Quantum criticality of generalized Aubry-André models with exact mobility edges using fidelity susceptibility.

In this study, we explore the quantum critical phenomena in generalized Aubry-André models, with a particular focus on the scaling behavior at various filling states. Our approach involves using quantum fidelity susceptibility to precisely identify the mobility edges in these systems. Through a finite-size scaling analysis of the fidelity susceptibility, we are able to determine both the correlation-length critical exponent and the dynamical critical exponent at the critical point of the generalized Aubry-André model. Based on the Diophantine equation conjecture, we can determines the number of subsequences of the Fibonacci sequence and the corresponding scaling functions for a specific filling fraction, as well as the universality class. Our findings demonstrate the effectiveness of employing the generalized fidelity susceptibility for the analysis of unconventional quantum criticality and the associated universal information of quasiperiodic systems in cutting-edge quantum simulation experiments.

Eigen microstates in self-organized criticality.

We employ the eigen microstates approach to explore the self-organized criticality (SOC) in two celebrated sandpile models, namely the BTW model and the Manna model. In both models, phase transitions from the absorbing state to the critical state can be understood by the emergence of dominant eigen microstates with significantly increased weights. Spatial eigen microstates of avalanches can be uniformly characterized by a linear system size rescaling. The first temporal eigen microstates reveal scaling relations in both models. Furthermore, by finite-size scaling analysis of the first eigen microstates, we numerically estimate critical exponents, i.e., sqrt[σ_{0}w_{1}]/v[over ̃]_{1}∝L^{D} and v[over ̃]_{1}∝L^{D(1-τ_{s})/2}. Our findings could provide profound insights into eigen microstates of the universality and phase transition in nonequilibrium complex systems governed by self-organized criticality.

Order parameter dynamics in complex systems: From models to data.

Collective ordering behaviors are typical macroscopic manifestations embedded in complex systems and can be ubiquitously observed across various physical backgrounds. Elements in complex systems may self-organize via mutual or external couplings to achieve diverse spatiotemporal coordinations. The order parameter, as a powerful quantity in describing the transition to collective states, may emerge spontaneously from large numbers of degrees of freedom through competitions. In this minireview, we extensively discussed the collective dynamics of complex systems from the viewpoint of order-parameter dynamics. A synergetic theory is adopted as the foundation of order-parameter dynamics, and it focuses on the self-organization and collective behaviors of complex systems. At the onset of macroscopic transitions, slow modes are distinguished from fast modes and act as order parameters, whose evolution can be established in terms of the slaving principle. We explore order-parameter dynamics in both model-based and data-based scenarios. For situations where microscopic dynamics modeling is available, as prototype examples, synchronization of coupled phase oscillators, chimera states, and neuron network dynamics are analytically studied, and the order-parameter dynamics is constructed in terms of reduction procedures such as the Ott-Antonsen ansatz, the Lorentz ansatz, and so on. For complicated systems highly challenging to be well modeled, we proposed the eigen-microstate approach (EMP) to reconstruct the macroscopic order-parameter dynamics, where the spatiotemporal evolution brought by big data can be well decomposed into eigenmodes, and the macroscopic collective behavior can be traced by Bose-Einstein condensation-like transitions and the emergence of dominant eigenmodes. The EMP is successfully applied to some typical examples, such as phase transitions in the Ising model, climate dynamics in earth systems, fluctuation patterns in stock markets, and collective motion in living systems.

Random adsorption process of linear k-mers on square lattices under the Achlioptas process.

We study the explosive percolation with k-mer random sequential adsorption (RSA) process. We consider both the Achlioptas process (AP) and the inverse Achlioptas process (IAP), in which giant cluster formation is prohibited and accelerated, respectively. By employing finite-size scaling analysis, we confirm that the percolation transitions are continuous, and thus we calculate the percolation threshold and critical exponents. This allows us to determine the universality class of the k-mer explosive percolation transition. Interestingly, the numerical simulation suggests that the universality class of the explosive percolation transition with the AP alters when the k-mer size changes. In contrast, the universality class of the transition with the IAP is independent of k, but it differs from that of the RSA without the IAP.

Universal Scaling and Critical Exponents of the Anisotropic Quantum Rabi Model.

We investigate the quantum phase transition of the anisotropic quantum Rabi model, in which the rotating and counterrotating terms are allowed to have different coupling strengths. The model interpolates between two known limits with distinct universal properties. Through a combination of analytic and numerical approaches, we extract the phase diagram, scaling functions, and critical exponents, which determine the universality class at finite anisotropy (identical to the isotropic limit). We also reveal other interesting features, including a superradiance-induced freezing of the effective mass and discontinuous scaling functions in the Jaynes-Cummings limit. Our findings are extended to the few-body quantum phase transitions with N>1 spins, where we expose the same effective parameters, scaling properties, and phase diagram. Thus, a stronger form of universality is established, valid from N=1 up to the thermodynamic limit.

MoPex19, which is essential for maintenance of peroxisomal structure and woronin bodies, is required for metabolism and development in the rice blast fungus.

Peroxisomes are present ubiquitously and make important contributions to cellular metabolism in eukaryotes. They play crucial roles in pathogenicity of plant fungal pathogens. The peroxisomal matrix proteins and peroxisomal membrane proteins (PMPs) are synthesized in the cytosol and imported post-translationally. Although the peroxisomal import machineries are generally conserved, some species-specific features were found in different types of organisms. In phytopathogenic fungi, the pathways of the matrix proteins have been elucidated, while the import machinery of PMPs remains obscure. Here, we report that MoPEX19, an ortholog of ScPEX19, was required for PMPs import and peroxisomal maintenance, and played crucial roles in metabolism and pathogenicity of the rice blast fungus Magnaporthe oryzae. MoPEX19 was expressed in a low level and Mopex19p was distributed in the cytoplasm and newly formed peroxisomes. MoPEX19 deletion led to mislocalization of peroxisomal membrane proteins (PMPs), as well peroxisomal matrix proteins. Peroxisomal structures were totally absent in Δmopex19 mutants and woronin bodies also vanished. Δmopex19 exhibited metabolic deficiency typical in peroxisomal disorders and also abnormality in glyoxylate cycle which was undetected in the known mopex mutants. The Δmopex19 mutants performed multiple disorders in fungal development and pathogenicity-related morphogenesis, and lost completely the pathogenicity on its hosts. These data demonstrate that MoPEX19 plays crucial roles in maintenance of peroxisomal and peroxisome-derived structures and makes more contributions to fungal development and pathogenicity than the known MoPEX genes in the rice blast fungus.

Continuous percolation phase transitions of random networks under a generalized Achlioptas process.

Using finite-size scaling, we have investigated the percolation phase transitions of evolving random networks under a generalized Achlioptas process (GAP). During this GAP, the edge with a minimum product of two connecting cluster sizes is taken with a probability p from two randomly chosen edges. This model becomes the Erdös-Rényi network at p=0.5 and the random network under the Achlioptas process at p=1. Using both the fixed point of the size ratio s{2}/s{1} and the straight line of lns{1}, where s{1} and s{2} are the reduced sizes of the largest and the second-largest cluster, we demonstrate that the phase transitions of this model are continuous for 0.5 ≤ p ≤ 1. From the slopes of lns{1} and ln(s{2}/s{1})' at the critical point, we get critical exponents ß and ν of the phase transitions. At 0.5 ≤ p ≤ 0.8, it is found that ß, ν, and s{2}/s{1} at critical point are unchanged and the phase transitions belong to the same universality class. When p ≥ 0.9, ß, ν, and s{2}/s{1} at critical point vary with p and the universality class of phase transitions depends on p.