We study the dynamics of a one-dimensional lattice model of hard core bosons which is initially in a superfluid phase with a current being induced by applying a twist at the boundary. Subsequently, the twist is removed and the system is subjected to periodic δ-function kicks in the staggered on-site potential. We present analytical expressions for the current and work done in the limit of an infinite number of kicks. Using these, we show that the current (work done) exhibit a number of dips (peaks) as a function of the driving frequency and eventually saturates to zero (a finite value) in the limit of large frequency. The vanishing of the current (and the saturation of the work done) can be attributed to a dynamic localization of the hard core bosons occurring as a consequence of the periodic driving. Remarkably, we show that for some specific values of the driving amplitude, the localization occurs for any value of the driving frequency. Moreover, starting from a half-filled lattice of hard core bosons with the particles localized in the central region, we show that the spreading of the particles occurs in a light-cone-like region with a group velocity that vanishes when the system is dynamically localized.

We study the scaling of the decoherence factor of a qubit (spin−1/2) using the central spin model in which the central spin (qubit) is globally coupled to a transverse XY spin chain. The aim here is to study the non-equilibrium generation of decoherence when the spin chain is driven across (along) quantum critical points (lines) and derive the scaling of the decoherence factor in terms of the driving rate and some of the exponents associated with the quantum critical points. Our studies show that the scaling of logarithm of decoherence factor is identical to that of the defect density in the final state of the spin chain following a quench across isolated quantum critical points for both linear and non-linear variations of a parameter even if the defect density may not satisfy the standard Kibble-Zurek scaling. However, one finds an interesting deviation when the spin chain is driven along a critical line. Our analytical predictions are in complete agreement with numerical results. Our study, though limited to integrable two-level systems, points to the existence of a universality in the scaling of the decoherence factor which is not necessarily identical to the scaling of the defect density. PACS numbers:When a quantum many-body system is slowly driven across a quantum critical point (QCP)1 by varying a parameter in the Hamiltonian, defects are generated in the final state; this is a consequence of the diverging relaxation time close to the QCP, so that the dynamics is no longer adiabatic however slow may the variation be 2-4 . If a parameter λ of the Hamiltonian describing a d−dimensional system is changed linearly as λ(t) = t/τ, − ∞ < t < ∞, (with the QCP at λ = 0), the defect density (n) in the final state satisfies the KibbleZurek (KZ) scaling relation, 2-8 n ∼ τ −νd/(νz+1) ; here, τ is the inverse rate of quenching, and ν and z are the correlation length and dynamical critical exponents, respectively, associated with the QCP.In parallel, there are a plethora of studies which connect quantum information theory to quantum critical systems (for a review, see 7,8 ). One of the major issues in this regard is the study of decoherence, namely, the loss of coherence in a quantum system due to its interaction with the environment 9 . To elucidate these studies, the central spin model (CSM) has been proposed 10 . In this model, a central spin (CS) (i.e., the qubit) has a global interaction with a quantum many body system (e.g., with all the spins of a quantum spin chain) which acts as the environment. The interaction between the qubit and the environment in fact provides two channels of time evolution of the environmental spin chain. It has been observed that the purity of the CS is given in terms of the Loschmidt echo (LE) or the decoherence factor (DF) which is the measure of the square of the overlap of the wave function evolved along the two different channels as a function of time. The LE or DF which appears in the off-diagonal term of the reduced density matrix of the qubit is minimum at the QCP signifying a m...

Higher-order topological (HOT) states, hosting topologically protected modes on lowerdimensional boundaries, such as hinges and corners, have recently extended the realm of the static topological phases. Here we demonstrate the possibility of realizing a two-dimensional Floquet second-order topological insulator, featuring corner-localized zero quasienergy modes and characterized by quantized Floquet qudrupolar moment Q Flq xy = 0.5, by periodically kicking a quantum spin Hall insulator (QSHI) with a discrete fourfold (C4) and time-reversal (T ) symmetry breaking Dirac mass perturbation. Furthermore, we show that Q Flq xy becomes independent of the choice of origin as the system approaches the thermodynamic limit. We also analyze the dynamics of a corner mode after a sudden quench, when the C4 and T symmetry breaking perturbation is switched off, and find that the corresponding survival probability displays periodic appearances of complete, partial and no revival for long time, encoding the signature of corner modes in a QSHI. Our protocol is sufficiently general to explore the territory of dynamical HOT phases in insulators and gapless systems.

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