Order Parameter Research Articles

Microscopic pathways of transition from low-density to high-density amorphous phase of water.

In recent years, much attention has been devoted to understanding the pathways of phase transition between two equilibrium condensed phases (such as liquids and solids). However, the microscopic pathways of transition involving non-equilibrium, non-diffusive amorphous (glassy) phases still remain poorly understood. In this work, we have employed computer simulations, persistence homology (a tool rooted in topological data analysis), and machine learning to probe the microscopic pathway of pressure-induced non-equilibrium transition between the low- and high-density amorphous (LDA and HDA, respectively) ice phases of the TIP4P/2005 and ST2 water models. Using persistence homology and machine learning, we introduced a new order parameter that unambiguously identifies the LDA- and HDA-like local environments. The LDA phase transitions continuously and collectively into the corresponding HDA phase via a pre-ordered intermediate phase during the isothermal compression. The local order parameter susceptibilities show a maximum near the transition pressure (P*)-suggesting maximum structural heterogeneities near P*. The HDA-like clusters are structurally ramified and spatially delocalized inside the LDA phase near the transition pressure. We also found manifestations of the first-order low-density to high-density liquid transition in the sharpness of the order parameter change during the LDA to HDA transition. We further investigated the (geometrical) structures and topologies of the LDA and HDA ices formed via different protocols and also studied the dependence of the (microscopic) pathway of phase transition on the protocol followed to prepare the initial LDA phase. Finally, the method adopted here to study the phase transition pathways is not restricted to the system under consideration and provides a robust way of probing phase transition pathways involving any two condensed phases at both equilibrium and out-of-equilibrium conditions.

AMPLITUDE EQUATIONS AND ORDER PARAMETERS OF HUMAN SARS-COV-2 INFECTIONS AND IMMUNE REACTIONS: A MODEL-BASED APPROACH

Several recent modeling studies have attempted to understand the human immune reaction to SARS-CoV-2 infections. Such a model-based understanding provides a sound basis for fighting COVID-19 on the level of individual patients. However, in this context, a worked-out nonlinear physics analysis providing insights into underlying amplitude equations and potential COVID-19 order parameters has not been conducted so far. In order to conduct such an analysis, a three-variable virus dynamics model is considered that can account for the human immune reaction to SARS-CoV-2 infections. The model amplitudes equations are derived and the relevant order parameter is determined. In line with theoretical reasoning, it is demonstrated that the order parameter and its amplitude determine the initial stage of SARS-CoV-2 infections, in general, and the initial dynamics of immune reactions, in particular. Explicitly, this finding is demonstrated for data from four COVID-19 patients. For those patients it is also demonstrated that the remnant of the order parameter determines the final disease decline phase. In this context, a time-resolved eigenvalue analysis is conducted that reveals that the transition from the initial stage to the decline stage which is associated with a switch of the leading eigenvalue from a positive to a negative value. It is argued that the immune reaction essentially contributes to this switch. From a medical-physics point of view, this observation suggests that the immune reaction of COVID-19 patients can stabilize the virus-free fixed point of affected sites.

Overlap renormalization group transformations for disordered systems

Abstract We establish a renormalization group approach which is implemented on the degrees of freedom defined by the overlap of two replicas to determine the critical fixed point and to extract four critical exponents for the phase transition of the three-dimensional Edwards-Anderson model. In addition, we couple the overlap order parameter to a fictitious field and introduce it within the two-replica Hamiltonian of the system to study its explicit symmetry-breaking with the renormalization group. Overlap transformations do not require a renormalization of the random couplings of a system to extract the critical exponents associated with the relevant variables of the renormalization group. We conclude by discussing the applicability of such transformations in the study of any phase transition which is fully characterized by an overlap order parameter.

Is the effective potential effective for dynamics?

We critically examine the applicability of the effective potential within dynamical situations and find, in short, that the answer is negative. An important caveat of the use of an effective potential in dynamical equations of motion is an explicit violation of energy conservation. An effective potential is introduced in a consistent quasistatic approximation, and its narrow regime of validity is discussed. Two ubiquitous instances in which even the adiabatic effective potential is not valid in dynamics are studied in detail: parametric amplification in the case of oscillating mean fields, and spinodal instabilities associated with spontaneous symmetry breaking. In both cases profuse particle production is directly linked to the failure of the effective potential to describe the dynamics. We introduce a consistent, renormalized, energy conserving dynamical framework that is amenable to numerical implementation. Energy conservation leads to the emergence of asymptotic highly excited, entangled stationary states from the dynamical evolution. As a corollary, decoherence via dephasing of the density matrix in the adiabatic basis is argued to lead to an emergent entropy, formally equivalent to the entanglement entropy. The results suggest novel characterization of asymptotic equilibrium states in terms of order parameter vs energy density. Published by the American Physical Society 2024

Multiple coherent amplitude modes and exciton-phonon coupling in quasi-one-dimensional excitonic insulator Ta2NiSe5.

An excitonic insulator (EI) is an intriguing correlated electronic phase of condensed excitons. Ta2NiSe5 is a model material for investigating condensed excitonic states. Herein, femtosecond pump-probe spectroscopy is used to study the coherent phonon dynamics and associated exciton-phonon coupling in single-crystal Ta2NiSe5. The reflectivity time series consists of exponential decay due to hot carriers and damped oscillations due to the Ag phonon vibration. Given the in-plane anisotropic thermal conductivity of Ta2NiSe5, coherent phonon oscillations are stronger with perpendicular polarization to its quasi-one-dimensional chains. The 1-, 2-, and 4-THz vibration modes show coherent amplitude responses in the EI phase of Ta2NiSe5 with increasing temperature, totally different from those of normal coherent phonons (the 3- and 3.7-THz modes). The amplitude modes at higher frequencies decouple with the EI order parameter at lower temperatures, as supported by theoretical analysis with a model Hamiltonian of the exciton-phonon coupling system. Our work provides valuable insights into the character of the EI order parameter and its coupling to multiple coherent amplitude modes.

Coupling of the Structure and Magnetism to Spin Splitting in Hybrid Organic-Inorganic Perovskites.

Hybrid organic-inorganic perovskites are famous for the diversity of their chemical compositions, phases, phase transitions, and associated physical properties. We use a combination of experimental and computational techniques to reveal a strong coupling between structure, magnetism, and spin splitting in a representative of the largest family of hybrid organic-inorganic perovskites: the formates. With the help of first-principles simulations, we find spin splitting in both conduction and valence bands of [NH2NH3]Co(HCOO)3 induced by spin-orbit interactions, which can reach up to 14 meV. Our magnetic measurements reveal that this material exhibits canted antiferromagnetism below 15.5 K. The direction of the associated antiferromagnetic order parameter is strongly coupled with spin splitting in the centrosymmetric phase, allowing for the creation and annihilation of spin splitting through the application of a magnetic field. Furthermore, the structural phase transition to the experimentally observed polar Pna21 phase completely changes the aforementioned spin splitting and its coupling to magnetic degrees of freedom. This reveals that in [NH2NH3]Co(HCOO)3, the structure and magnetism are strongly coupled to spin splitting and can be manipulated through electric and magnetic fields. We believe that our findings offer an important step toward a fundamental understanding and practical applications of materials with coupled properties.

Analysis of the recording of Fibonacci lenses on photopolymers with 3-D diffusion model

In this work a three-dimensional diffusion model is used to model photopolymers as a recording media. This model allows us to predict the properties of the Diffractive Optical Elements (DOEs) once we recorded into the photopolymer. This model had never been tested with more complex elements, such as multifocal diffractive lenses, as presented in the following in this work. In addition, the model includes; the estimation of the refractive index modulation, the low-pass filtering effect due to the experimental optical setup, and the evolution of the transverse intensity distribution. In this way, the selection of the appropriate material characteristics depending on the intended DOE application is made possible. Specifically, an acrylamide-based PVA/AA photopolymer is simulated using the proposed model. Moreover, coverplating and index matching systems are considered together to avoid the effects of thickness variation. Furthermore, in order to compare their properties using the proposed model, we focus on Fibonacci lenses (FL), a type of bifocal lenses. This allows us to evaluate the dependence of the focii intensity on the polymerisation rate, the diffusivity parameter, low-pass filtering effect and the use of the index matching system for these lenses. This enables us to know the recording parameters in order to produce this type of multifocal diffractive lenses with higher quality and precision.

Deconfinement, center symmetry and the ghost propagator in Landau gauge pure SU(3) Yang-Mills theory

The temperature dependence of the Landau gauge ghost propagator is investigated in pure SU(3) Yang-Mills theory with lattice QCD simulations. Its behavior around the confined-deconfined phase transition temperature, Tc ∼ 270 MeV, is investigated. The simulations show that in the deconfined phase, the ghost propagator is enhanced for small momenta, ≲ 1 GeV. Furthermore, the analysis of the spontaneous breaking of center symmetry on the ghost propagator is studied. Similarly as observed for the gluon propagator, the simulations result in a decoupling of the sectors where the phase of the Polyakov loop is either 0 or ±2π/3 sectors, with the latter remaining indistinguishable. The results point to the possible use of the ghost propagator as an “order parameter” for the confined-deconfined phase transition.

Coexistence of topological semimetal states in holography

We introduce a holographic model that exhibits a coexistence state of the Weyl semimetal and the topological nodal line state, providing us with a valuable tool to investigate the system’s behavior in the strong coupling regime. Nine types of bulk solutions exhibiting different IR behaviors have been identified, corresponding to nine different types of boundary states. These nine states include four distinct phases, namely the Weyl-nodal phase, the gap-nodal phase, the Weyl gap phase and the gap-gap phase, four phase boundaries, which are the Weyl-Dirac phase, the gap-Dirac phase, the Dirac-gap phase and the Dirac-nodal phase, and finally a double critical point. A phase diagram is plotted that exhibits qualitative similarity to the one obtained in the weak coupling limit. The anomalous Hall conductivity, which serves as an order parameter, and the free energy are calculated, with the latter showing the continuity of the topological phase transitions within the system. Our study highlights the similarities and differences in such a topological system between the weak and strong coupling regimes, paving the way for further experimental observations.

Spin-orbit torque manipulation of sub-terahertz magnons in antiferromagnetic α-Fe2O3

The ability to electrically manipulate antiferromagnetic magnons, essential for extending the operating speed of spintronic devices into the terahertz regime, remains a major challenge. This is because antiferromagnetic magnetism is challenging to perturb using traditional methods such as magnetic fields. Recent developments in spin-orbit torques have opened a possibility of accessing antiferromagnetic magnetic order parameters and controlling terahertz magnons, which has not been experimentally realised yet. Here, we demonstrate the electrical manipulation of sub-terahertz magnons in the α-Fe2O3/Pt antiferromagnetic heterostructure. By applying the spin-orbit torques in the heterostructure, we can modify the magnon dispersion and decrease the magnon frequency in α-Fe2O3, as detected by time-resolved magneto-optical techniques. We have found that optimal tuning occurs when the Néel vector is perpendicular to the injected spin polarisation. Our results represent a significant step towards the development of electrically tunable terahertz spintronic devices.

Work statistics for quantum spin chains: Characterizing quantum phase transitions, benchmarking time evolution, and examining passivity of quantum states

We study three aspects of work statistics in the context of the fluctuation theorem for quantum spin chains up to 1024 sites by numerical methods based on matrix-product states (MPSs). First, we use our numerical method to evaluate the moments/cumulants of work done by the sudden quench process on the Ising or Haldane spin chains, and we study their behaviors across the quantum phase transitions. Our results show that, up to the fourth cumulant, the work statistics can indicate the quantum phase transition characterized by the local order parameters but barely for purely topological phase transitions. Second, we propose to use the fluctuation theorem, such as Jarzynski's equality, which relates the real-time correlator to the ratio of the thermal partition functions, as a benchmark indicator for the numerical real-time evolving methods. Third, we study the passivity of ground and thermal states of quantum spin chains under some cyclic impulse processes. We show that the passivity of thermal states and ground states under the Hermitian actions is ensured by the second laws and variational principles, respectively, and we also verify this by numerical calculations. In addition, we also consider the passivity of ground states under non-Hermitian actions, for which the variational principle cannot be applied. Despite that, we find no violation of passivity from our numerical results for all the cases considered in the Ising and Haldane chains. Overall, we demonstrate that the work statistics for the sudden quench and impulse processes can be evaluated precisely by the numerical MPS method to characterize quantum phase transitions and examine the passivity of quantum states. We also propose to exploit the universality of the fluctuation theorem to benchmark the numerical real-time evolutions in an algorithmic and model-independent way. Published by the American Physical Society 2024

Thermal evolution of spin excitations in honeycomb Ising antiferromagnetic FePSe3

We use elastic and inelastic neutron scattering (INS) to study the antiferromagnetic (AF) phase transitions and spin excitations in the two-dimensional (2D) zig-zag antiferromagnet FePSe3. By determining the magnetic order parameter across the AF phase transition, we conclude that the AF phase transition in FePSe3 is first-order in nature. In addition, our INS measurements reveal that the spin waves in the AF ordered state have a large easy-axis magnetic anisotropy gap, consistent with an Ising Hamiltonian, and possible biquadratic magnetic exchange interactions. On warming across TN, we find that dispersive spin excitations associated with three-fold rotational symmetric AF fluctuations change into FM spin fluctuations above TN. These results suggest that the first-order AF phase transition in FePSe3 may arise from the competition between C3 symmetric AF and C1 symmetric FM spin fluctuations around TN, in place of a conventional second-order AF phase transition.

Dome structure in pressure dependence of superconducting transition temperature for HgBa2Ca2Cu3O8 : Studies by ab initio low-energy effective Hamiltonian

The superconducting (SC) cuprate HgBa2Ca2Cu3O8 (Hg1223) has the highest SC transition temperature Tc among cuprates at ambient pressure Pamb, namely, Tcopt≃138 K experimentally at the optimal hole doping concentration. Tcopt further increases under pressure P and reaches 164 K at optimal pressure Popt≃30 GPa, then Tcopt decreases with increasing P>Popt generating a dome structure [Gao , ]. This nontrivial and nonmonotonic P dependence of Tcopt calls for a theoretical understanding and mechanism. To answer this open question, we consider the low-energy effective Hamiltonian (LEH) for the antibonding (AB) Cu3dx2−y2/O2pσ band derived generally for the cuprates. In the AB LEH for cuprates with Nℓ≤2 laminated CuO2 planes between block layers, it was proposed that Tcopt is determined by a universal scaling Tcopt≃0.16|t1|FSC [Schmid , ], where t1 is the nearest-neighbor hopping, and the SC order parameter at optimal hole doping FSC mainly depends on the ratio u=U/|t1| where U is the onsite effective Coulomb repulsion: The u dependence of FSC has a peak at uopt≃8.5 and a steep decrease with decreasing u in the region u<uopt irrespective of materials dependent on other parameters. In this paper, we show that |t1| increases with P, whereas u decreases with P in the Hamiltonian of Hg1223. Based on these facts, we show that the domelike P dependence of Tcopt can emerge at least qualitatively if we assume Hg1223 with Nℓ=3 follows the same universal scaling for Tcopt, and Hg1223 is located at the slightly strong coupling region u≳uopt at Pamb and u≃uopt at Popt by taking account of expected corrections to our calculation. The consequence of these assumptions is the following: With increasing P within the range P<Popt, the increase in Tcopt is accounted for by the increase in |t1|, whereas FSC is insensitive to the decrease in u around ≃uopt and hence to P as well. At P>Popt, the decrease in Tcopt is accounted for by the decrease in u below uopt, which causes a rapid decrease in FSC dominating over the increase in |t1|. We further argue the appropriateness of these assumptions based on the insight from studies on other cuprate compounds in the literature. In addition, we discuss the dependencies of u and |t1| on each crystal parameter (CP), which provides hints for design of even higher Tcopt materials. Published by the American Physical Society 2024

Fast collective motions of backbone in transmembrane α helices are critical to water transfer of aquaporin.

Fast collective motions are widely present in biomolecules, but their functional relevance remains unclear. Herein, we reveal that fast collective motions of backbone are critical to the water transfer of aquaporin Z (AqpZ) by using solid-state nuclear magnetic resonance (ssNMR) spectroscopy and molecular dynamics (MD) simulations. A total of 212 residue site-specific dipolar order parameters and 158 15N spin relaxation rates of the backbone are measured by combining the 13C- and 1H-detected multidimensional ssNMR spectra. Analysis of these experimental data by theoretic models suggests that the small-amplitude (~10°) collective motions of the transmembrane α helices on the nanosecond-to-microsecond timescales are dominant for the dynamics of AqpZ. The MD simulations demonstrate that these collective motions are critical to the water transfer efficiency of AqpZ by facilitating the opening of the channel and accelerating the water-residue hydrogen bonds renewing in the selectivity filter region.

Perspective: Probing elasto-quantum materials with X-ray techniques and in situ anisotropic strain.

Anisotropic lattice deformation plays an important role in the quantum mechanics of solid state physics. The possibility of mediating the competition and cooperation among different order parameters by applying in situ strain/stress on quantum materials has led to discoveries of a variety of elasto-quantum effects on emergent phenomena. It has become increasingly critical to have the capability of combining the in situ strain tuning with X-ray techniques, especially those based on synchrotrons, to probe the microscopic elasto-responses of the lattice, spin, charge, and orbital degrees of freedom. Herein, we briefly review the recent studies that embarked on utilizing elasto-X-ray characterizations on representative material systems and demonstrated the emerging opportunities enabled by this method. With that, we further discuss the promising prospect in this rising area of quantum materials research and the bright future of elasto-X-ray techniques.&#xD.

Non-extensive effects on the QCD equation of state and fluctuations of conserved charges within Polyakov quark meson model

The influence of non-extensive Tsallis statistics on the hadron phase structure has been investigated using the Polyakov-quark-meson (PQM) model. The analysis examines the non-extensive effects on the temperature dependence of PQM order parameters, thermodynamic quantities related to the quantum chromodynamics (QCD) equation of state, and fluctuations of conserved charges at varying chemical potentials. The results show that non-extensive effects have the most significant deviations near the crossover region. The pseudo-critical temperature T χ (μ B ) is not a universal constant and decreases with increasing non-extensive q parameter. The chiral phase diagram of the PQM model indicates a decrease in the behavior of the (T χ − μ B ) plane with increasing non-extensive q parameter. The PQM model exhibits good qualitative agreement with lattice QCD calculations. Moreover, these findings suggest the existence of a Tsallis limit, which serves as an alternative to the Stefan–Boltzmann limit for the massless ideal gas. The critical endpoint exhibits lower temperature but higher chemical potential with increasing non-extensive q parameter. Overall, this study highlights the importance of non-extensive Tsallis statistics in characterizing the quark-hadron phase structure of the PQM model and contributes to a deeper understanding of non-extensive effects in the quark-hadron phase transition.

Spacetime magnetic hopfions from internal excitations and braiding of skyrmions

Spatial topology endows topological solitons, such as skyrmions and hopfions, with fascinating dynamics. However, the temporal dimension has so far provided a passive stage on which topological solitons evolve. Here we construct spacetime magnetic hopfions: magnetic textures in two spatial dimensions that when excited by a time-periodic drive develop spacetime topology. We uncover two complementary construction routes using skyrmions by braiding their center of mass position and by controlling their internal low-energy excitations. Spacetime magnetic hopfions can be realized in nanopatterned grids to braid skyrmions and in frustrated magnets under an applied AC electric field. Their topological invariant, the spacetime Hopf index, can be tuned by the applied electric field as demonstrated by our collective coordinate modeling and micromagnetic simulations. The principles we have introduced to actively control spacetime topology are not limited to magnetic solitons, opening avenues to explore spacetime topology of general order parameters and fields.

Sketching phase diagrams using low-depth variational quantum algorithms

Abstract Mapping out phase diagrams of quantum systems using classical simulations can be challenging or intractable due to the computational resources required to simulate even small quantum systems far away from the thermodynamic limit. We investigate using quantum computers and the Variational Quantum Eigensolver (VQE) for this task. In contrast to the task of preparing the exact ground state using VQE, sketching phase diagrams might require less quantum resources and accuracy, because low fidelity approximations to the ground state may be enough to correctly identify different phases. We used classical numerical simulations of low-depth VQE circuits to compute order parameters for four well-studied spin and fermion models which represent a mix of 1D and 2D, and exactly-solvable and classically hard systems. We find that it is possible to predict the location of phase transitions up to reasonable accuracy using states produced by VQE even when their overlap with the true ground state is small. Further, we introduce a model-agnostic predictor of phase transitions based on the speed with which the VQE energy improves with respect to the circuit depth, and find that in some cases this is also able to predict phase transitions.

Evidence for a finite-momentum Cooper pair in tricolor d-wave superconducting superlattices

Fermionic superfluidity with a nontrivial Cooper-pairing, beyond the conventional Bardeen-Cooper-Schrieffer state, is a captivating field of study in quantum many-body systems. In particular, the search for superconducting states with finite-momentum pairs has long been a challenge, but establishing its existence has long suffered from the lack of an appropriate probe to reveal its momentum. Recently, it has been proposed that the nonreciprocal electron transport is the most powerful probe for the finite-momentum pairs, because it directly couples to the supercurrents. Here we reveal such a pairing state by the non-reciprocal transport on tricolor superlattices with strong spin-orbit coupling combined with broken inversion-symmetry consisting of atomically thin d-wave superconductor CeCoIn5. We find that while the second-harmonic resistance exhibits a distinct dip anomaly at the low-temperature (T)/high-magnetic field (H) corner in the HT-plane for H applied to the antinodal direction of the d-wave gap, such an anomaly is absent for H along the nodal direction. By carefully isolating extrinsic effects due to vortex dynamics, we reveal the presence of a non-reciprocal response originating from intrinsic superconducting properties characterized by finite-momentum pairs. We attribute the high-field state to the helical superconducting state, wherein the phase of the order parameter is spontaneously spatially modulated.

Gradient elasticity in Swift–Hohenberg and phase-field crystal models

The Swift–Hohenberg (SH) and phase-field crystal (PFC) models are minimal yet powerful approaches for studying phenomena such as pattern formation, collective order, and defects via smooth order parameters. They are based on a free-energy functional that inherently includes elasticity effects. This study addresses how gradient elasticity (GE), a theory that accounts for elasticity effects at microscopic scales by introducing additional characteristic lengths, is incorporated into SH and PFC models. After presenting the fundamentals of these theories and models, we first calculate the characteristic lengths for various lattice symmetries in an approximated setting. We then discuss numerical simulations of stress fields at dislocations and comparisons with analytic solutions within first and second strain-gradient elasticity. Effective GE characteristic lengths for the elastic fields induced by dislocations are found to depend on the free-energy parameters in the same manner as the phase correlation length, thus unveiling how they change with the quenching depth. The findings presented in this study enable a thorough discussion and analysis of small-scale elasticity effects in pattern formation and crystalline systems using SH and PFC models and, importantly, complete the elasticity analysis therein. Additionally, we provide a microscopic foundation for GE in the context of order-disorder phase transitions.