arXiv subjects

Brandon B. Le

Publications and source records attributed to Brandon B. Le.

15 recordsLinked to original sources

arXiv2026

Dynamical signatures of deconfined spinons in dimerized sawtooth chains

We study the ground-state properties and dynamical response of the Heisenberg model on the sawtooth chain in and away from the exactly solvable valence-bond-solid (VBS) point. We employ U(1)-symmetric density-matrix renormalization group (DMRG) and time-dependent variational principle (TDVP) methods to compute equilibrium diagnostics and the zero-temperature dynamical structure factor (DSF) $S^{zz}(q,\omega)$ across the dimerized phase, a valence-bond-ordered state in which the two symmetry-equivalent apex--base bonds of each triangle develop unequal spin correlations, probing the approach to the continuous lower phase boundary, the exact VBS point, and the approach to the first-order upper boundary. In every regime, the DSF is a broad continuum dominated by a bright band at its lower edge, with the intensity at the one-triplon energy $\omega \simeq J_{AB}$ suppressed. We identify the spectrum as a deconfined two-spinon continuum of kink and antikink domain walls between the two degenerate singlet coverings. Closed-form spinon dispersions fix the continuum edges and track the dominant band across the zone in all three regimes, while an explicit finite-separation two-kink calculation in a constrained Hilbert space reproduces the measured intensity distribution. Our results provide a microscopic picture of fractionalized excitations in the dimerized sawtooth chain and are relevant to the recently discovered Ti$^{3+}$ kagome fluorides, where strongly anisotropic exchange interactions can generate sawtooth-chain building blocks.

cond-mat.str-el↗

arXiv2026

Frustrated neurons: Energy landscapes and relaxation dynamics in repulsive phase oscillators

Geometrical frustration, a central paradigm in condensed matter physics, provides a unifying language for systems in which locally preferred interactions cannot be made globally compatible. Here, we use this language to formulate a minimal theory of frustrated neural timing, mapping repulsively coupled rhythmic units onto antiferromagnetic XY models. Within this framework, the condensed-matter concepts of local constraints, degenerate ground-state manifolds, metastability, and quench dynamics become a concrete diagnostic framework for structured neural phase dynamics. We analyze a hierarchy of geometries: a triangle as the minimal frustrated motif with two chiral 120{\deg} timing states, a tetrahedron whose reduced ground-state manifold consists of intersecting continuous branches associated with antipodal pairings, and a kagome lattice on which local constraints define a constrained three-coloring manifold. The kagome lattice reveals the central dynamical result: zero-temperature relaxation suppresses global synchrony but typically selects low-energy metastable torque-balanced states rather than exact ground states. Finally, we show how the phase theory can be carried back towards biophysical neural models by treating it as an effective-interaction target, where geometrical timing frustration is realized through preferred phase lags that become incompatible around closed motifs. This perspective suggests that weak global coherence in neural systems does not necessarily signal disordered activity, but can reflect structured local timing order shaped by a frustrated dynamical landscape.

cond-mat.dis-nn↗

arXiv2026

Active-learning mapping of the Vicsek model phase diagram

The Vicsek model is a minimal model of collective motion, capturing how local alignment interactions can generate macroscopic nonequilibrium order in systems such as bird flocks. In this work, we use active learning to map the Vicsek phase diagram as a function of noise strength, density, and particle speed. A neural-network classifier is trained on global polar-order labels, and classifier entropy is used to select new simulations near uncertain crossover regions. The resulting phase map resolves a high-noise disordered gas, a low-noise polar ordered regime, and an intermediate coexistence-candidate regime whose noise window shifts upward and broadens with increasing density. Independent density and local-order diagnostics indicate that the intermediate regime contains dense, locally ordered bands coexisting with a dilute, weakly ordered background. Comparison with the ordered regime shows that banded coexistence is identified by the joint enhancement of band contrast, local-order heterogeneity, and positive density-order correlation. Overall, these results establish a machine-learning-guided workflow for active matter, in which active learning constructs an operational phase map and independent spatial diagnostics convert classifier-defined regimes into physically interpretable nonequilibrium morphologies.

cond-mat.soft↗

arXiv2026

Schwinger-Boson Mean-Field Study of the Anisotropic Kagome Antiferromagnet

We investigate the effect of spatial exchange anisotropy on the spin-$1/2$ kagome antiferromagnet using Schwinger-boson mean-field theory. The anisotropy is introduced by strengthening the Heisenberg exchange along one set of nearest-neighbor bonds relative to the other two, and is controlled by a parameter $δ$ that measures the deviation from the isotropic limit. Incorporating the reduced lattice symmetry, we construct the corresponding projective-symmetry-group ansätze and focus on representative $0$- and $π$-flux states connected to the conventional $q=0$ and $\sqrt{3}\times\sqrt{3}$ kagome states. We find that anisotropy predominantly reconstructs the low-energy spinon sector, leading to a strong softening of the lowest spinon branch and a downward shift of the two-spinon continuum. At sufficiently large $δ$, the spinon gap closes at ansatz-dependent values, signaling an instability toward spinon condensation and the onset of magnetic order. From the soft Bogoliubov eigenmodes, we reconstruct the associated incipient spin textures and show that the resulting magnetic orders are intrinsically anisotropic, with suppressed moments on strongly coupled bonds and enhanced moments on more weakly connected sites. These results provide a microscopic picture of how exchange anisotropy drives the transition from kagome spin-liquid states to magnetic order, and offer a framework for interpreting recent experiments on anisotropic kagome materials, particularly titanium-based spin-$1/2$ compounds.

cond-mat.str-el↗

arXiv2026

Compton Form Factor Extraction using Quantum Deep Neural Networks

We extract Compton form factors (CFFs) from deeply virtual Compton scattering measurements at the Thomas Jefferson National Accelerator Facility (JLab) using quantum-inspired deep neural networks (QDNNs). The analysis implements the twist-2 Belitsky-Kirchner-Müller formalism and employs a fitting strategy that emulates standard local fits. Using pseudodata, we benchmark QDNNs against classical deep neural networks (CDNNs) and find that QDNNs often deliver higher predictive accuracy and tighter uncertainties at comparable model complexity. Guided by these results, we introduce a quantitative selection metric that indicates when QDNNs or CDNNs are optimal for a given experimental fit. After obtaining local extractions from the JLab data, we perform a standard neural-network global CFF fit and compare with previous global analyses. The results support QDNNs as an efficient and complementary tool to CDNNs for CFF determination and for future multidimensional studies of parton distributions and hadronic structure.

cs.LG↗

arXiv2026

Basis for non-derivative baryon-number-violating operators

We present a minimal basis for non-derivative baryon-number-violating operators in the Standard Model Effective Field Theory up to mass dimension 11, as well as for the $(ΔB,ΔL) = (2,2)$ and $(2,-2)$ operators at dimension 12. Compared to existing results, our bases generally contain fewer terms and simpler contractions, although we also highlight select cases where a minimal basis is incompatible with simple structures.

hep-ph↗

arXiv2026

Energy landscape of the kagome antiferromagnet: Characterization of multiple energy scales

We investigate the energy landscape of the kagome Heisenberg antiferromagnet within its coplanar ground-state manifold. Although coplanar states are degenerate at harmonic order, transitions between them require collective weathervane-loop rotations whose barriers grow strongly with loop size. To characterize this structure, we construct disconnectivity graphs using two complementary approaches: exact enumeration and minimax-barrier calculations for small lattices, and a statistical construction for large lattices based on random walks through configuration space, with loop length used as a proxy for barrier height. The exact landscape reveals a dominant low-barrier scale associated with elementary six-spin loops and a broader higher-barrier sector from longer rearrangements. For large systems, the statistical analysis exposes a hierarchy of barrier scales, including a pronounced six-spin-loop peak and an intermediate scale-free regime of loop lengths. This hierarchy provides a natural basis for multiple dynamical time scales: six-spin loops govern the fastest local relaxation, while slower collective dynamics arise from activation of longer loops. These results show that the coplanar manifold is dynamically rugged, with its low-energy dynamics governed by a hierarchy of loop-mediated barriers.

cond-mat.stat-mech↗

arXiv2026

Quantum Qualifiers for Neural Network Model Selection in Hadronic Physics

As quantum machine-learning architectures mature, a central challenge is no longer their construction, but identifying the regimes in which they offer practical advantages over classical approaches. In this work, we introduce a framework for addressing this question in data-driven hadronic physics problems by developing diagnostic tools - centered on a quantitative quantum qualifier - that guide model selection between classical and quantum deep neural networks based on intrinsic properties of the data. Using controlled classification and regression studies, we show how relative model performance follows systematic trends in complexity, noise, and dimensionality, and how these trends can be distilled into a predictive criterion. We then demonstrate the utility of this approach through an application to Compton form factor extraction from deeply virtual Compton scattering, where the quantum qualifier identifies kinematic regimes favorable to quantum models. Together, these results establish a principled framework for deploying quantum machine-learning tools in precision hadronic physics.

cs.LG↗

arXiv2026

Phase-space networks and connectivity of the kagome antiferromagnet

We study the coplanar ground-state manifold of the kagome Heisenberg antiferromagnet using a phase-space network representation, in which nodes correspond to coplanar ground states and edges represent transitions generated by weathervane loop rotations. In the coplanar manifold, each configuration can be mapped to a three-coloring problem on the dual honeycomb lattice, where a weathervane mode corresponds to a closed loop of two alternating colors. By comparing networks that include all weathervane loops with networks restricted to elementary six-spin loops, we examine how energetic constraints shape phase-space structure. We find that connectivity distributions are sharply peaked in large systems, while restrictions to short loops reduce typical connectivity. Spectral properties further distinguish the two cases, with short-loop networks exhibiting Gaussian spectra and full networks displaying non-Gaussian features associated with correlated loop updates. Finally, a box-counting analysis reveals distinct fractal properties of the two networks, demonstrating how energetic constraints control the global geometry of configuration space. These results show that the hierarchy of weathervane loop rotations provides a direct link between microscopic constraints and emergent phase-space geometry in a frustrated magnet.

cond-mat.stat-mech↗

arXiv2025

Final state sensitivity and fractal basin boundaries from coupled Chialvo neurons

We investigate and quantify the basin geometry and extreme final state uncertainty of two identical electrically asymmetrically coupled Chialvo neurons. The system's diverse behaviors are presented, along with the mathematical reasoning behind its chaotic and nonchaotic dynamics as determined by the structure of the coupled equations. The system is found to be multistable with two qualitatively different attractors. Although each neuron is individually nonchaotic, the chaotic basin takes up the vast majority of the coupled system's state space, but the nonchaotic basin stretches to infinity due to chance synchronization. The boundary between the basins is found to be fractal, leading to extreme final state sensitivity. This uncertainty and its potential effect on the synchronization of biological neurons may have significant implications for understanding human behavior and neurological disease.

nlin.CD↗

arXiv2025

Chaotic Dynamics and Fractal Geometry in Ring Lattice Systems of Nonchaotic Rulkov Neurons

This paper investigates the complex dynamics and fractal attractors that arise in a 60-dimensional ring lattice system of electrically coupled nonchaotic Rulkov neurons. While networks of chaotic Rulkov neurons have been widely studied, systems of nonchaotic Rulkov neurons have not been extensively explored due to the piecewise complexity of the nonchaotic Rulkov map. Here, we find that rich dynamics emerge from the electrical coupling of regular-spiking Rulkov neurons, including chaotic spiking, synchronized chaotic bursting, and synchronized hyperchaos. By systematically varying the electrical coupling strength between neurons, we also uncover general trends in the maximal Lyapunov exponent across the system's dynamical regimes. By means of the Kaplan-Yorke conjecture, we examine the fractal geometry of the ring system's high-dimensional chaotic attractors and find that these attractors can occupy as many as 45 of the 60 dimensions of state space. We further explore how variations in chaotic behavior - quantified by the full Lyapunov spectra - correspond to changes in the attractors' fractal dimensions. This analysis advances our understanding of how complex collective behavior can emerge from the interaction of multiple simple neuron models and highlights the deep interplay between dynamics and geometry in high-dimensional systems.

nlin.CD↗

arXiv2025

Ubiquity of Uncertainty in Neuron Systems

We demonstrate that final-state uncertainty is ubiquitous in multistable systems of coupled neuronal maps, meaning that predicting whether one such system will eventually be chaotic or nonchaotic is often nearly impossible. We propose a "chance synchronization" mechanism that governs the emergence of unpredictability in neuron systems and support it by using basin classification, uncertainty exponent, and basin entropy techniques to analyze five simple discrete-time systems, each consisting of a different neuron model. Our results illustrate that uncertainty in neuron systems is not just a product of noise or high-dimensional complexity; it is also a fundamental property of low-dimensional, deterministic models, which has profound implications for understanding brain function, modeling cognition, and interpreting unpredictability in general multistable systems.

q-bio.NC↗

arXiv2025

Hyperchaos and complex dynamical regimes in $N$-dimensional neuron lattices

We study the dynamics of $N$-dimensional lattices of nonchaotic Rulkov neurons coupled with a flow of electrical current. We consider both nearest-neighbor and next-nearest-neighbor couplings, homogeneous and heterogeneous neurons, and small and large lattices over a wide range of electrical coupling strengths. As the coupling strength is varied, the neurons exhibit a number of complex dynamical regimes, including unsynchronized chaotic spiking, local quasi-bursting, synchronized chaotic bursting, and synchronized hyperchaos. For lattices in higher spatial dimensions, we discover dynamical effects arising from the "destructive interference" of many connected neurons and miniature "phase transitions" from coordinated spiking threshold crossings. In large two- and three-dimensional neuron lattices, we observe emergent dynamics such as local synchronization, quasi-synchronization, and lag synchronization. These results illustrate the rich dynamics that emerge from coupled neurons in multiple spatial dimensions, highlighting how dimensionality, connectivity, and heterogeneity critically shape the collective behavior of neuronal systems.

nlin.CD↗

arXiv2025

Asymmetric coupling of nonchaotic Rulkov neurons: Fractal attractors, quasimultistability, and final state sensitivity

Although neuron models have been well studied for their rich dynamics and biological properties, limited research has been done on the complex geometries that emerge from the basins of attraction and basin boundaries of multistable neuron systems. In this paper, we investigate the geometrical properties of the strange attractors, four-dimensional basins, and fractal basin boundaries of an asymmetrically electrically coupled system of two identical nonchaotic Rulkov neurons. We discover a quasimultistability in the system emerging from the existence of a chaotic spiking-bursting pseudo-attractor, and we classify and quantify the system's basins of attraction, which are found to have complex fractal geometries. Using the method of uncertainty exponents, we also find that the system exhibits extreme final state sensitivity, which results in a dynamical uncertainty that could have important applications in neurobiology.

nlin.CD↗

arXiv2024

Exploring Geometrical Properties of Chaotic Systems Through an Analysis of the Rulkov Neuron Maps

While extensive research has been conducted on chaos emerging from a dynamical system's temporal dynamics, our research examines extreme sensitivity to initial conditions in discrete-time dynamical systems from a geometrical perspective. Specifically, we develop methods of detecting, classifying, and quantifying geometric structures that lead to chaotic behavior in maps, including certain bifurcations, fractal geometry, strange attractors, multistability, fractal basin boundaries, and Wada basins of attraction. We also develop slow-fast dynamical systems theory for discrete-time systems, with a specific application to modeling the spiking and bursting behavior emerging from the electrophysiology of biological neurons. Our research mainly focuses on two simple low-dimensional slow-fast Rulkov maps, which model both non-chaotic and chaotic spiking-bursting neuronal behavior. We begin by exploring the maps' individual dynamics and parameter spaces, performing bifurcation analyses, describing and quantifying their chaotic dynamics, and modeling an injection of current into them. Then, by putting these neurons into different physical arrangements and coupling them with a flow of current, we find that complex dynamics and geometries emerge from the existence of multistability and final state sensitivity in higher-dimensional state space. We then analyze the complexity and fractalization of these coupled neuron systems' attractors and basin boundaries using our mathematical and computational methods. This paper begins with a conversational introduction to the geometry of chaos, then integrates mathematics, physics, neurobiology, computational modeling, and electrochemistry to present original research that provides a novel perspective on how types of geometrical sensitivity to initial conditions appear in discrete-time neuron systems.

nlin.CD↗