Floquet dynamical quantum phase transitions (FDQPTs) are signified by recurrent nonanalytic behaviors of observables in time. In this work, we introduce a quench-free and generic approach to engineer and control FDQPTs for both pure and mixed Floquet states. By applying time-periodic modulations with two driving frequencies to a general class of spin chain model, we find multiple FDQPTs within each driving period. The model is investigated with equal, commensurate and incommensurate driving frequencies. The nonanalytic cusps of return probability form sublattice structures in time domain. Notably, the number and time locations of these cusps can be flexibly controlled by tuning the Hamiltonian parameter and the frequencies of the drive. We further employ the dynamical topological order parameter, which shows a quantized jump whenever a DQPT happens, to identify the topological feature of FDQPTs. Our findings reveal the advantage of engineering nonequilibrium phase transitions with multifrequency driving fields.
Floquet dynamical quantum phase transitions (FDQPTs) are signified by recurrent nonanalytic behaviors of observables in time. In this work, we introduce a quench-free and generic approach to engineer and control FDQPTs for both pure and mixed Floquet states. By applying time-periodic modulations with two driving frequencies to a general class of spin chain model, we find multiple FDQPTs within each driving period. The model is investigated with equal, commensurate and incommensurate driving frequencies. The nonanalytic cusps of return probability form sublattice structures in time domain. Notably, the number and time locations of these cusps can be flexibly controlled by tuning the Hamiltonian parameter and the frequencies of the drive. We further employ the dynamical topological order parameter, which shows a quantized jump whenever a DQPT happens, to identify the topological feature of FDQPTs. Our findings reveal the advantage of engineering nonequilibrium phase transitions with multifrequency driving fields.
Dynamical quantum phase transitions (DQPTs) are characterized by nonanalytic behaviors of physical observables as functions of time. When a system is subject to time-periodic modulations, the nonanalytic signatures of its observables could recur periodically in time, leading to the phenomena of Floquet DQPTs. In this work, we systematically explore Floquet DQPTs in a class of periodically quenched one-dimensional system with chiral symmetry. By tuning the strength of quench, we find multiple Floquet DQPTs within a single driving period, with more DQPTs being observed when the system is initialized in Floquet states with larger topological invariants. Each Floquet DQPT is further accompanied by the quantized jump of a dynamical topological order parameter, whose values remain quantized in time if the underlying Floquet system is prepared in a gapped topological phase. The theory is demonstrated in a piecewise quenched lattice model, which possesses rich Floquet topological phases and is readily realizable in quantum simulators like the nitrogen-vacancy center in diamonds. Our discoveries thus open a new perspective for the Floquet engineering of DQPTs and the dynamical detection of topological phase transitions in Floquet systems.
Dynamical quantum phase transitions (DQPTs) are manifested by time-domain nonanalytic behaviors of many-body systems. Introducing a quench is so far understood as a typical scenario to induce DQPTs. In this work, we discover a type of DQPTs, termed Floquet DQPTs, as intrinsic features of time-periodic systems. Floquet DQPTs occur within each period of continuous driving, without the need for any quenches. In particular, in a harmonically driven spin chain model, we find analytically the existence of Floquet DQPTs in and only in a parameter regime hosting a certain nontrivial Floquet topological phase. The Floquet DQPTs are further characterized by a dynamical topological invariant defined as the winding number of the Pancharatnam geometric phase versus quasimomentum. These findings are experimentally demonstrated with a single spin in diamond. This work thus opens a door for future studies of DQPTs in connection with topological matter.
Floquet dynamical quantum phase transitions (FDQPTs) reveal many nonequilibrium critical phenomena in periodically driven quantum systems, and their underlying mechanisms have attracted deep attention in recent years. In this paper, we consider an extended XY spin chain under a periodic flux-quench protocol, and demonstrate the effect of the flux difference within each micromotion period on the emergence of FDQPTs, by analyzing physical quantities such as the Loschmidt echo, rate function, and dynamical topological order parameter (DTOP), etc. We also generalize the concept of quench fidelity to periodically driven systems, i.e., Floquet quench fidelity, and discuss the necessary and sufficient conditions for FDQPTs. In contrast to conventional single-quench scenarios, the occurrence of FDQPTs is determined by the requirement of Floquet fidelity condition and segment duration. Our framework may be applied generally to arbitrary periodically driven parameters, providing fundamental insights into how periodic protocols control nonequilibrium phase transitions in quantum many-body systems.
Out-of-time-order correlators (OTOCs) progressively play an important role in different fields of physics, particularly in the nonequilibrium quantum many-body systems. In this paper, we show that OTOCs can be used to probe the Floquet dynamical quantum phase transitions (FDQPTs). We investigate the OTOCs of two exactly solvable Floquet spin models, namely, Floquet XY chain and synchronized Floquet XY model. We show that the border of driving frequency range, over which the Floquet XY model shows FDQPT, is signaled by the global minimum of the infinite-temperature time averaged OTOC. Moreover, our results manifest that OTOCs decay algebraically in the long time, for which the decay exponent in the FDQPT region is different from that in the region where the system does not show FDQPTs. In addition, for the synchronized Floquet XY model, which reveals FDQPT at any driving frequency depending on the initial infinite or finite temperature, the imaginary part of the OTOCs becomes zero whenever the system shows FDQPT.
Floquet dynamical quantum phase transitions (DQPTs), which are nonanalytic phenomena recuring periodically in time-periodic driven quantum many-body systems, have been widely studied in recent years. In this article, the Floquet DQPTs in transverse XY spin chains under the modulation of δ-function periodic kickings are investigated. We analytically solve the system, and by considering the eigenstate as well as the ground state as the initial state of the Floquet dynamics, we study the corresponding multiple Floquet DQPTs emerged in the micromotion with different kicking moments. The rate function of return amplitude, the Pancharatnam geometric phase and the dynamical topological order parameter are calculated, which consistently verify the emergence of Floquet DQPTs in the system.
This work investigates dynamical quantum phase transitions (DQPTs) in a one-dimensional Ising model subjected to a periodically modulated transverse field. In contrast to sudden quenches, we demonstrate that a DQPT can be induced in two distinct ways. First, when the system remains within a given phase--ferromagnetic (FM) or paramagnetic (PM), a resonant periodic drive can trigger a DQPTs when its frequency matches the energy-level transition of the system. This DQPT is intimately connected to the emergence of Floquet topological phases. The timescale for the transition is governed by the perturbation strength λ′, the critical mode kc, and its energy gap Δkc, following the scaling relation τ∝Δkcλ′−1csckc. Second, for drives across the critical point between the FM and PM phases, low frequencies can always induce DQPT, regardless of resonance. This behavior stems from the degeneracy of the energy-level at the critical point, which ensures that any drive with a frequency lower than the system's intrinsic transition frequency will inevitably excite the system. However, in the high-frequency regime, such excitation will be strongly suppressed, thereby inhibiting the occurrence of DQPTs. This study provides deeper insight into the nonequilibrium dynamics of quantum spin chains.