We define a class of machine-learned flow-based sampling algorithms for lattice gauge theories that are gauge invariant by construction. We demonstrate the application of this framework to U(1) gauge ...theory in two spacetime dimensions, and find that, at small bare coupling, the approach is orders of magnitude more efficient at sampling topological quantities than more traditional sampling procedures such as hybrid Monte Carlo and heat bath.
A lattice model for super LLT polynomials Curran, Michael J.; Frechette, Claire; Yost-Wolff, Calvin ...
Combinatorial theory,
09/2023, Letnik:
3, Številka:
2
Journal Article
We present large-scale dynamical simulations of electronic phase separation in the single-band double-exchange model based on deep-learning neural-network potentials trained from small-size exact ...diagonalization solutions. We uncover an intriguing correlation-induced freezing behavior as doped holes are segregated from half filled insulating background during equilibration. While the aggregation of holes is stabilized by the formation of ferromagnetic clusters through Hund's coupling between charge carriers and local magnetic moments, this stabilization also creates confining potentials for holes when antiferromagnetic spin-spin correlation is well developed in the background. The dramatically reduced mobility of the self-trapped holes prematurely disrupts further growth of the ferromagnetic clusters, leading to an arrested phase separation. Implications of our findings for phase separation dynamics in materials that exhibit colossal magnetoresistance effect are discussed.
The Lieb-Robinson theorem states that information propagates with a finite velocity in quantum systems on a lattice with nearest-neighbor interactions. What are the speed limits on information ...propagation in quantum systems with power-law interactions, which decay as 1/rα at distance r? Here, we present a definitive answer to this question for all exponents α > 2d and all spatial dimensions d. Schematically, information takes time at least rmin{1,α−2d} to propagate a distance r. As recent state transfer protocols saturate this bound, our work closes a decades-long hunt for optimal Lieb-Robinson bounds on quantum information dynamics with power-law interactions.
The discovery of graphene has led to the devotion of intensive efforts, theoretical and experimental, to produce two-dimensional (2D) materials that can be used for developing functional materials ...and devices. This work provides a brief review of the recent developments in the lattice models of 2D Dirac materials and their relevant real material counterparts that are crucial for understanding the origins of 2D Dirac cones in electronic band structures as well as their material design and device applications. We focus on the roles of lattice symmetry, atomic orbital hybridization, and spin–orbit coupling in the presence of a Dirac cone. A number of lattice models, such as honeycomb, kagome, ruby, star, Cairo, and line-centered honeycomb, with different symmetries are reviewed based on the tight-binding approach. Inorganic and organic 2D materials, theoretically proposed or experimentally synthesized to satisfy these 2D Dirac lattice models, are summarized.
We develop a mesoscopic lattice model to study the morphology formation in interacting ternary mixtures with the evaporation of one component. As concrete potential application of our model, we wish ...to capture morphologies as they are typically arising during the fabrication of organic solar cells. In this context, we consider an evaporating solvent into which two other components are dissolved, as a model for a 2-component coating solution that is drying on a substrate. We propose a 3-spins dynamics to describe the evolution of the three interacting species. As main tool, we use a Monte Carlo Metropolis-based algorithm, with the possibility of varying the system’s temperature, mixture composition, interaction strengths, and evaporation kinetics. The main novelty is the structure of the mesoscopic model – a bi-dimensional lattice with periodic boundary conditions, divided into square cells to encode a mesoscopic range interaction among the units. We investigate the effect of the model parameters on the structure of the resulting morphologies. Finally, we compare the results obtained with the mesoscopic model with corresponding ones based on an analogous lattice model with a short range interaction among the units, i.e. when the mesoscopic length scale coincides with the microscopic length scale of the lattice.
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