In periodically driven open quantum systems, nonnormality renders the Floquet spectrum insufficient as the system approaches the thermodynamic limit, so that pseudospectra are needed to characterize the dynamics accurately. While conventional approaches mainly focus on the local dynamics of isolated pseudospectra, their global connections and the resulting physical consequences for observables have remained largely unexplored. Here, we uncover this collective behavior by classifying the unit disk into distinct domains of exponential, algebraic, and bounded accuracy according to the asymptotic size-scaling laws of pseudospectral residuals, yielding an underlying geometric structure. We demonstrate the physical implications of this structure through two exactly solvable models. First, in a dissipative shift chain, parameter tuning drives geometric transitions that are detectable via spin-wave observables. Second, in a chiral XY model, we use this geometric structure to explain the origin of a measurable phenomenon: two correlation signals exchange their retention order under continuous parameter tuning. Our findings not only establish a new theoretical paradigm for understanding dissipative Floquet quantum systems, but also predict geometry-driven observables for quantum computing experiments.
In periodically driven open quantum systems, nonnormality renders the Floquet spectrum insufficient as the system approaches the thermodynamic limit, so that pseudospectra are needed to characterize the dynamics accurately. While conventional approaches mainly focus on the local dynamics of isolated pseudospectra, their global connections and the resulting physical consequences for observables have remained largely unexplored. Here, we uncover this collective behavior by classifying the unit disk into distinct domains of exponential, algebraic, and bounded accuracy according to the asymptotic size-scaling laws of pseudospectral residuals, yielding an underlying geometric structure. We demonstrate the physical implications of this structure through two exactly solvable models. First, in a dissipative shift chain, parameter tuning drives geometric transitions that are detectable via spin-wave observables. Second, in a chiral XY model, we use this geometric structure to explain the origin of a measurable phenomenon: two correlation signals exchange their retention order under continuous parameter tuning. Our findings not only establish a new theoretical paradigm for understanding dissipative Floquet quantum systems, but also predict geometry-driven observables for quantum computing experiments.
We investigate the non-equilibrium topology of the steady state of a periodically driven, dissipative Su-Schrieffer-Heeger (SSH) chain using the ensemble geometric phase (EGP) φEGP, a generalisation of the Zak phase to mixed states. The coupling to thermal reservoirs is treated microscopically within Floquet-Born-Markov theory without the rotating-wave approximation. We classify the steady state rather than the generator of the dynamics, using its purity spectrum as the analogue of a band structure. We show that, within the EGP framework, the Z×Z structure of isolated chiral-symmetric Floquet SSH systems generally does not carry over to the steady state. Instead, the steady state carries a single invariant whose type is set by an underlying symmetry. When this symmetry holds, the invariant is Z2-valued, with quantised φEGP=±π/2 at all times and finite temperatures. The EGP can switch within a driving period, tracking the presence of edge modes in the open-boundary purity spectrum and thereby establishing a bulk-boundary correspondence. The fraction of each period spent in the nontrivial regime varies continuously with the driving frequency, and the switching disappears if the dependence of the dissipator on the drive is neglected. When the symmetry is broken, φEGP is no longer quantised, but its winding over a drive period T defines an invariant νT∈Z, with no purity-spectrum bulk-boundary correspondence. We propose that its changes signal temperature- and frequency-driven topological phase transitions. Our formalism extends to general quadratic fermionic systems with linear bath couplings.
Engineering dissipative dynamics in open quantum systems is under active focus, especially in topological settings where resilient edge modes are expected to exhibit decay rates distinct from the bulk. In this letter, we propose an efficient dynamical scheme to discern such long-lived excitations. Employing a Floquet-Lindblad framework, we explore how periodic driving reshapes the key features of a paradigmatic topological model, namely a Creutz ladder. Our results bear testimony to a drive-induced unipolar-bipolar transition in the Liouvillian skin effect, which gets dynamically manifested as a chiral-helical damping crossover. Such a transition effectively rescales the bulk localization length, giving rise to a polarization drift that we identify as a new invariant for efficient diagnosis of the nontrivial phases. As the transition becomes more gradual via tuning drive-rescaled parameters, we uncover signatures of a scale-free localization where skin and extended modes co-exist with distinct decay rates. The emergent hierarchy of the decay rates yields two disparate timescales: a chiral wavefront that rapidly empties the bulk followed by a long-lived regime dominated by robust edge modes. Overall, our results provide convincing evidence that periodic driving serves as a powerful handle to manipulate dissipative topological phases and dynamically isolate the boundary modes.
The geometry of quantum states could offer indispensable insights for characterizing the topological properties, phase transitions, and entanglement nature of many-body systems. In this work, we reveal the quantum geometry and the associated entanglement entropy (EE) of Floquet topological states in one-dimensional periodically driven systems. The quantum metric tensors of Floquet states are found to show nonanalytic signatures at topological phase transition points. Away from the transition points, the bipartite geometric EE of Floquet states exhibits an area-law scaling vs the system size, which holds for a Floquet band at any filling fractions. For a uniformly filled Floquet band, the EE further becomes purely quantum geometric. At phase transition points, the geometric EE scales logarithmically with the system size and displays cusps in the nearby parameter ranges. These discoveries are demonstrated by investigating typical Floquet models including periodically driven spin chains, Floquet topological insulators, and superconductors. Our findings uncover the rich quantum geometries of Floquet states, unveiling the geometric origin of EE for gapped Floquet topological phases, and introducing information-theoretic means of depicting topological transitions in Floquet systems.
Dissipative phase transitions (DPTs) are traditionally characterized through the spectrum of a time-independent Liouvillian superoperator. However, this definition does not apply to time-periodic (Floquet) systems that cannot be exactly recast as time-independent problems. Here, we develop a general framework to characterize DPTs in time-periodic open quantum systems through the spectrum of the Floquet propagator. We first study driven-dissipative Kerr resonators, known to display a DPT, showing that counter-rotating terms in the drive shift the critical point and significantly change the time scales associated with the transition. We then investigate DPTs in the driven quantum Rabi model and its time-independent approximation, the driven Jaynes-Cummings model, finding that the Rabi model exhibits distinct critical features as the ultrastrong coupling regime is approached. Moreover, our Floquet analysis unveils the disappearance of the DPT in the deep strong coupling regime, due to light-matter decoupling. Our approach sets the stage for the study of dissipative criticality in a broad class of time-dependent open quantum systems.
Prethermalization, by introducing emergent quasiconserved observables, plays a crucial role in protecting periodically driven (Floquet) many-body phases over an exponentially long time, while the ultimate fate of such quasiconserved operators can signal thermalization to infinite temperature. To elucidate the properties of prethermal quasiconservation in many-body Floquet systems, here we systematically analyze infinite-temperature correlations between observables. We numerically show that the late-time behavior of the autocorrelations unambiguously distinguishes quasiconserved observables from nonconserved ones, allowing one to single out a set of linearly independent quasiconserved observables. By investigating two Floquet spin models, we identify two different mechanisms underlying the quasiconservation law. First, we numerically verify energy quasiconservation when the driving frequency is large, so that the system dynamics is approximately described by a static prethermal Hamiltonian. More interestingly, under moderate driving frequency, another quasiconserved observable can still persist if the Floquet driving contains a large global rotation. We show theoretically how to calculate this conserved observable and provide numerical verification. Having systematically identified all quasiconserved observables, we can finally investigate their behavior in the infinite-time limit and thermodynamic limit, using autocorrelations obtained from both numerical simulation and experiments in solid-state nuclear magnetic resonance systems.
In isolated quantum many-body systems periodically driven in time, the asymptotic dynamics at late times can exhibit distinct behavior such as thermalization or dynamical freezing. Understanding the properties of and the convergence towards infinite-time (nonequilibrium) steady states, however, remains a challenging endeavor. We propose a physically motivated Krylov space perspective on Floquet thermalization which offers a natural framework to study rates of convergence towards steady states and, simultaneously, an efficient numerical algorithm to evaluate infinite-time averages of observables within the diagonal ensemble. The effectiveness of our algorithm is demonstrated by applying it to the periodically driven mixed-field Ising model, reaching system sizes of up to 30 spins. Our method successfully resolves the transition between the ergodic and dynamically frozen phases and provides insight into the nature of the Floquet eigenstates across the phase diagram. Furthermore, we show that the long-time behavior is encoded within the localization properties of the Ritz vectors under the Floquet evolution, providing an accurate diagnostic of ergodicity.