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Register a new userOut-of-equilibrium phase transitions induced by Floquet resonances in a periodically quench-driven XY spin chain
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Added by
Isaac P\\'erez Castillo
Publication date
2018
fields
Physics
and research's language is
English
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We consider the dynamics of an XY spin chain subjected to an external transverse field which is periodically quenched between two values. By deriving an exact expression of the Floquet Hamiltonian for this out-of-equilibrium protocol with arbitrary driving frequencies, we show how, after an unfolding of the Floquet spectrum, the parameter space of the system is characterized by alternations between local and non-local regions, corresponding respectively to the absence and presence of Floquet resonances. The boundary lines between regions are obtained analytically from avoided crossings in the Floquet quasi-energies and are observable as phase transitions in the synchronized state. The transient behaviour of dynamical averages of local observables similarly undergoes a transition, showing either a rapid convergence towards the synchronized state in the local regime, or a rather slow one exhibiting persistent oscillations in the non-local regime, where explicit decay coefficients are presented.
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We study the Floquet phase diagram of two-dimensional Dirac materials such as graphene and the one-dimensional (1D) spin-1/2 $XY$ model in a transverse field in the presence of periodic time-varying terms in their Hamiltonians in the low drive frequency ($omega$) regime where standard $1/omega$ perturbative expansions fail. For graphene, such periodic time dependent terms are generated via the application of external radiation of amplitude $A_0$ and time period $T = 2pi/omega$, while for the 1D $XY$ model, they result from a two-rate drive protocol with time-dependent magnetic field and nearest-neighbor couplings between the spins. Using the adiabatic-impulse method, we provide several semi-analytic criteria for the occurrence of changes in the topology of the phase bands of such systems. For irradiated graphene, we point out the role of the symmetries of $H(t)$ and $U$ behind such topology changes. Our analysis reveals that at low frequencies, phase band topology changes may also happen at $t= T/3, 2T/3$ (apart from $t=T$). We chart out the phase diagrams at $t=T/3, 2T/3,, {rm and }, T$ as a function of $A_0$ and $T$ using exact numerics, and compare them with the prediction of the adiabatic-impulse method. We show that several characteristics of these phase diagrams can be analytically understood from results obtained using the adiabatic-impulse method and point out the crucial contribution of the high-symmetry points in the graphene Brillouin zone to these diagrams. Finally we study the 1D $XY$ model with a two-rate driving protocol using the adiabatic-impulse method and exact numerics revealing a phase band crossing at $t=T/2$ and $k=pi/2$. We also study the anomalous end modes generated by such a drive. We suggest experiments to test our theory.
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The extraction of membrane tubes by molecular motors is known to play an important role for the transport properties of eukaryotic cells. By studying a generic class of models for the tube extraction, we discover a rich phase diagram. In particular we show that the density of motors along the tube can exhibit shocks, inverse shocks and plateaux, depending on parameters which could in principle be probed experimentally. In addition the phase diagram exhibits interesting reentrant behavior.
We analytically and numerically study the Loschmidt echo and the dynamical order parameters in a spin chain with a deconfined phase transition between a dimerized state and a ferromagnetic phase. For quenches from a dimerized state to a ferromagnetic phase, we find that the model can exhibit a dynamical quantum phase transition characterized by an associating dimerized order parameters. In particular, when quenching the system from the Majumdar-Ghosh state to the ferromagnetic Ising state, we find an exact mapping into the classical Ising chain for a quench from the paramagnetic phase to the classical Ising phase by analytically calculating the Loschmidt echo and the dynamical order parameters. By contrast, for quenches from a ferromagnetic state to a dimerized state, the system relaxes very fast so that the dynamical quantum transition may only exist in a short time scale. We reveal that the dynamical quantum phase transition can occur in systems with two broken symmetry phases and the quench dynamics may be independent on equilibrium phase transitions.
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