exemplify this in (a) a single oscillator, (b) a dimerized interacting one-dimensional chain of spinless fermions, (c) a BCS-type superconductor, and (d) the topological Kitaev chain. We solve these models with a combination of methods: either exactly, numerically using the density matrix renormalization group, or within an approximate functional renormalization group scheme. The designed states show strongly nonthermal behavior in each of the considered models. For example, for the chain of spinless fermions we exemplify how long-ranged nonthermal power-law correlations can be stabilized, and for the Kitaev chain we elucidate how the nonthermal ensemble can largely alter the transition temperature separating topological and trivial phases. [ABSTRACT FROM AUTHOR]

We study the expectation values of observables and correlation functions at long times after a global quantum quench. Our focus is on metallic ("gapless") fermionic many-body models and small quenches. The system is prepared in an eigenstate of an initial Hamiltonian, and the time evolution is performed with a final Hamiltonian which differs from the initial one in the value of one global parameter. We first derive general relations between time-averaged expectation values of observables as well as correlation functions and those obtained in an eigenstate of the final Hamiltonian. Our results are valid to linear and quadratic order in the quench parameter g and generalize prior insights in several essential ways. This allows us to develop a phenomenology for the thermalization of local quantities up to a given order in g. Our phenomenology is put to a test in several case studies of one-dimensional models representative of four distinct classes of Hamiltonians: quadratic ones, effectively quadratic ones, those characterized by an extensive set of (quasi-) local integrals of motion, and those for which no such set is known (and believed to be nonexistent). We show that for each of these models, all observables and correlation functions thermalize to linear order in g. The more local a given quantity, the longer the linear behavior prevails when increasing g. Typical local correlation functions and observables for which the term O(g) vanishes thermalize even to order g². Our results show that lowest-order thermalization of local observables is an ubiquitous phenomenon even in models with extensive sets of integrals of motion. [ABSTRACT FROM AUTHOR]

We study the thermal conductivity of the one-dimensional Fermi-Hubbard model at a finite temperature using a density matrix renormalization group approach. The integrability of this model gives rise to ballistic thermal transport. We calculate the temperature dependence of the thermal Drude weight at half filling for various interaction strengths. The finite-frequency contributions originating from the fact that the energy current is not a conserved quantity are investigated as well. We report evidence that breaking the integrability through a nearest-neighbor interaction leads to vanishing Drude weights and diffusive energy transport. Moreover, we demonstrate that energy spreads ballistically in local quenches with initially inhomogeneous energy density profiles in the integrable case. We discuss the relevance of our results for thermalization in ultracold quantum-gas experiments and for transport measurements with quasi-one-dimensional materials. [ABSTRACT FROM AUTHOR]

We study the properties of excited states in one-dimensional many-body localized (MBL) systems using a matrix product state algorithm. First, the method is tested for a large disordered noninteracting system, where for comparison we compute a quasiexact reference solution via a Monte Carlo sampling of the single-particle levels. Thereafter, we present extensive data obtained for large interacting systems of L~100 sites and large bond dimensions χ~1700, which allows us to quantitatively analyze the scaling behavior of the entanglement S in the system. The MBL phase is characterized by a logarithmic growth S(L)~log(L) over a large scale separating the regimes where volume and area laws hold. We check the validity of the eigenstate thermalization hypothesis. Our results are consistent with the existence of a mobility edge. [ABSTRACT FROM AUTHOR]

We investigate the thermodynamics and transient dynamics of the (unbiased) Ohmic two-state system by exploiting the equivalence of this model to the interacting resonant level model. For the thermodynamics, we show, by using the numerical renormalization group (NRG) method, how the universal specific heat and susceptibility curves evolve with increasing dissipation strength α from those of an isolated two-level system at vanishingly small dissipation strength, with the characteristic activatedlike behavior in this limit, to those of the isotropic Kondo model in the limit α→1−. At any finite α>0, and for sufficiently low temperature, the behavior of the thermodynamics is that of a gapless renormalized Fermi liquid. Our results compare well with available Bethe ansatz calculations at rational values of α, but go beyond these, since our NRG calculations, via the interacting resonant level model, can be carried out efficiently and accurately for arbitrary dissipation strengths 0≤α<1−. We verify the dramatic renormalization of the low-energy thermodynamic scale T0 with increasing α, finding excellent agreement between NRG and density matrix renormalization group (DMRG) approaches. For the zero-temperature transient dynamics of the two-level system, P(t)=⟨σz(t)⟩, with initial-state preparation P(t≤0)=+1, we apply the time-dependent extension of the NRG (TDNRG) to the interacting resonant level model, and compare the results obtained with those from the noninteracting-blip approximation (NIBA), the functional renormalization group (FRG), and the time-dependent density matrix renormalization group (TD-DMRG). We demonstrate excellent agreement on short to intermediate time scales between TDNRG and TD-DMRG for 0≲α≲0.9 for P(t), and between TDNRG and FRG in the vicinity of α=12. Furthermore, we quantify the error in the NIBA for a range of α, finding significant errors in the latter even for 0.1≤α≤0.4. We also briefly discuss why the long-time errors in the present formulation of the TDNRG prevent an investigation of the crossover between coherent and incoherent dynamics. Our results for P(t) at short to intermediate times could act as useful benchmarks for the development of new techniques to simulate the transient dynamics of spin-boson problems. [ABSTRACT FROM AUTHOR]

We study the zero-frequency current noise of the interacting resonant level model for arbitrary bias voltages using a functional renormalization group approach. For this we extend the existing nonequilibrium scheme by deriving and solving flow equations for the current-vertex functions. On-resonance artificial divergences of the latter found in lowest-order perturbation theory in the two-particle interaction are consistently removed. Away from resonance they are shifted to higher orders. This allows us to gain a comprehensive picture of the current noise in the scaling limit. At high bias voltages, the current noise exhibits a universal power-law decay, whose exponent is, to leading order in the interaction, identical to that of the current. The effective charge on resonance is analyzed in detail, employing properties of the vertex correction. We find that it is only modified to second or higher order in the two-particle interaction. [ABSTRACT FROM AUTHOR]

We employ a novel, unbiased renormalization-group approach to investigate nonequilibrium phase transitions in infinite lattice models. This allows us to address the delicate interplay of fluctuations and ordering tendencies in low dimensions out of equilibrium. We study a prototypical model for the metal to insulator transition of spinless interacting fermions coupled to electronic baths and driven out of equilibrium by a longitudinal static electric field. The closed system features a Berezinskii-Kosterlitz-Thouless transition between a metallic and a charge-ordered phase in the equilibrium limit. We compute the nonequilibrium phase diagram and illustrate a highly nonmonotonic dependence of the phase boundary on the strength of the electric field: for small fields, the induced currents destroy the charge order, while at higher electric fields it reemerges due to many-body Wannier-Stark localization physics. Finally, we show that the current in such an interacting nonequilibrium system can counter-intuitively flow opposite to the direction of the electric field. This nonequilibrium steady state is reminiscent of an equilibrium distribution function with an effective negative temperature. [ABSTRACT FROM AUTHOR]

We report on strong renormalization encountered in periodically driven interacting quantum dots in the nonadiabatic regime. Correlations between lead and dot electrons enhance or suppress the amplitude of driving depending on the sign of the interaction. Employing a newly developed flexible renormalization-group-based approach for periodic driving to an interacting resonant level we show analytically that the magnitude of this effect follows a power law. Our setup can act as a non-Markovian, single-parameter quantum pump. [ABSTRACT FROM AUTHOR]

We show how second-order Floquet engineering can be employed to realize systems in which many-body localization coexists with topological properties in a driven system. This allows one to implement and dynamically control a symmetry protected topologically ordered qubit even at high energies, overcoming the roadblock that the respective states cannot be prepared as ground states of nearest-neighbor Hamiltonians. Floquet engineering--the idea that a periodically driven nonequilibrium system can effectively emulate the physics of a different Hamiltonian--is exploited to approximate an effective three-body interaction among spins in one dimension, using time-dependent two-body interactions only. In the effective system, emulated topology and disorder coexist, which provides an intriguing insight into the interplay of many-body localization that defies our standard understanding of thermodynamics and into the topological phases of matter, which are of fundamental and technological importance. We demonstrate explicitly how combining Floquet engineering, topology, and many-body localization allows one to harvest the advantages (time-dependent control, topological protection, and reduction of heating, respectively) of each of these subfields while protecting them from their disadvantages (heating, static control parameters, and strong disorder). [ABSTRACT FROM AUTHOR]

The properties of prototypical examples of one-dimensional fermionic systems undergoing a sudden quantum quench from a gapless state to a (partially) gapped state are analyzed. By means of a generalized Gibbs ensemble analysis or by numerical solutions in the interacting cases, we observe an anomalous, nonmonotonic response of steady-state correlation functions as a function of the strength of the mechanism opening the gap. In order to interpret this result, we calculate the full dynamical evolution of these correlation functions, which shows a freezing of the propagation of the quench information (light cone) for large quenches. We argue that this freezing is responsible for the nonmonotonous behavior of observables. In continuum noninteracting models, this freezing can be traced back to a Klein-Gordon equation in the presence of a source term. We conclude by arguing in favor of the robustness of the phenomenon in the cases of nonsudden quenches and higher dimensionality. [ABSTRACT FROM AUTHOR]