Lattice Systems Research Articles

Continuous extension of the discrete shift translations on one-dimensional quantum lattice systems

We study the continuous extension of discrete shift translations on one-dimensional quantum lattice systems. We explore a specific example provided by a quasi-free C ∗ {C}^{\ast } -flow on the one-dimensional fermion lattice system, comparing it with its original discrete shift-translations. Specifically, we demonstrate its explicit dynamical formula, which reveals violations of causality and locality. Furthermore, we prove that this quasi-free C ∗ {C}^{\ast } -flow on the one-dimensional fermion lattice system cannot be extended to the one-dimensional quantum spin lattice system via the Jordan-Wigner transformation.

An advanced cryptographic scheme for DICOM medical image encryption using a novel spatiotemporal chaotic lattice

Ensuring the privacy and security of medical imaging data is crucial. Most existing methods focus on encrypting images in common formats, neglecting the unique challenges posed by medical formats. In this paper an advanced encryption algorithm based on a multi-dimensional and multi-parametric spatiotemporal coupled chaotic lattice (Double-MsCcL) system is proposed. The Double-MsCcL system enhances the complexity of chaotic sequences, and provides a robust foundation for medical image encryption. The encryption method proposed combines double-layer random DNA diffusion and fractal random permutation. Medical information is embedded in the image pixels, serving as the cryptosystem key. The designed double-layer DNA random diffusion algorithm alters pixel values, while the fractal random permutation algorithm disrupts pixel positions. This proposed approach effectively hides sensitive information, strengthens resistance to plaintext attacks, and address the often-overlooked Uint16 format of DICOM images. Comprehensive performance evaluations have shown that the proposed encryption scheme offers significant advantages in protecting sensitive medical imaging data. Our algorithm exhibits better performance in resisting plaintext analysis, statistical, and differential attacks, demonstrating significant security compared to existing state-of-the-art methods, which can be widely applied in the field of modern medical data protection.

Half-quantum mirror Hall effect

We predict a half-quantized mirror Hall effect induced by mirror symmetry in strong topological insulator films. These films are known to host a pair of gapless Dirac cones in the first Brillouin zone associated with surface electrons. Our findings reveal that mirror symmetry assigns a unique mirror parity to each Dirac cone, resulting in a half-quantized Hall conductance of ±e22h\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\pm \\! \\frac{{e}^{2}}{2h}$$\\end{document} for each cone. Despite the total electrical Hall conductance being null due to time-reversal invariance, the difference in the Hall conductance between the two cones yields a quantized Hall conductance of e2h\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\frac{{e}^{2}}{h}$$\\end{document} for the difference in mirror currents. The effect of helical edge mirror current - a crucial feature of this quantum effect - may, in principle, be determined by means of electrical measurements. The half-quantum mirror Hall effect reveals a type of mirror-symmetry induced quantum anomaly in a time-reversal invariant lattice system, giving rise to a topological metallic state of matter with time-reversal invariance.

Manifestation of the quantum metric in chiral lattice systems

Recent years have seen a surge in research on the role of quantum geometry in condensed matter physics. For instance, the Aharonov-Bohm effect is a physical phenomenon where the vector potential induces a phase shift of electron wavepackets in regions with zero magnetic fields due to an obstruction in space associated with a magnetic flux. A similar effect can be observed in solid-state systems, where the topology of the Berry connection can influence electron dynamics. These are paradigmatic examples of how the dynamics can be affected by the system’s geometry. Here, we show that in chiral-symmetric processes the quantum metric has a measurable effect on the mean chiral displacement of delocalized wavefunctions. This finding is supported by a photonic experiment realizing a topological quantum walk and demonstrates an effect that can be attributed directly to the geometry of the state space.

Measure Attractors of Stochastic Fractional Lattice Systems

This paper seeks to establish the measure attractors in stochastic fractional lattice systems. First, the presence of these attractor measures is proven by the uniform estimates of the solution. Subsequently, the study also looks at the upper semicontinuous dependence of the measure attractors on the noise intensity as the latter goes to zero. The given asymptotic compactness for the family of probability measures occurring with the solution probability distributions is exhibited by a uniform prior estimation of the far-field solution values.

Asymptotically autonomous robustness of random attractors for the stochastic wave lattice equations with random viscosity

In this paper, we focus on the asymptotic behavior of solutions to the non-autonomous stochastic wave lattice systems with random viscosity and multiplicative white noise. Under proper conditions, we first prove the existence and uniqueness of the pullback random attractors and then show their backward compactness in a weighted space. Finally, we establish the asymptotically autonomous robustness of pullback random attractors when the nonlinearity is bounded and the time-dependent forcing term converges to the time-independent counterpart.

Real-time dynamics of angular momentum transfer from spin to acoustic chiral phonon in oxide heterostructures.

Chiral phonons have recently been explored as a novel degree of freedom in quantum materials. The angular momentum carried by these quasiparticles is generated by the breaking of chiral degeneracy of phonons, owing to the chiral lattice structure or the rotational motion of ions of the material. In ferromagnets, a mechanism for generating non-equilibrium chiral phonons has been suggested, but their temporal evolution, which obeys Bose-Einstein statistics, remains unclear. Here we report the real-time dynamics of thermalized chiral phonons in an artificial superlattice composed of ferromagnetic metallic SrRuO3 and non-magnetic insulating SrTiO3. Following the photo-induced ultrafast demagnetization in the SrRuO3 layer, we observed the appearance of a magneto-optic signal in the superlattice, which is absent in the SrRuO3 single films. This magneto-optic signal exhibits thermally driven dynamic properties and a clear correlation with the thickness of the non-magnetic SrTiO3 layer, implying that it originates from thermalized chiral phonons. We use numerical calculations considering the magneto-elastic coupling in SrRuO3 to validate our experimental observations and the angular momentum transfer mechanism between the lattice and spin systems in ferromagnetic systems and also to the non-magnetic system.

Scaling limit of the ground state Bethe roots for the inhomogeneous XXZ spin - [formula omitted] chain

It is known that for the Heisenberg XXZ spin - 12 chain in the critical regime, the scaling limit of the vacuum Bethe roots yields an infinite set of numbers that coincide with the energy spectrum of the quantum mechanical 3D anharmonic oscillator. The discovery of this curious relation, among others, gave rise to the approach referred to as the ODE/IQFT (or ODE/IM) correspondence. Here we consider a multiparametric generalization of the Heisenberg spin chain, which is associated with the inhomogeneous six-vertex model. When quasi-periodic boundary conditions are imposed the lattice system may be explored within the Bethe Ansatz technique. We argue that for the critical spin chain, with a properly formulated scaling limit, the scaled Bethe roots for the ground state are described by second order differential equations, which are multi-parametric generalizations of the Schrödinger equation for the anharmonic oscillator.

Chaos synchronization of two coupled map lattice systems using safe reinforcement learning

When synchronizing two continuous typical chaotic systems, the state variables of the response system are usually bounded and satisfy the Lipschitz condition. This permits a universal synchronization method. In the synchronization of two high-dimensional discrete chaotic systems such as the coupled map lattice systems, the state variables of the response system often diverge, which makes it difficult to seek a universal synchronization method. To overcome this difficulty, bounded and hard constraints, which correspond to the concept of safety level III in reinforcement learning terms, on the state variables must be imposed, when the discrete response system is perturbed. We propose a universal method for synchronizing two discrete systems based on safe reinforcement learning (RL). In this method, the RL agent’s policy is used to reach the goal of synchronization and a safety layer added directly on top of the policy is used to satisfy safety level III. The safety layer consists of a one-step predictor for the perturbed response system and an action correction formulation. The one-step predictor, based on a next generation reservoir computing, is used to identify whether the next state of the perturbed system is within the chaotic domain, and if not, the action correction formula is activated to modify the corresponding perturbing force component to zero. In this way, the state of the perturbed system will remain in the bounded chaotic domain. We demonstrate that the proposed method succeeds in synchronization without divergence through a numerical example with two coupled map lattice systems, and the average synchronization time is 12.66 iteration steps over 1000 different initial conditions. The method works even when parameter mismatches and disturbances exist in the system. We compare the performance in both cases with and without the safety layer and find that successful synchronization is only possible in the former case, emphasizing the significance of the safety layer. The performance of the algorithm with optimal hyper-parameters obtained by Bayesian optimization is robust and stable.

Compact Spinning with Different Fibre Types: An Experimental Investigation on Yarn Properties in the Condensing Zone with 3D-Printed Guiding Device

Abstract The lattice apron-based compact spinning system is a form of pneumatic compact spinning that employs airflow to condense fibres into a bundle, enhancing the yarn’s attributes. To explore the airflow dynamics in pneumatic compact spinning, researchers primarily employ traditional theoretical approaches, experimental measurement techniques, and computational fluid dynamics (CFD) methods. In our previous research, we utilized CFD to observe the airflow patterns in pneumatic compact spinning. In this study, we implemented experimental measurement techniques to assess the impact of a 3D-printed guiding device (B-type) on yarn properties. We tested different fibre types in the condensing zone of the compact spinning system with a lattice apron. We used three types of roving to spin the yarn: pure cotton, cotton/polyester (80/20), and polyester/viscose (65/35). The findings revealed that yarns spun using the guiding device exhibited superior strength, hairiness, and evenness compared to those spun without the device.

Discrete-continuum-discrete approach for the modeling of the dynamic behavior of 2D lattice systems

This work presents a new methodology to model elastic lattice systems through a two-step approach that permits to reliably capture its dynamic behavior with a lower computational cost than modeling the lattice explicitly. The first step consists of a non-standard continualization accounting for scale effects. Several methods are explored to derive new continuum models, whose dispersive and vibrational behaviors are compared to that of the lattice, considered as a reference. Non-classical models with micro-inertia reveal high accuracy, not presenting physical inconsistencies. The second step follows a FEM spatial discretization of the developed continua, accounting for micro inertia terms in the mass matrix. Finally, the FEM formulation allows the use of element sizes larger (up to four times) than the physical length scale of the lattice system, thus significantly reducing the computational cost while maintaining accuracy and enabling a versatile application to materials, geometries and boundary conditions. The methodology is tested here for a 2D system with displacements in the plane, but can be extended to other lattice typologies as well.

Attractors for Hopfield lattice model in weighted spaces

The investigation into the dynamic behavior of infinite lattice systems holds paramount significance in the realm of physical phenomena, particularly in mechanics. This intricate domain has captivated the attention of both mathematicians and physicists.In acknowledgment of the inherent noise prevalent in real-world environments, our study embraces this aspect by introducing a random term into our model. This deliberate inclusion of stochasticity engenders a novel perspective, giving rise to a stochastic lattice differential equation. This model proves to be a versatile tool for accurately characterizing spatial structures characterized by discrete components and the associated uncertainties that pervade them. This research elucidates the intricate interplay between lattice dynamics and environmental noise, shedding light on the complex behavior of such systems in a realistic context. Our result generalizes many results in three directions: extending the connections between the terms to non-linear, extending the connection neighborhood from 3 (as in most cases) to arbitrary value n, and extending the results that are in ℓ2 to ℓρ2.

Weyl Points on Nonorientable Manifolds.

Weyl fermions are hypothetical chiral particles that can also manifest as excitations near three-dimensional band crossing points in lattice systems. These quasiparticles are subject to the Nielsen-Ninomiya "no-go" theorem when placed on a lattice, requiring the total chirality across the Brillouin zone to vanish. This constraint results from the topology of the (orientable) manifold on which they exist. Here, we ask to what extent the concepts of topology and chirality of Weyl points remain well defined when the underlying manifold is nonorientable. We show that the usual notion of chirality becomes ambiguous in this setting, allowing for systems with a nonzero total chirality. This circumvention of the Nielsen-Ninomiya theorem stems from a generic discontinuity of the vector field whose zeros are Weyl points. Furthermore, we discover that Weyl points on nonorientable manifolds carry an additional Z_{2} topological invariant which satisfies a different no-go theorem. We implement such Weyl points by imposing a nonsymmorphic symmetry in the momentum space of lattice models. Finally, we experimentally realize all aspects of their phenomenology in a photonic platform with synthetic momenta. Our work highlights the subtle but crucial interplay between the topology of quasiparticles and of their underlying manifold.

An Exploration of the Phonon Frequency Spectrum and Born–von Karman Periodic Boundary Conditions in 1D and 2D Lattice Systems Using a Computational Approach

Periodic boundary conditions (PBCs) are a pivotal concept in the treatment of ideal lattices of infinite extent as a finite lattice. Most undergraduate texts that delve into the analytical treatment of lattice dynamics solve the problem in the reciprocal space with an implicit assumption of PBCs. While the traditional approach centered in the reciprocal or [Formula: see text]-space is elegant for simple one-dimensional lattice structures, the method becomes mathematically cumbersome for more complex lattices with real-world applications, such as a honeycomb lattice involving a [Formula: see text] secular determinant. In this work, we have explored the solution of lattice dynamics in direct space numerically, by constructing unit cells through an explicit implementation of Born–von Karman PBCs and solving the lattice dynamical equations in the displacement–time domain using the fourth-order Runge–Kutta algorithm. The Fast Fourier Transform technique is then used to obtain the phonon frequency spectrum corresponding to the computed instantaneous displacements. The fidelity of the model is validated by the agreement of the computational results obtained for the phonon spectrum at high symmetry points in the Brillouin zone with the analytical values for the given problem. Initially, the dynamics and the phonon spectrum are explored for monatomic and diatomic linear lattices which serve to act as introductory cases for the approach before investigating the 2D monatomic square and honeycomb lattices using the nearest and next-nearest neighbor approximations. A short-range force constant model employing the central forces and angular forces is used for the monatomic square lattice to account for the interatomic interactions. Our computational approach is expected to be physically more intuitive for a student for visualizing the periodicity of a given lattice and understanding its related dynamics. The approach demonstrates the usage of Born–von Karman PBCs in constructing a unit cell that effectively captures the dynamics of a lattice system, complementing the traditional secular determinant formalism. The work also illustrates an instance of how the computer programming can be used as a tool to empower the students to explore abstract concepts in physics. A honing of programming and computational skills of students enables them to interact with dynamic models in physics and gain deeper insight into the real-world applications of physics principles. Target group of this work is the students and educators at undergraduate level who seek a thorough and didactic comprehension of lattice dynamics.

Ground state solitons for periodic Schrödinger lattice systems with saturable nonlinearities and spectrum 0

Ground state solitons for periodic Schrödinger lattice systems with saturable nonlinearities and spectrum 0

Quench dynamics in lattices above one dimension: The free fermionic case

We begin a systematic investigation of quench dynamics in higher-dimensional lattice systems considering the case of noninteracting fermions with conserved particle number. We prepare the system in a translational-invariant nonequilibrium initial state, the simplest example being a classical configuration with fermions at fixed positions on the lattice, and let it evolve in time. We characterize the system's dynamics by measuring the entanglement between a finite connected region and its complement. We observe the transmutation of entanglement entropy into thermodynamic entropy and investigate how this process depends on the shape and orientation of the region with respect to the underlying lattice. Interestingly, we find that irregular regions display a distinctive multislope entanglement growth, while the dependence on the orientation angle is generically fairly weak. This is particularly true for regions with a large (discrete) rotational symmetry group. The main tool of our analysis is the celebrated quasiparticle picture of Calabrese and Cardy, which we generalize to describe the case at hand. Specifically, we show that for generic initial configurations (even when restricting to classical ones) one has to allow for the production of multiplets involving n>2 quasiparticles and carrying nondiagonal correlations. We obtain quantitatively accurate predictions, tested against exact numerics, and propose an efficient Monte Carlo based scheme to evaluate them for arbitrary connected regions of generic higher-dimensional lattices. Published by the American Physical Society 2024

Utilizing topological invariants for encoding and manipulating chiral phonon devices

As a fundamental degree of freedom, phonon chirality is expected to promote the development of quantum information technology just like electron spin. Currently, central to this area is the realization of efficient transmission and control of chiral information. In this paper, we propose an approach by integrating topological theory, leveraging topologically invariant Chern numbers, to encode hexagonal lattice systems. Our investigation reveals the presence of topologically protected chiral interface states within the shared band gaps of both trivial and non-trivial system units. By precisely modulating the magnetic field distribution within the encoding system, we can effectively manipulate the topological pathways. Building upon this framework, we design and implement a chiral phonon three-port device. Through dynamic calculations, we demonstrate the transmission process of chiral information, showcasing the chiral phonon switching effect and logical OR operation. Our findings not only establish a fundamental mechanism for the manipulation and control of phonon chiral information but also provide a promising direction for research in harnessing chirality degrees of freedom in practical applications.

Estimation of spreading speeds and travelling waves for the lattice pioneer-climax competition system

ABSTRACT This paper concerns the invasion dynamics of the lattice pioneer-climax competition model with parameter regions in which the system is non-monotone. We estimate the spreading speeds and establish appropriate conditions under which the spreading speeds are linearly selected. Moreover, the existence of travelling waves is determined by constructing suitable upper and lower solutions. It shows that the spreading speed coincides with the minimum wave speed of travelling waves if the diffusion rate of the invasive species is larger or equal to that of the native species. Our results are new to estimate the spreading speed of non-monotone lattice pioneer-climax systems, and the techniques developed in this work can be used to study the invasion dynamics of the pioneer-climax system with interaction delays, which could extend the results in the literature. The analysis replies on the construction of auxiliary systems, upper and lower solutions, and the monotone dynamical system approach.

Higher-order topological states in T-graphene and their realization in photonic crystals

Higher-order topological states extend the power of nontrivial topological states beyond the bulk-edge correspondence. Here we study the higher-order topological states (corner states) in an open-boundary two-dimensional T-graphene lattice. Unlike the common zero-energy corner states, our findings reveal non-zero energy corner states in such lattice systems, and the energy could be controlled by modifying the hopping parameters. Moreover, the corner states could be transferred away from the lattice corners by designing the position-specific vacancy defects. The strong robustness of the corner states is also demonstrated against the uniaxial strain and vacancy defects, respectively. A plasmonic crystal is constructed to testify to the theory, in which the corner states are realized in optical modes and their higher-order topological properties are verified. Our results open the avenue of corner-states engineering, which holds significant physical implications of higher-order topological states for the design of photonic and electronic devices with specialized functionalities.

Fusion surface models: 2+1d lattice models from fusion 2-categories

We construct (2+1)-dimensional lattice systems, which we call fusion surface models. These models have finite non-invertible symmetries described by general fusion 2-categories. Our method can be applied to build microscopic models with, for example, anomalous or non-anomalous one-form symmetries, 2-group symmetries, or non-invertible one-form symmetries that capture non-abelian anyon statistics. The construction of these models generalizes the construction of the 1+1d anyon chains formalized by Aasen, Fendley, and Mong. Along with the fusion surface models, we also obtain the corresponding three-dimensional classical statistical models, which are 3d analogues of the 2d Aasen-Fendley-Mong height models. In the construction, the “symmetry TFTs” for fusion 2-category symmetries play an important role.