Critical Scaling Behavior Research Articles

Quantum phase transition of chiral Majorana fermions in the presence of disorder

We study the quantum phase transitions of a disordered two-dimensional quantum anomalous Hall insulator with $s$-wave superconducting proximity, which are governed by the percolation theory of chiral Majorana fermions. Based on symmetry arguments and a renormalization group analysis, we show there are generically two phase transitions from Bogoliubov-de Gennes Chern number $\mathcal{N}=0$ to $\mathcal{N}=1$ ($p+ip$ chiral topological superconductor) and then to $\mathcal{N}=2$, in agreement with the conclusion from the band theory without disorders. Further, we discuss the critical scaling behavior of the $e^2/2h$ conductance half plateau induced by $\mathcal{N}=1$ chiral topological superconductor recently observed in the experiment. In particular, we compare the critical behavior of the half plateau induced by topological superconductor with that predicted recently by alternative explanations of the half plateau, and show that they can be distinguished in experiments.

Thermodynamic and dynamical heterogeneities during glass transition of water

Understanding the glass transition of water is still a major scientific challenge. Here we propose a dynamic density functional renormalization group approach to analyze the liquid–liquid phase transitions and diffusion dynamics of water molecules under supercooling condition. We find that, as the temperature approaches the glass transition point, the metastable phase transition displays the confined critical scaling behavior, and the dynamic correlation length actually diverges simultaneously. The predicted glass temperature is 142.5K, close to the experimental value of 136K. These results suggest a deep coupling feature of the thermodynamic and dynamical heterogeneities during the glass transition of supercooled water.

Quantum criticality in the coupled two-leg spin ladder Ba2CuTeO6

We report on zero-field muon spin rotation, electron spin resonance and polarized Raman scattering measurements of the coupled quantum spin ladder Ba2CuTeO6. Zero-field muon spin rotation and electron spin resonance probes disclose a successive crossover from a paramagnetic through a spin-liquid-like into a magnetically ordered state with decreasing temperature. More significantly, the two-magnon Raman response obeys a T-linear scaling relation in its peak energy, linewidth and intensity. This critical scaling behavior presents an experimental signature of proximity to a quantum critical point from an ordered side in Ba2CuTeO6.

Critical behavior in the presence of an order-parameter pinning field

Can one investigate more efficiently quantum critical behavior by employing a local order-parameter pinning field, which explicitly breaks the symmetry of the model under investigation? To answer this question, the authors consider the two-dimensional square-lattice bilayer quantum Heisenberg model using a world-line quantum Monte Carlo method. The pinning-field approach is found to accurately locate the quantum critical point over a wide range of pinning-field strengths. However, the identification of the quantum critical scaling behavior is found to be complicated by the fact that the pinning field introduces strong corrections to scaling. A renormalization group analysis exhibits important analogies to surface critical phenomena, and a crossover effect to an infinite pinning-field fixed point, which the authors study in detail by simulations of an improved classical lattice model in the three-dimensional Ising universality class. At the infinite pinning-field fixed point, the short-distance expansion of the order-parameter profile exhibits a new universal critical exponent, which characterizes the experimentally relevant critical adsorption on a line defect. This result also implies the presence of slowly decaying scaling corrections, which are analyzed here in detail.

Quantum criticality in an organic spin-liquid insulator κ-(BEDT-TTF)2Cu2(CN)3.

A quantum spin-liquid state, an exotic state of matter, appears when strong quantum fluctuations enhanced by competing exchange interactions suppress a magnetically ordered state. Generally, when an ordered state is continuously suppressed to 0 K by an external parameter, a quantum phase transition occurs. It exhibits critical scaling behaviour, characterized only by a few basic properties such as dimensions and symmetry. Here we report the low-temperature magnetic torque measurements in an organic triangular-lattice antiferromagnet, κ-(BEDT-TTF)2Cu2(CN)3, where BEDT-TTF stands for bis(ethylenedithio)tetrathiafulvalene. It is found that the magnetic susceptibilities derived from the torque data exhibit a universal critical scaling, indicating the quantum critical point at zero magnetic field, and the critical exponents, γ=0.83(6) and νz=1.0(1). These exponents greatly constrain the theoretical models for the quantum spin liquid, and at present, there is no theory to explain the values, to the best of our knowledge.

Critical scaling of icosahedral medium-range order in CuZr metallic glass-forming liquids.

The temperature evolution of icosahedral medium-range order formed by interpenetrating icosahedra in CuZr metallic glassforming liquids was investigated via molecular dynamics simulations. Scaling analysis based on percolation theory was employed, and it is found that the size distribution of clusters formed by the central atoms of icosahedra at various temperatures follows a very good scaling law with the cluster number density scaled by S−τ and the cluster size S scaled by |1 − Tc/T|−1/σ, respectively. Here Tc is scaling crossover-temperature. τ and σ are scaling exponents. The critical scaling behaviour suggests that there would be a structural phase transition manifested by percolation of locally favoured structures underlying the glass transition, if the liquid could be cooled slowly enough but without crystallization intervening. Furthermore, it is revealed that when icosahedral short-range order (ISRO) extends to medium-range length scale by connection, the atomic configurations of ISROs will be optimized from distorted ones towards more regular ones gradually, which significantly lowers the energies of ISROs and introduces geometric frustration simultaneously. Both factors make key impacts on the drastic dynamic slow-down of supercooled liquids. Our findings provide direct structure-property relationship for understanding the nature of glass transition.

Equilibrium and non-equilibrium concentration fluctuations in a critical binary mixture.

When a macroscopic concentration gradient is present across a binary mixture, long-ranged non-equilibrium concentration fluctuations (NCF) appear as a consequence of the coupling between the gradient and spontaneous equilibrium velocity fluctuations. Long-ranged equilibrium concentration fluctuations (ECF) may be also observed when the mixture is close to a critical point. Here we study the interplay between NCF and critical ECF in a near-critical mixture aniline/cyclohexane in the presence of a vertical concentration gradient. To this aim, we exploit a commercial optical microscope and a simple, custom-made, temperature-controlled cell to obtain simultaneous static and dynamic scattering information on the fluctuations. We first characterise the critical ECF at fixed temperature T above the upper critical solution temperature Tc, in the wide temperature range [Formula: see text] °C. In this range, we observe the expected critical scaling behaviour for both the scattering intensity and the mass diffusion coefficient and we determine the critical exponents [Formula: see text], [Formula: see text] and [Formula: see text], which are found in agreement with the 3D Ising values. We then study the system in the two-phase region (T < T c). In particular, we characterise the interplay between ECF and NCF when the mixture, initially at a temperature Ti, is rapidly brought to a temperature T f > T i. During the transient, a vertical diffusive mass flux is present that causes the onset of NCF, whose amplitude vanishes with time, as the flux goes to zero. We also study the time dependence of the equilibrium scattering intensity I eq, of the crossover wave vector q co and of the diffusion coefficient D during diffusion and find that all these quantities exhibit an exponential relaxation enslaved to the diffusive kinetics.

Quantum critical transport at a continuous metal-insulator transition

In contrast to the first-order correlation-driven Mott metal-insulator transition, continuous disorder-driven transitions are intrinsically quantum critical. Here, we investigate transport quantum criticality in the Falicov-Kimball model, a representative of the latter class in the strong disorder category. Employing cluster-dynamical mean-field theory, we find clear and anomalous quantum critical scaling behavior manifesting as perfect mirror symmetry of scaling curves on both sides of the MIT. Surprisingly, we find that the beta function $\ensuremath{\beta}(g)$ scales as $log(g)$ deep into the bad-metallic phase as well, providing a sound unified basis for these findings. We argue that such strong localization quantum criticality may manifest in real three-dimensional systems where disorder effects are more important than electron-electron interactions.

Ising Nematic Quantum Critical Point in a Metal: A Monte Carlo Study

The Ising nematic quantum critical point (QCP) associated with the zero temperature transition from a symmetric to a nematic {\it metal} is an exemplar of metallic quantum criticality. We have carried out a minus sign-free quantum Monte Carlo study of this QCP for a two dimensional lattice model with sizes up to $24\times 24$ sites. The system remains non-superconducting down to the lowest accessible temperatures. The results exhibit critical scaling behavior over the accessible ranges of temperature, (imaginary) time, and distance. This scaling behavior has remarkable similarities with recently measured properties of the Fe-based superconductors proximate to their putative nematic QCP.

Quantum nonergodicity and fermion localization in a system with a single-particle mobility edge

We study the many-body localization aspects of single-particle mobility edges in fermionic systems. We investigate incommensurate lattices and random disorder Anderson models. Many-body localization and quantum nonergodic properties are studied by comparing entanglement and thermal entropy, and by calculating the scaling of subsystem particle number fluctuations, respectively. We establish a nonergodic extended phase as a generic intermediate phase (between purely ergodic extended and nonergodic localized phases) for the many-body localization transition of non-interacting fermions where the entanglement entropy manifests a volume law (`extended'), but there are large fluctuations in the subsystem particle numbers (`nonergodic'). We argue such an intermediate phase scenario may continue holding even for the many-body localization in the presence of interactions as well. We find for many-body states in non-interacting 1d Aubry-Andre and 3d Anderson models that the entanglement entropy density and the normalized particle-number fluctuation have discontinuous jumps at the localization transition where the entanglement entropy is sub-thermal but obeys the "volume law". In the vicinity of the localization transition we find that both the entanglement entropy and the particle number fluctuations obey a single parameter scaling. We argue using numerical and theoretical results that such a critical scaling behavior should persist for the interacting many-body localization problem with important consequences. Our work provides persuasive evidence in favor of there being two transitions in many-body systems with single-particle mobility edges, the first one indicating a transition from the purely localized nonergodic many-body localized phase to a nonergodic extended many-body metallic phase, and the second one being a transition eventually to the usual ergodic many-body extended phase.

A new model for spherically symmetric anisotropic compact star

In this article we obtain a new anisotropic solution for Einstein’s field equations of embedding class one metric. The solution represents realistic objects such as Her X-1 and RXJ 1856-37. We perform a detailed investigation of both objects by solving numerically the Einstein field equations with anisotropic pressure. The physical features of the parameters depend on the anisotropic factor i.e. if the anisotropy is zero everywhere inside the star then the density and pressures will become zero and the metric turns out to be flat. We report our results and compare with the above mentioned two compact objects as regards a number of key aspects: the central density, the surface density onset and the critical scaling behaviour, the effective mass and radius ratio, the anisotropization with isotropic initial conditions, adiabatic index and red shift. Along with this we have also made a comparison between the classical limit and theoretical model treatment of the compact objects. Finally we discuss the implications of our findings for the stability condition in a relativistic compact star.

Emergence of a Fermionic Finite-Temperature Critical Point in a Kondo Lattice

The underlying Dirac point is central to the profound physics manifested in a wide class of materials. However, it is often difficult to drive a system with Dirac points across the massless fermionic critical point. Here by exploiting screening of local moments under spin-orbit interactions in a Kondo lattice, we show that below the Kondo temperature, the Kondo lattice undergoes a topological transition from a strong topological insulator to a weak topological insulator at a finite temperature T_{D}. At T_{D}, massless Dirac points emerge and the Kondo lattice becomes a Dirac semimetal. Our analysis indicates that the emergent relativistic symmetry dictates nontrivial thermal responses over large parameter and temperature regimes. In particular, it yields critical scaling behaviors both in magnetic and transport responses near T_{D}.

A new model for charged anisotropic compact star

In this article we obtain a new anisotropic solution for Einstein's field equation of embedding class one metric. The solution is representing the realistic objects such as $Her~X-1$ and $RXJ~1856-37$. We perform detailed investigation of both objects by solving numerically the Einstein field equations under with anisotropic pressure. The physical features of the parameters depend on the anisotropic factor i.e. if anisotropy is zero everywhere inside the star then the density and pressures will become zero and metric turns out to be flat. We report our results and compare with the above mentioned two compact objects on a number of key aspects: the central density, the surface density onset and the critical scaling behavior, the effective mass and radius ratio, the anisotropization with isotropic initial conditions, adiabatic index and red shift. Along with this we have also made a comparison between the classical limit and theoretical model treatment of the compact objects. Finally we discuss the implications of our findings for the stability condition in relativistic compact star.

강자성 Co&lt;sub&gt;0.5&lt;/sub&gt;Fe&lt;sub&gt;0.5&lt;/sub&gt; 합금 박막에서의 자화역전현상 연구

alloy films using the magneto-optical Kerrmicroscope capable of the direct observation of time-resolved domain patterns. Interestingly enough, as the sample thickness increasesthe magnetization reversal behavior becomes changed from a single domain wall motion to the random nucleations of domains. Also,from the stochastic analysis of the domain jump sizes during the domain wall motion, it was found that the magnetization reversalbehavior in the samples shows the critical scaling behavior with the critical exponent of τ~1.33.Keywords: magnetization reversal, domain wall dynamics, critical scaling behavior, ferromagnetic film

Active-to-absorbing-state phase transition in an evolving population with mutation.

We study the active to absorbing phase transition (AAPT) in a simple two-component model system for a species and its mutant. We uncover the nontrivial critical scaling behavior and weak dynamic scaling near the AAPT that shows the significance of mutation and highlights the connection of this model with the well-known directed percolation universality class. Our model should be a useful starting point to study how mutation may affect extinction or survival of a species.

Reservoir interactions during Bose-Einstein condensation: Modified critical scaling in the Kibble-Zurek mechanism of defect formation

As a test of the Kibble-Zurek mechanism (KZM) of defect formation, we simulate the Bose-Einstein condensation transition in a toroidally confined Bose gas using the stochastic projected Gross-Pitaevskii equation (SPGPE), with and without the energy-damping reservoir interaction. Energy-damping alters the scaling of the winding number distribution with the quench time - a departure from the universal KZM theory that relies on equilibrium critical exponents. Numerical values are obtained for the correlation-length critical exponent $\nu$ and the dynamical critical exponent $z$ for each variant of reservoir interaction theory. The energy-damping reservoir interactions cause significant modification of the dynamical critical exponent of the phase transition, whilst preserving the essential KZM critical scaling behavior. Comparison of numerical and analytical two-point correlation functions further illustrates the effect of energy damping on the correlation length during freeze out.

Non-Fermi Liquid Behavior Close to a Quantum Critical Point in a Ferromagnetic State without Local Moments

A quantum critical point (QCP) occurs upon chemical doping of the weak itinerant ferromagnet Sc_{3.1}In. Remarkable for a system with no local moments, the QCP is accompanied by non-Fermi liquid (NFL) behavior, manifested in the logarithmic divergence of the specific heat both in the ferro- and the paramagnetic states. Sc_{3.1}In displays critical scaling and NFL behavior in the ferromagnetic state, akin to what had been observed only in f-electron, local moment systems. With doping, critical scaling is observed close to the QCP, as the critical exponents, and delta, gamma and beta have weak composition dependence, with delta nearly twice, and beta almost half of their respective mean-field values. The unusually large paramagnetic moment mu_PM~1.3 mu_B/F.U. is nearly composition-independent. Evidence for strong spin fluctuations, accompanying the QCP at x_c = 0.035 +- 0.005, may be ascribed to the reduced dimensionality of Sc_{3.1}In, associated with the nearly one-dimensional Sc-In chains.

Critical dynamical heterogeneities close to continuous second-order glass transitions.

We analyze, using inhomogeneous mode-coupling theory, the critical scaling behavior of the dynamical susceptibility at a distance ε from continuous second-order glass transitions. We find that the dynamical correlation length ξ behaves generically as ε(-1/3) and that the upper critical dimension is equal to six. More surprisingly, we find that ξ grows with time as ln²t exactly at criticality. All of these results suggest a deep analogy between the glassy behavior of attractive colloids or randomly pinned supercooled liquids and that of the random field Ising model.

Critical energy distribution function of the Baxter–Wu model

In this work we examine the critical finite-size scaling behavior of the energy probability distribution function and its corresponding Binder cumulant at critical point. Based on the results of Monte Carlo simulations at zero external magnetic field using the recently developed triangle-cluster algorithm, we calculate the energy distribution function’s exponents and we derive the scaling relations for the energy Binder cumulant. Finally, we predict the exact form of the scaled energy distribution function. Most of our conclusions seem applicable not only to the Baxter–Wu model but also to other Ising-like models.

Critical scaling in random-field systems: 2 or 3 independent exponents?

We show that the critical scaling behavior of random-field systems with short-range interactions and disorder correlations cannot be described in general by only two independent exponents, contrary to previous claims. This conclusion is based on a theoretical description of the whole domain of the d-dimensional random-field O(N) model (RFO(N)M) and points to the role of rare events that are overlooked by the proposed derivations of two-exponent scaling. Quite strikingly, however, the numerical estimates of the critical exponents of the random-field Ising model are extremely close to the predictions of the two-exponent scaling in d = 3 and d = 4, so that the issue cannot be decided only on the basis of numerical simulations in these spatial dimensions.