Dynamical Phase Diagram Research Articles

Metamagnetic anomalies in the kinetic Blume–Capel model with arbitrary spin

Using the effective-field theory, we have investigated the dynamic behavior of a kinetic spin-S Blume Capel model which is an extension of the conventional kinetic Ising model with S≥1. For integer and half-integer spins, we have evaluated the dynamic phase diagrams. By introducing a constant bias field hb, we have focused on the emergence of metamagnetic anomalies in dynamic susceptibility versus bias field curves which arise for a narrow range of the bias field. For long periods, a close examination of susceptibility versus bias field data leads to a linear variation in 1/(h0−|hbpeak|)−logP curves where P is the field period. This result confirms that |hbpeak| asymptotically approaches the oscillating field amplitude h0 as 1/logP in the slow critical dynamics regime. Our calculations indicate that recent findings regarding the DPT in kinetic Ising model also extents to the kinetic Blume–Capel model with arbitrary spin.

Dissipative time crystal in an atom-cavity system: Influence of trap and competing interactions

While the recently realized dissipative time crystal in a laser-pumped atom-cavity system in the experiment of Ke{\ss}ler et al. [Phys. Rev. Lett. 127, 043602 (2021)] is qualitatively consistent with a theoretical description in an idealized limit, here, we investigate the stability of this dissipative time crystal in the presence of an inhomogeneous potential provided by a harmonic trap, and competing short- and infinite-range interactions. We note that these features are ubiquitous in any realization of atom-cavity systems. By mapping out the dynamical phase diagram and studying how it is modified by the harmonic trap and short-range interactions, we demonstrate the persistence of long-lived dissipative time crystals beyond the idealized limit. We show the emergence of metastable dissipative time crystals with and without prethermalization plateaus for tight harmonic confinement and strong contact interaction, respectively.

Engineering an effective three-spin Hamiltonian in trapped-ion systems for applications in quantum simulation

Trapped-ion quantum simulators, in analog and digital modes, are considered a primary candidate to achieve quantum advantage in quantum simulation and quantum computation. The underlying controlled ion–laser interactions induce all-to-all two-spin interactions via the collective modes of motion through Cirac–Zoller or Mølmer–Sørensen schemes, leading to effective two-spin Hamiltonians, as well as two-qubit entangling gates. In this work, the Mølmer–Sørensen scheme is extended to induce three-spin interactions via tailored first- and second-order spin–motion couplings. The scheme enables engineering single-, two-, and three-spin interactions, and can be tuned via an enhanced protocol to simulate purely three-spin dynamics. Analytical results for the effective evolution are presented, along with detailed numerical simulations of the full dynamics to support the accuracy and feasibility of the proposed scheme for near-term applications. With a focus on quantum simulation, the advantage of a direct analog implementation of three-spin dynamics is demonstrated via the example of matter-gauge interactions in the U(1) lattice gauge theory within the quantum link model. The mapping of degrees of freedom and strategies for scaling the three-spin scheme to larger systems, are detailed, along with a discussion of the expected outcome of the simulation of the quantum link model given realistic fidelities in the upcoming experiments. The applications of the three-spin scheme go beyond the lattice gauge theory example studied here and include studies of static and dynamical phase diagrams of strongly interacting condensed-matter systems modeled by two- and three-spin Hamiltonians.

On the dynamically arrested states of equilibrium and non-equilibrium gels: a comprehensive Brownian dynamics study

In this work a systematic study over a wide number of final thermodynamic states for two gel-forming liquids was performed. Such two kind of gel formers are distinguished by their specific interparticle interaction potential. We explored several thermodynamic states determining the thermodynamic, structural and dynamic properties of both liquids after a sudden temperature change. The thermodynamic analysis allows to identify that the liquid with short range attraction and long range repulsion lacks of a stable gas–liquid phase separation liquid, in contrast with the liquid with short range attractions. Thus, although for some thermodynamic states the structural behavior, measured by the static structure factor, is similar to and characteristic of the gel phase, for the short range attractive fluid the gel phase is a consequence of a spinodal decomposition process. In contrast, gelation in the short range attraction and long range repulsion liquid is not due to a phase separation. We also analyze the similarities and differences of the dynamic behavior of both systems through the analysis of the mean square displacement, the self part of the intermediate scattering function, the diffusion coefficient and the α relaxation time. Finally, using one of the main results of the non-equilibrium self-consistent generalized Langevin equation theory (NE-SCGLE), we determine the dynamic arrest phase diagram in the volume fraction and temperature (φ vs T) plane.

Finite Time Large Deviations via Matrix Product States.

Recent work has shown the effectiveness of tensor network methods for computing large deviation functions in constrained stochastic models in the infinite time limit. Here we show that these methods can also be used to study the statistics of dynamical observables at arbitrary finite time. This is a harder problem because, in contrast to the infinite time case, where only the extremal eigenstate of a tilted Markov generator is relevant, for finite time the whole spectrum plays a role. We show that finite time dynamical partition sums can be computed efficiently and accurately in one dimension using matrix product states and describe how to use such results to generate rare event trajectories on demand. We apply our methods to the Fredrickson-Andersen and East kinetically constrained models and to the symmetric simple exclusion process, unveiling dynamical phase diagrams in terms of counting field and trajectory time. We also discuss extensions of this method to higher dimensions.

Engineering infinite-range SU(n) interactions with spin-orbit-coupled fermions in an optical lattice

We study multilevel fermions in an optical lattice described by the Hubbard model with on-site $\mathrm{SU}(n)$-symmetric interactions. We show that in an appropriate parameter regime this system can be mapped onto a spin model with all-to-all $\mathrm{SU}(n)$-symmetric couplings. Raman pulses that address internal spin states modify the atomic dispersion relation and induce spin-orbit coupling, which can act as a synthetic inhomogeneous magnetic field that competes with the $\mathrm{SU}(n)$ exchange interactions. We investigate the mean-field dynamical phase diagram of the resulting model as a function of $n$ and different initial configurations that are accessible with Raman pulses. Consistent with previous studies for $n=2$, we find that for some initial states the spin model exhibits two distinct dynamical phases that obey simple scaling relations with $n$. Moreover, for $n>2$ we find that dynamical behavior can be highly sensitive to initial intraspin coherences. Our predictions are readily testable in current experiments with ultracold alkaline-earth-metal(-like) atoms.

Dynamic multicritical phase diagrams of the mixed spin (2, 5/2) Blume-Emery-Griffiths model with repulsive biquadratic coupling

We investigated the dynamic phase transitions (DPTs) in the mixed spin (2, 5/2) Blume-Emery Griffiths model with repulsive biquadratic interaction in the presence of a time-varying magnetic field. We used the path probability method to obtain the set of the dynamic equations. We numerically solved these dynamic equations to characterize the nature of first- and second-order phase transitions and to find the DPT temperatures as well as obtain the phases in the system. We constructed the dynamic phase diagrams (DPDs) in reduced temperature and amplitude of oscillating magnetic field plane. We observed that the DPDs display richer, complex and more topological various type of phase diagrams. In particular, DPDs exhibit the disordered phase, antiquadrupolar or staggered phase, six different ferrimagnetic phases, three different nonmagnetic phases, and numerous mixed phases. DPDs also display two dynamic tricritical points for only smaller values of crystal-field interactions, multiple critical end and double critical end points, one zero-temperature critical point, one inverse critical end point, and a quadruple point depending on interaction parameters. The system always shows the reentrant behaviors for the higher values of magnetic field amplitude, but it does not exhibit the dynamic tricritical behavior for higher values of crystal-field parameter.

Localization and spin dynamics of spin-orbit-coupled Bose-Einstein condensates in deep optical lattices.

We analytically and numerically discuss the dynamics of two pseudospin components Bose-Einstein condensates (BECs) with spin-orbit coupling (SOC) in deep optical lattices. Rich localized phenomena, such as breathers, solitons, self-trapping, and diffusion, are revealed and strongly depend on the strength of the atomic interaction, SOC, Raman detuning, and the spin polarization (i.e., the initial population difference of atoms between the two pseudospin components of BECs). The critical conditions for the transition of localized states are derived analytically. Based on the critical conditions, the detailed dynamical phase diagram describing the different dynamical regimes is derived. When the Raman detuning satisfies a critical condition, localized states with a fixed initial spin polarization can be observed. When the critical condition is not satisfied, we use two quenching methods, i.e., suddenly and linearly quenching Raman detuning from the soliton or breather state, to discuss the spin dynamics, phase transition, and wave packet dynamics by numerical simulation. The sudden quenching results in a damped oscillation of spin polarization and transforms the system to a new polarized state. Interestingly, the linear quenching of Raman detuning induces a controllable phase transition from an unpolarized phase to an expected polarized phase, while the soliton or breather dynamics is maintained.

Topological and geometric patterns in optimal bang-bang protocols for variational quantum algorithms: Application to the XXZ model on the square lattice

In this work, we address the challenge of uncovering patterns in variational optimal protocols for taking the system to ground states of many-body Hamiltonians, using variational quantum algorithms. We develop highly optimized classical Monte Carlo (MC) algorithms to find the optimal protocols for transformations between the ground states of the square-lattice XXZ model for finite systems sizes. The MC method obtains optimal bang-bang protocols, as predicted by Pontryagin's minimum principle. We identify the minimum time needed for reaching an acceptable error for different system sizes as a function of the initial and target states and uncover correlations between the total time and the wave-function overlap. We determine a dynamical phase diagram for the optimal protocols, with different phases characterized by a topological number, namely the number of on-pulses. Bifurcation transitions as a function of initial and final states, associated with new jumps in the optimal protocols, demarcate these different phases. The number of pulses correlates with the total evolution time. In addition to identifying the topological characteristic above, i.e., the number of pulses, we introduce a correlation function to characterize bang-bang protocols' quantitative geometric similarities. We find that protocols within one phase are indeed geometrically correlated. Identifying and extrapolating patterns in these protocols may inform efficient large-scale simulations on quantum devices.

Active matter shepherding and clustering in inhomogeneous environments.

We consider a mixture of active and passive run-and-tumble disks in an inhomogeneous environment where only half of the sample contains quenched disorder or pinning. The disks are initialized in a fully mixed state of uniform density. We identify several distinct dynamical phases as a function of motor force and pinning density. At high pinning densities and high motor forces, there is a two-step process initiated by a rapid accumulation of both active and passive disks in the pinned region, which produces a large density gradient in the system. This is followed by a slower species phase separation process where the inactive disks are shepherded by the active disks into the pin-free region, forming a nonclustered fluid and producing a more uniform density with species phase separation. For higher pinning densities and low motor forces, the dynamics becomes very slow and the system maintains a strong density gradient. For weaker pinning and large motor forces, a floating clustered state appears, and the time-averaged density of the system is uniform. We illustrate the appearance of these phases in a dynamic phase diagram.

General existence and determination of conjugate fields in dynamically ordered magnetic systems.

We investigate experimentally as well as theoretically the dynamic magnetic phase diagram and its associated order parameter Q upon the application of a non-antisymmetric magnetic field sequence composed of a fundamental harmonic component H_{0}, a constant bias field H_{b}, and a second-harmonic component H_{2}. The broken time antisymmetry introduced by the second-harmonic field component H_{2} leads to an effective bias effect that is superimposed onto the influence of the static bias H_{b}. Despite this interference, we can demonstrate the existence of a generalized conjugate field H^{*} for the dynamic order parameter Q, to which both the static bias field and the second-harmonic Fourier amplitude of the field sequence contribute. Hereby, we observed that especially the conventional paramagnetic dynamic phase is very susceptible to the impact of the second-harmonic field component H_{2}, whereas this additional field component leads to only very minor phase-space modifications in the ferromagnetic and anomalous paramagnetic regions. In contrast to prior studies, we also observe that the critical point of the phase transition is shifted upon introducing a second-harmonic field component H_{2}, illustrating that the overall dynamic behavior of such magnetic systems is being driven by the total effective amplitude of the field sequence.

Propagation of phase-imprinted solitons from superfluid core to Mott-insulator shell and superfluid shell

We study phase-imprinted solitons of ultracold bosons in an optical lattice with a harmonic trap, which shows the superfluid (SF) and Mott-insulator (MI) shell structures. The earlier study [Konstantin V. Krutitsky, J. Larson, and M. Lewenstein, Phys. Rev. A 82, 033618 (2010).] reported three types of phase-imprinted solitons in the Bose-Hubbard model: in-phase soliton, out-of-phase soliton, and wavelet. In this paper, we uncover the dynamical phase diagram of these phase-imprinted solitons, and find another type of the phase-imprinted soliton namely, the hybrid soliton. In the harmonically trapped system, the solitonic excitations created at the SF core cannot penetrate into the outer SF shell. This repulsion at the surface of the outer SF shell can be cured by inposing a repulsive potential at the center of the trap. These results can be interpreted as a kind of the impedance matching of excitations in BECs in terms of the effective chemical potentials or the local particle numbers in the shell, and the analogous results can be observed also in the sound wave created by the local single-shot pulse potential.

Dynamical phase transitions in quantum spin models with antiferromagnetic long-range interactions

In recent years, dynamical phase transitions and out-of-equilibrium criticality have been at the forefront of ultracold gases and condensed matter research. Whereas universality and scaling are established topics in equilibrium quantum many-body physics, out-of-equilibrium extensions of such concepts still leave much to be desired. Using exact diagonalization and the time-dependent variational principle in uniform martrix product states, we calculate the time evolution of the local order parameter and Loschmidt return rate in transverse-field Ising chains with antiferromagnetic power law-decaying interactions, and map out the corresponding rich dynamical phase diagram. \textit{Anomalous} cusps in the return rate, which are ubiquitous at small quenches within the ordered phase in the case of ferromagnetic long-range interactions, are absent within the accessible timescales of our simulations in the antiferromagnetic case, showing that long-range interactions are not a sufficient condition for their appearance. We attribute this to much weaker domain-wall binding in the antiferromagnetic case. For quenches across the quantum critical point, \textit{regular} cusps appear in the return rate and connect to the local order parameter changing sign, indicating the concurrence of two major concepts of dynamical phase transitions. Our results consolidate conclusions of previous works that a necessary condition for the appearance of anomalous cusps in the return rate after quenches within the ordered phase is for topologically trivial local spin flips to be the energetically dominant excitations in the spectrum of the quench Hamiltonian. Our findings are readily accessible in modern trapped-ion setups, and we outline the associated experimental considerations.

Dynamics and nonmonotonic drag for individually driven skyrmions

We examine the motion of an individual skyrmion driven through an assembly of other skyrmions in the absence of quenched disorder. The skyrmion behavior is determined by the ratio of the damping and Magnus terms, known as the intrinsic skyrmion Hall angle. For fixed drive in the damping dominated regime, the effective viscosity decreases monotonically with increasing skyrmion density. In contrast, in the Magnus dominated regime, the velocity varies nonmonotonically with density, and there is a regime in which the skyrmion moves faster with increasing density, as well as a pronounced speed-up effect in which a skyrmion traveling through a dense medium moves more rapidly than for low densities or the single-particle limit. The velocity-force curves in the Magnus-dominated regime exhibit an overshoot effect and other differences from the damping-dominated regime. We find a finite threshold force for skyrmion motion which increases with density as well as a drive-dependent skyrmion Hall angle. We map dynamic phase diagrams showing the threshold for motion, nonlinear flow, speed-up, and saturation regimes. In some cases, increasing the density can reduce the skyrmion Hall angle while producing a velocity boost, which could be valuable for applications.

Dynamical phase diagram of a one-dimensional Bose gas in a box with a tunable weak link: From Bose-Josephson oscillations to shock waves

We study the dynamics of one-dimensional bosons trapped in a box potential, in the presence of a barrier creating a tunable weak-link, thus realizing a one dimensional Bose Josephson junction. By varying the initial population imbalance and the barrier height we evidence different dynamical regimes. In particular we show that at large barriers a two mode model captures accurately the dynamics, while for low barriers the dynamics involves dispersive shock waves and solitons. We study a quench protocol that can be readily implemented in experiments and show that self-trapping resonances can occur. This phenomenon can be understood qualitatively within the two-mode model.

Nonequilibrium magnetic properties of the Sr2FeMoO6 type double perovskite structure

The Glauber-type stochastic dynamic interpreted by the mean-field theory has been applied to investigate the dynamic magnetic properties of the Sr2FeMoO6 type double perovskite structure under the time varying magnetic field. First, we used the Glauber dynamics to obtain the dynamic mean-field equations. The time varying average Fe and Mo magnetizations are examined to find the phase region of the system. The dynamic Fe and Mo magnetizations, hysteresis loop areas and correlations are calculated depending on the temperature in order to determine the nature of the first and second order phase transitions, as well as to get the dynamic transition points for different ratio of the system parameters. The dynamic phase diagrams (DPDs) are constructed in the plane of reduced temperature and external magnetic field amplitude (T, h). The DPDs contain paramagnetic (p), ferromagnetic (f), ferrimagnetic-1 (i1), ferrimagnetic-2 (i2) phases and six mixed regions, (f + p), (f + i1), (f + i2), (i1 + p), (i2 + p) and (i1 + i2). The DPDs also exhibit dynamic tricritical points and reentrant phenomena, which strongly depend on interaction parameters.

Characterizing the dynamical phase diagram of the Dicke model via classical and quantum probes

We theoretically study the dynamical phase diagram of the Dicke model in both classical and quantum limits using large, experimentally relevant system sizes. Our analysis elucidates that the model features dynamical critical points that are distinct from previously investigated excited-state equilibrium transitions. Moreover, our numerical calculations demonstrate that mean-field features of the dynamics remain valid in the exact quantum dynamics, but we also find that in regimes where quantum effects dominate signatures of the dynamical phases and chaos can persist in purely quantum metrics such as entanglement and correlations. Our predictions can be verified in current quantum simulators of the Dicke model including arrays of trapped ions.

A Numerical Investigation of the Effect of External Resistance and Applied Potential on the Distribution of Periodicity and Chaos in the Anodic Dissolution of Nickel

In the latest years, the world has witnessed intense research on the synthesis of nanostructured materials. One of the most interesting methodologies recently proposed to this end is the use self-organized electrochemical reactions, on which the structuring emerges spontaneously from the reaction, permanently engraved on the electrodes. To achieve a robust process for a rational synthesis utilizing this technique, however, one must have a detailed description of the reaction’s dynamical properties, as they are closely related to the nanometric patterns formed [ChemElectroChem, 2020, 7, 2979].One of such self-organized electrochemical reactions is the anodic dissolution of nickel. This reaction has the added benefit of being successfully modelled computationally in the literature, contributing to the dynamical studies on the system [J. Phys. Chem., 1992, 96, 2676]. This work presents a numerical exploration of the system’s dynamics, and its relation to the applied voltage and external resistance, two parameters that can be readily accessed on the experimental counterpart. Dynamical phase diagrams were built by varying these parameters (used in their dimensionless form), using the morphological period and Lyapunov exponents of the time-series to characterize its dynamical behavior.Magnifications of the diagrams’ chaotic regions revealed the presence of self-similar periodic islands (often referred as shrimps) on them, a feature commonly found on chaotic electrochemical dynamics. Period-doubling, a frequent route to chaos, was found on these shrimps, and a period-adding sequence was successfully identified on a shrimp dispersion, even though the shrimp density on the diagrams were low, when compared to other chaotic electrochemical systems.The shrimps were deformed as both control parameters were increased, being stretched diagonally when the system moved from potentiostatic to galvanostatic condition. For large values of external resistance and potential applied, this stretching was so extreme that the shrimps gave place to parallel linear diagonal domains of periodicity intertwined by chaotic regions. Period-doubling cascades were also found in these domains, suggesting that some dynamical properties from the shrimps were preserved after the stretching. The hypothesis that the stretching is closely related to the exponential terms on the Butler-Volmer equations that makes up the kinetic model was raised. Figure 1

Cavity-QED Quantum Simulator of Dynamical Phases of a Bardeen-Cooper-Schrieffer Superconductor.

We propose to simulate dynamical phases of a BCS superconductor using an ensemble of cold atoms trapped in an optical cavity. Effective Cooper pairs are encoded via the internal states of the atoms, and attractive interactions are realized via the exchange of virtual photons between atoms coupled to a common cavity mode. Control of the interaction strength combined with a tunable dispersion relation of the effective Cooper pairs allows exploration of the full dynamical phase diagram of the BCS model as a function of system parameters and the prepared initial state. Our proposal paves the way for the study of the nonequilibrium features of quantum magnetism and superconductivity by harnessing atom-light interactions in cold atomic gases.

Long-time relaxation dynamics of a spin coupled to a Chern insulator

The authors compute the dynamical phase diagram for the relaxation of a classical spin, exchange coupled to the local magnetic moment at an edge site of the one-dimensional spinful Su-Schrieffer-Heeger model. The role of the topological edge state and its internal Zeeman splitting for the spin-relaxation process, as well as incomplete spin relaxation on long time scales, can be explained within the framework of a renormalized linear response approach, when explicitly taking retardation effects and nonequilibrium spin-exchange processes into account.