Floquet dynamical quantum phase transitions in transverse XY spin chains under periodic kickings

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 ofδ-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.

Dynamical phase transitions in a two-species bosonic Josephson junction

We investigate dynamical phase transitions that are induced by interspecies interaction in a two-species bosonic Josephson junctions （B J J）, based on semi-classical theory. In zero-phase mode, similar to the case of a single-species B J J, we observe the well-known dynamical phase transition from Josephson oscillation to self-trapping, which can be induced by both enhanced repulsive and attractive interspecies interactions. In π phase mode, dynamical phase transitions are even more interesting and counter- intuitive. We characterize a dynamical phase transition with the merging of two separate phase space domains into one, which is induced by increasing repulsive interspecies interaction. On the other hand, we find that by increasing attractive interspecies interaction, a phase separation of two formally overlapped phase space domains will occur. At last, we reveal that these intriguing dynamical phase transitions are caused by different kinds of bifurcations.

Dynamical quantum phase transition in XY chains with the Dzyaloshinskii-Moriya and XZY-YZX three-site interactions

We study the dynamical quantum phase transitions(DQPTs)in the XY chains with the Dzyaloshinskii-Moriya interaction and the XZY-YZX type of three-site interaction after a sudden quench.Both the models can be mapped to the spinless free fermion models by the Jordan-Wigner and Bogoliubov transformations with the form■where the quasiparticle excitation spectraεkmay be smaller than 0 for some k and are asymmetrical■It is found that the factors of Loschmidt echo equal 1 for some k corresponding to the quasiparticle excitation spectra of the pre-quench Hamiltonian satisfyingε_(k)·ε_(-k)<0,when the quench is from the gapless phase.By considering the quench from different ground states,we obtain the conditions for the occurrence of DQPTs for the general XY chains with gapless phase,and find that the DQPTs may not occur in the quench across the quantum phase transitions regardless of whether the quench is from the gapless phase to gapped phase or from the gapped phase to gapless phase.This is different from the DQPTs in the case of quench from the gapped phase to gapped phase,in which the DQPTs will always appear.Moreover,we analyze the different reasons for the absence of DQPTs in the quench from the gapless phase and the gapped phase.The conclusion can also be extended to the general quantum spin chains.

Dynamic phase transition of ferroelectric nanotube described by a spin-1/2 transverse Ising model

The dynamic phase transition properties for ferroelectric nanotube under a spin-1/2 transverse Ising model are studied under the effective field theory(EFT)with correlations.The temperature effects on the pseudo-spin systems are unveiled in three-dimensional(3-D)and two-dimensional(2-D)phase diagrams.Moreover,the dynamic behaviors of exchange interactions on the 3-D and 2-D phase transitions under high temperature are exhibited.The results present that it is hard to obtain pure ferroelectric phase under high temperature;that is,the vibration of orderly pseudo-spins cannot be eliminated completely.

Stochastic resonance and nonequilibrium dynamic phase transition of Ising spin system driven by a joint external field

The dynamic response and stochastic resonance of a kinetic Ising spin system （ISS） subject to the joint action of an external field of weak sinusoidal modulation and stochastic white-nolse are studied by solving the mean-field equation of motion based on Glauber dynamics. The periodically driven stochastic ISS shows that the characteristic stochastic resonance as well as nonequilibrium dynamic phase transition （NDPT） occurs when the frequency ω and amplitude h0 of driving field, the temperature t of the system and noise intensity D are all specifically in accordance with each other in quantity. There exist in the system two typical dynamic phases, referred to as dynamic disordered paramagnetic and ordered ferromagnetic phases respectively, corresponding to a zero- and a unit-dynamic order parameter. The NDPT boundary surface of the system which separates the dynamic paramagnetic phase from the dynamic ferromagnetic phase in the 3D parameter space of ho-t-D is also investigated. An interesting dynamical ferromagnetic phase with an intermediate order parameter of 0.66 is revealed for the first time in the ISS subject to the perturbation of a joint determinant and stochastic field. The intermediate order dynamical ferromagnetic phase is dynamically metastable in nature and owns a peculiar characteristic in its stability as well as the response to external driving field as compared with a fully order dynamic ferromagnetic phase.

Dynamic Investigations of Pressure-Induced Abnormal Phase Transitions in PbTiO3

The effects of pressure on phonon modes of ferroeleetrie tetragonal P4mm and paraelectric cubic Pm3m PbTiOa are systematically investigated by using first-principles simulations. The pressure-induced tetragonal-to-cubie and subsequent cubic-to-tetragonal phase transitions are the second-order transitions, which are different from the phase transitions induced by temperature [Phys. Rev. Lett. 25 （1970） 167]. As pressure increases, the lowest A1 and E modes of the tetragonal phase become softer and converge to the F1u mode of the cubic phase. As pressure further increases, the lowest Flu mode first hardens and then softens again, and finally diverges into A1 and E modes. The behaviors of optical phonon modes confirm the ferroelectric-to-paraelectric-to-ferroeleetric phase transitions.

Phase transition in a two-dimensional Ising ferromagnet based on the generalized zero-temperature Glauber dynamics

At zero temperature, based on the Ising model, the phase transition in a two-dimensional square lattice is studied using the generalized zero-temperature Glauber dynamics. Using Monte Carlo （MC） renormalization group methods, the static critical exponents and the dynamic exponent are studied; the type of phase transition is found to be of the first order.

Numerical method for simulating rarefaction shocks in the approximation of phase-flip hydrodynamics

A finite-difference algorithm is proposed for numerical modeling of hydrodynamic flows with rarefaction shocks, in which the fluid undergoes a jump-like liquid-gas phase transition. This new type of flow discontinuity, unexplored so far in computational fluid dynamics, arises in the approximation of phase-flip(PF) hydrodynamics, where a highly dynamic fluid is allowed to reach the innermost limit of metastability at the spinodal, upon which an instantaneous relaxation to the full phase equilibrium(EQ) is assumed. A new element in the proposed method is artificial kinetics of the phase transition, represented by an artificial relaxation term in the energy equation for a "hidden"component of the internal energy, temporarily withdrawn from the fluid at the moment of the PF transition. When combined with an appropriate variant of artificial viscosity in the Lagrangian framework, the latter ensures convergence to exact discontinuous solutions, which is demonstrated with several test cases.

Critical Spreading of Active Region in a Ladder Model Possessing Infinite AbsorbingStates

The spreading of active region of the ladder model is simulated. Finite-time scaling behaviors are observedin the vicinity of the critical point.

Demage Spreading in the Ising Model with a special Metropolis Dynamics Approach

The time evolution of the Hamming distance (damage spreading) for the and Ising models on the square lattice is performed with a special metropolis dynamics algorithm. Two distinct regimes are observed according to the temperature range for both models: a low-temperature one where the distance in the long-time limit is finite and seems not to depend on the initial distance and the system size; a high-temperature one where the distance vanishes in the long-time limit. Using the finite size scaling method, the dynamical phase transition (damage spreading transition) temperature is obtained as for the Ising model.

Nonequilibrium Phase Transition in Spin-S Ising Ferromagnet Driven by Propagating and Standing Magnetic Field Wave

The dynamical response of spin-S(S=1, 3/2, 2, 3) Ising ferromagnet to the plane propagating wave, standing magnetic field wave and uniformly oscillating field with constant frequency are studied separately in two dimensions by extensive Monte Carlo simulation. Depending upon the strength of the magnetic field and the value of the spin state of the Ising spin lattice two different dynamical phases are observed. For a fixed value of S and the amplitude of the propagating magnetic field wave the system undergoes a dynamical phase transition from propagating phase to pinned phase as the temperature of the system is cooled down. Similarly in case with standing magnetic wave the system undergoes dynamical phase transition from high temperature phase where spins oscillate coherently in alternate bands of half wavelength of the standing magnetic wave to the low temperature pinned or spin frozen phase. For a fixed value of the amplitude of magnetic field oscillation the transition temperature is observed to decrease to a limiting value as the value of spin S is increased. The time averaged magnetisation over a full cycle of the magnetic field oscillation plays the role of the dynamic order parameter. A comprehensive phase boundary is drawn in the plane of magnetic field amplitude and dynamic transition temperature. It is found that the phase boundary shrinks inwards for high value of spin state S.Also in the low temperature(and high field) region the phase boundaries are closely spaced.

Nonequilibrium behavior of the kinetic metamagnetic spin-5/2 Blume–Capel model

The dynamic magnetic behavior of the kinetic metamagnetic spin-5/2 Blume-Capel model is examined, within a mean-field approach, under a time-dependent oscillating magnetic field. To describe the kinetics of the system, Glauber- type stochastic dynamics has been utilized. The mean-field dynamic equations of the model are obtained from the Master equation. Firstly, these dynamic equations are solved to find the phases in the system. Then, the dynamic phase transition temperatures are obtained by investigating the thermal behavior of dynamic sublattice magnetizations. Moreover, from this investigation, the nature of the phase transitions （first- or second-order） is characterized. Finally, the dynamic phase diagrams are plotted in five different planes. It is found that the dynamic phase diagrams contain the paramagnetic （P）, antiferromagnetic （AF5/2, AF3/2, AF1/2） phases and five different mixed phases. The phase diagrams also display many dynamic critical points, such as tricritical point, triple point, quadruple point, double critical end point and separating point.

Dynamic property of phase transition for non-linear charged anti-de Sitter black holes

Understanding the thermodynamic phase transition of black holes can provide deep insights into the fundamental properties of black hole gravity and help to establish quantum gravity.In this work,we investigate the phase transition and its dynamics for the charged EPYM AdS black hole.Through reconstructing Maxwell's equal-area law,we find there exists a high-/low-potential black hole(HPBH/LPBL)phase transition,not only the pure large/small black hole phase transition.The Gibbs free energy landscape(G_(L))is treated as a function of the black hole horizon,which is the order parameter of the phase transition due to thermal fluctuation.From the viewpoint of G_(L),the stable HPBH/LPBL states correspond to two wells of G_(L),which have the same depth.The unstable intermediate-potential black hole state corresponds to the local maximum of G_(L).Then we focus on the probability evolution governed by the Fokker-Planck equation.Through solving the Fokker-Planck equation with different reflection/absorption boundary conditions and initial conditions,the dynamics of switching between the coexistent HPBH and LPBL phases is probed within the first passage time.Furthermore,the effect of temperature on the dynamic properties of the phase transition is also investigated.

Magnetic Properties of Transverse Ising Model under a Time Oscillating Longitudinal Field

A transverse Ising spin system, in the presence of time-dependent longitudinal field, is studied by the effective-field theory （EFT）. The effective-field equations of motion of the average magnetization are given for the simple cubic lattice （Z ---- 6） and the honeycomb lattice （Z = 3）. The Liapunov exponent A is calculated for discussing the stability of the magnetization and it is used to determine the phase boundary. The dynamic phase transition diagrams in ho/ZJ - F/ZJ plane and in ho/ZJ - T/ZJ plane have been drawn, and there is no dynamical tricritical point on the dynamic phase transition boundary. The effect of the thermal fluctuations upon the dynamic phase boundary has been discussed.

The dynamic compensation temperature in a kinetic spin-5/2 Ising model on a hexagonal lattice

We present a study of the dynamic behavior of a two-sublattice spin-5/2 Ising model with bilinear and crystal-field interactions in the presence of a time-dependent oscillating external magnetic field on alternating layers of a hexagonal lattice by using the Glauber-type stochastic dynamics.The lattice is formed by alternate layers of spins σ=5/2 and S=5/2.We employ the Glauber transition rates to construct the mean-field dynamic equations.First,we investigate the time variations of the average sublattice magnetizations to find the phases in the system and then the thermal behavior of the dynamic sublattice magnetizations to characterize the nature（first-or second-order） of the phase transitions and to obtain the dynamic phase transition（DPT） points.We also study the thermal behavior of the dynamic total magnetization to find the dynamic compensation temperature and to determine the type of the dynamic compensation behavior.We present the dynamic phase diagrams,including the dynamic compensation temperatures,in nine different planes.The phase diagrams contain seven different fundamental phases,thirteen different mixed phases,in which the binary and ternary combination of fundamental phases and the compensation temperature or the L-type behavior strongly depend on the interaction parameters.

Dynamic phase transition of charged dilaton black holes

The dynamic phase transition of charged dilaton black holes is investigated in this paper.The Gibbs free energy landscape is introduced,and the corresponding G_(L) is calculated for the dilaton black hole.We numerically solve the Fokker-Planck equation constrained by only the reflecting boundary condition.The effects of dilaton gravity on the probabilistic evolution of dilaton black holes are explored.Firstly,the horizon radius difference between a large dilaton black hole and a small dilaton black hole increases with the parameterα.Secondly,with increasingα,the system needs much more time to achieve a stationary distribution.Finally,the values attained forρ(rl,t)andρ(rs,t)vary withα.Additionally,by resolving the Fokker-Planck equation constrained by both the reflecting boundary condition and absorbing boundary condition,we investigate the first passage process of dilaton black holes.The initial peak decays more slowly with increasingα,which can also be observed via the slowing decay ofΣ(t)(the sum of the probability of the black hole system not having completed a first passage by time t).Moreover,the time corresponding to the single peak of the first passage time distribution is found to increase with the parameterα.Considering these observations,the dilaton field is found to slow down the dynamic phase transition process between a large black hole and a small black hole.

Dynamic Transition and Pattern Formation in Taylor Problem

The main objective of this article is to study both dynamic and structural transitions of the Taylor-Couette flow, by using the dynamic transition theory and geometric theory of incompressible flows developed recently by the authors. In particular, it is shown that as the Taylor number crosses the critical number, the system undergoes either a continuous or a jump dynamic transition, dictated by the sign of a computable, nondimensional parameter R. In addition, it is also shown that the new transition states have the Taylor vortex type of flow structure, which is structurally stable.