DOE OSTI · 1779375
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Herviou, Loïc (ORCID:0000000342208785), Bardarson, Jens H. (ORCID:0000000333288525), Regnault, Nicolas. 2021-04-21. Many-body localization in a fragmented Hilbert space. https://doi.org/10.1103/physrevb.103.134207
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Here, this work investigates Kolmogorov-Arnold network-based (KAN) wave-function Ansätz as viable representations for quantum Monte Carlo simulations. Through systematic analysis of one-dimensional model systems, we evaluate their computational efficiency and representational power against established methods. Our numerical experiments suggest some efficient training methods and we explore how the computational cost scales with desired precision, particle number, and system parameters. Roughly speaking, KANs seem to be 10 times cheaper computationally than other neural-network-based Ansätz . We also introduce a novel approach for handling strong short-range potentials—a persistent challenge for many numerical techniques—which generalizes efficiently to higher-dimensional, physically relevant systems with short-ranged strong potentials common in atomic and nuclear physics.
Using a computational crystal structure search in the Li-Fe-B ternary system, we predict a stable phase of Li 3 Fe 8 B 8 , featuring 1D channels that enable rapid Li-ion transport. Ab initio molecular dynamics simulations show that the Li-ion diffusion coefficient in Li 3 Fe 8 B 8 surpasses that of common electrode and conductive additive materials by several orders of magnitude. The high diffusion in Li 3 Fe 8 B 8 can be explained by the Frenkel–Kontorova model, which describes an incommensurate state between the Li diffusion chain and the periodic potential field caused by the FeB backbone structure. The favorable lithium-ion diffusivity and mechanical properties of Li 3 Fe 8 B 8 make it a promising conductive additive for battery materials. Furthermore, an external magnetic field can further manipulate the properties of this material due to its predicted itinerant ferromagnetism, which also offers a platform for exploring spin-dependent phenomena.
Density matrix embedding theory (DMET) provides a framework to describe ground-state expectation values in strongly correlated systems, but its extension to dynamical quantities is still an open problem. We show one route to obtaining excitations and dynamical spectral functions by using the techniques of DMET to approximate the matrix elements that arise in a single-mode inspired excitation ansatz. We demonstrate this approach in the one-dimensional Hubbard model, comparing the neutral excitations, single-particle density of states, charge, and spin dynamical structure factors to benchmarks from the Bethe ansatz and density matrix renormalization group. Finally, our work highlights the potential of these ideas in building computationally efficient approaches for dynamical quantities.