Session P50: Floquet and Nonequilibrium Models

Floquet control of indirect exchange interaction in periodically-driven magnetic lateral heterostructures

Controlling the indirect exchange interaction between ferromagnetic impurities is pivotal for spintronic information transfer and storage. We present a theory for the RKKY interaction in a monochromatically irradiated magnetic lateral heterostructure (MLH). The MLH is composed of a left-side ferromagnet, a two-dimensional electron gas, and a right-side ferromagnet. Using the Keldysh-Floquet formalism, we calculate the time-averaged spin susceptibility and RKKY interaction mediated by the irradiated MLHs. Our results show that the emergence of non-equilibrium Floquet states under periodic driving leads to two qualitatively different RKKY regimes: 1) when the n ≤ 0 Floquet bands intersect the Fermi level, the sign and period of oscillation of the RKKY interaction are controllable by the frequency and amplitude of the laser; 2) when the n ≤ -1 Floquet bands intersect the Fermi level, the RKKY coupling does not display oscillations and remains ferromagnetic, resembling the exchange interaction mediated by insulating spacers. Our work demonstrates the feasibility of optically controlling the indirect exchange interaction with coherent laser fields.   

Nonequilibrium susceptibility in photoinduced Floquet states

We investigate the nonequilibrium spin susceptibility in an electron system subject to a time-periodic electric field [1]. The spin susceptibility is formulated on the basis of the Floquet Green's function method, and is calculated numerically in a wide range of amplitude and frequency of light. When the frequency is larger than the bandwidth, the susceptibility is enhanced by the dynamical localization effect, and their peak positions in the momentum space are shifted due to the Fermi surface deformation. In the case of the small frequency and amplitude, a multiple-peak structure emerges in the susceptibility, originating from the electron-hole excitation in and between the Floquet sidebands. To confirm those numerical results and provide the interpretation, a perturbative expression of the susceptibility is derived for small electric-field amplitude.
[1] A. Ono and S. Ishihara, Phys. Rev. B 100, 075127 (2019).   

Promoting spontaneous symmetry breaking through Floquet band engineering

In itinerant electronic systems, spontaneous symmetry breaking results from an interplay between interactions and density of states: a large density of states allows electrons to form long-range correlations by reducing the associated kinetic energy cost. The prospect of realizing new correlated states of electrons motivates us to seek methods for engineering band structures exhibiting large densities of states. We show that "Floquet engineering" via application of strong electromagnetic fields provides means for obtaining the necessary density of states to realize a novel non-equilibrium spontaneous symmetry breaking transition. We show that the transition occurs in the steady-state of the system achieved due to interplay between the coherent external drive, electron-electron interactions, and dissipative processes due to coupling to phonons and the electromagnetic environment. We obtain the phase diagram of the system using numerical calculations that match predictions obtained from a phenomenological treatment and discuss the conditions on the system and the external drive under which spontaneous symmetry breaking occurs. Our results imply that Floquet engineering of the density of states provides a new route for obtaining correlated states of electrons "on-demand".   

Observation of Floquet prethermalization in dipolar spin chains

Periodically driven (Floquet) quantum systems provide a promising platform to study physics out of equilibrium, such as time crystalline phase and Floquet topological structure. However, the drive generically heats up the system to infinite temperature.
Still, it was shown theoretically that the heating rate is exponentially small in the driving frequency, giving rise to a long-lived prethermal stage that exhibits all the intriguing properties of Floquet systems.
Here we present nuclear magnetic resonance observation of Floquet prethermalization in dipolar spin chains. We first show that the system quickly converges to a prethermal state that agrees with the equilibrium statistics of a time-independent “prethermal” Hamiltonian (PTH). We then observe the exponentially slow heating of quasi-conserved quantities, by measuring the time-autocorrelation of the PTH itself. Intriguingly, we find that at timescale when the PTH is no longer conserved, the system may still possess other symmetries.
The results improve our understanding of thermalization in driven quantum systems and demonstrate the possibility to realize novel Floquet phases of matter and robust Floquet engineering in the prethermal regime.   

Approaching a Floquet Time Crystal phase in the periodically driven O(N) model

Results are presented for the dynamics of the periodically driven O(N) model starting from a prescribed initial state. This model is known to host ferromagnetic phases that, depending on microscopic parameters, are period doubled or period synchronized, the former being an example of a Floquet Time Crystal. Employing numerical simulations, and analytic calculations within a large-N approach, we study how an initial paramagnetic phase evolves into the Floquet time crystal phase following a quench. We identify regimes where the transient dynamics is characterized by an effective mass that approaches steady state as a universal power-law. Results for the one-loop corrections to correlations functions in this transient regime are presented. Analogies to transient dynamics at the critical point of the static O(N) model are highlighted. The possibility of universality in the transition from the paramagnetic and Floquet time crystal phase is discussed.   

Quantum butterfly effect in polarized Floquet systems with conservation laws

We explore quantum dynamics in Floquet many-body systems with local conservation laws in one spatial dimension, focusing on sectors of the Hilbert space which are highly polarized. We numerically compare the predicted charge diffusion constants and quantum butterfly velocity of operator growth between models of chaotic Floquet dynamics (with discrete time translation invariance) and random unitary circuits which vary both in space and time. We find that for any non-zero polarization per length (in the thermodynamic limit), the random unitary circuit correctly predicts the butterfly velocity but incorrectly predicts the diffusion constant. We argue that this is a consequence of quantum coherence on short time scales. Our work clarifies the settings in which random unitary circuits provide correct physical predictions, and the origin of the slow down of the butterfly effect in highly polarized systems.   

Floquet Conformal Field Theory

Conformal field theory provides an ideal platform to discuss examples of Floquet dynamics in an analytic and exact way. Earlier work solved for the Floquet dynamics using a particular driving Hamiltonian (the sl(2,R) generators) and restricted initial state (eigenstates). In this talk, we will generalize the original set-up to go beyond the sl(2,R) algebra and also discuss driving a thermal state. We will discuss the entanglement pattern and energy profile in these generalized set-ups and also describe some non-unversal features of the Floquet dynamics.   

Positivity of the Spectral Densities of Retarded Floquet Green Functions

Periodically driven nonequilibrium many-body systems are interesting because they have quasi-energy spectra, which can be tailored by controlling the external driving fields. We derive the general spectral representation of retarded Green functions in the Floquet regime, thereby generalizing the well-known Lehmann representation from equilibrium many-body physics. The derived spectral Floquet representation allows us to prove the non-negativity of spectral densities and to determine exact spectral sum rules, which can be employed to benchmark the accuracy of approximations to the exact Floquet many-body Green functions.

This work appears in Phys. Rev. Lett. 122, 130604 (2019).   

Floquet dynamics under spatially inhomogeneous drive

Floquet engineering has been shown to be a promising mechanism in realizing quantum information manipulations. While spatially homogeneous drives allow for block diagonalization in momentum, and have thus often been invoked in theoretical studies, in realistic systems, translation symmetry is typically broken. In this work, we discuss features of Floquet systems under inhomogeneous spatial drives, in the context of band theory, such as nondispersing traveling wave packets, simplification of dynamical Hilbert space, and a machine learning scheme which can predict time dynamics of arbitrary temporal driving profiles.   

Long-lived interacting phases of matter protected by multiple time-translation symmetries in quasiperiodically-driven systems

We show how a large family of interacting nonequilibrium phases of matter can arise from the presence of multiple time-translation symmetries, which occur by quasiperiodically driving an isolated quantum many-body system with two or more incommensurate frequencies. These phases are fundamentally different from those realizable in time-independent or periodically-driven (Floquet) settings. Focusing on high-frequency drives with smooth time-dependence, we rigorously establish general conditions for which these phases are stable in a parametrically long-lived `preheating' regime. We develop a formalism to analyze the effect of the multiple time-translation symmetries on the dynamics of the system, which we use to classify and construct explicit examples of the emergent phases. In particular, we discuss time quasi-crystals which spontaneously break the time-translation symmetries, as well as time-translation symmetry protected topological phases.   

Non-equilibrium steady state solutions of time-periodic driven Luttinger liquids

The recent development of Floquet engineering has made periodic driving a versatile tool for achieving new phases not accessible in static equilibrium systems. We now study the exact Floquet steady states of the periodically driven Tomonaga-Luttinger liquid without resorting to any high frequency approximations. We show that the time-dependent Schrödinger equation can be solved analytically for a large class of driven interacting 1D systems, which give the resulting non-equilibrium steady states. Remarkably, we observe regions of instabilities as a function of total momentum where the solution is not of Floquet form, which implies a loss of time translational invariance and therefore heating of excitations. For small driving amplitudes the instabilities are close to the naively expected resonance condition nω=2vq, but for stronger driving the heating regions separate a rich structure of bands of steady state solutions. Physical consequences are discussed.   

Spontaneously broken discrete time translation symmetry in driven quantum Brownian motion

Spontaneously broken discrete time translation symmetry (DTTS) in Floquet systems, often be dubbed as discrete time crystal or Floquet time crystal, draws a lot of attention in recent years. While most experimental realizations and theoretical studies of the DTTS breaking involve many-body localization to avoid heating, the effect of dissipation is an obvious alternative to prevent heating. In this work, we consider the quintessential model of quantum dissipation — the Caldeira-Leggett model and take into account the presence of a periodically driven external potential. Employ a perturbative approach within the framework of Feynman-Vernon influence functional enables us to demonstrate analytically that DTTS breaking would occur in such a simple model. The interplay between the driving frequency, the strength of dissipation, and the temperature are studied in detail. A crossover between the quantum and classical limit is examined as well. Owing to the ubiquitousness of the ordinary Caldeira-Leggett model, our findings pave a new avenue toward exploring the novel phenomena of DTTS breaking in broad systems.   

Dynamic Control of Metal-Insulator Transitions Out of Equilibrium

Dynamic switching between different phases of quantum matter offers many exciting theoretical and practical possibilities. We present recent results from our studies of switching across the Mott metal-insulator transition in the Hubbard model within the framework of non-equilibrium DMFT. We find that the metal to insulator transition is relatively easy to drive but for many quenches the insulator to metal transition occurs over a very long timescale. We present quench protocols that are able to overcome this difficulty and demonstrate controllable switching across the phase boundary in both directions.   

Photo-induced superconductivity in the Kondo lattice

The non-equilibrium dynamics can induce many interesting phenomena in strongly correlated quantum systems. For example, recent experiments have observed the photoinduced superconducting-like behavior in some of the high-T_c cuprates and the alkali-doped fullerenes even above T_c. In this context, we have previously studied theoretically the photo-excited states from the Mott insulating state in the Hubbard model and found that the pulse irradiation can induce the enhancement of superconducting correlations, which is attributed to eta-pairing formation [1]. Here, we show that the same mechanism can be applied to the Kondo lattice model, an effective model for heavy fermion systems, by demonstrating that the photo-irradiation indeed enhances the eta-pairing correlations. As in the Hubbard model, the non-linear optical process is essential to increase the number of photo-induced eta-pairs and thus enhance the superconducting correlations.
[1] T. Kaneko, T. Shirakawa, S. Sorella, and S. Yunoki, Phys. Rev. Lett. 122, 077002 (2019).