arXiv subjects

Tiago V. C. Antão

Publications and source records attributed to Tiago V. C. Antão.

7 recordsLinked to original sources

arXiv2026

Tensor-network methodology for real-space super-moiré excitons

Computing excitonic spectra in quasicrystal and super-moiré systems constitutes a formidable challenge due to the exceptional size of the excitonic Hilbert space. Here, we demonstrate a tensor-network method for the real-space Bethe-Salpeter Hamiltonian, allowing us to access the spectra of an excitonic $10^{18}$-dimensional Hamiltonian, and enabling the direct computation of bound-exciton spectral functions for systems exceeding one billion lattice sites, several orders of magnitude beyond the capabilities of conventional approaches. Our method combines a tensor-network encoding of the real-space Bethe-Salpeter Hamiltonian with a Chebyshev tensor network algorithm. This strategy bypasses explicit storage of the Hamiltonian while preserving full real-space resolution across widely different length scales. We demonstrate our methodology for one- and two-dimensional super-moiré systems, achieving the simultaneous resolution of atomistic and mesoscopic structures in the excitonic spectra in billion-size systems, showing exciton miniband formation and moiré-induced spatial confinement. Our results establish a real-space methodology enabling the simulation of excitonic physics in large-scale quasicrystal and super-moiré quantum matter.

cond-mat.str-el↗

arXiv2026

Observation of electromagnons in a monolayer multiferroic

Van der Waals multiferroics have emerged as a promising platform to explore novel magnetoelectric phenomena. Recently, it has been shown that monolayer NiI$_2$ hosts robust type-II multiferroicity down to the two-dimensional limit, a giant dynamical magnetoelectric coupling at terahertz frequencies, and an electrically switchable spin polarization. These developments present the possibility of engineering ultrafast, low-energy-consumption, and electrically-tunable spintronic devices based on the collective excitations of the multiferroic order, electromagnons. However, the direct visualization of these bosonic modes in real space and within the monolayer limit remains elusive. Here, we report the atomic-scale observation of electromagnons in monolayer NiI$_2$ using low-temperature scanning tunneling microscopy. By tracking the thermal evolution of the multiferroic phase, we establish the energy scale and resolve coherent in-gap excitations of the symmetry-broken multiferroic state. Comparison with first-principles and spin-model calculations reveals that the low-energy modes originate from electromagnon excitations. Spatially resolved inelastic tunneling spectroscopy maps show a stripe-like modulation of the local spectral function at electromagnon energies, matching theoretical predictions. These results provide direct evidence of the internal structure of electromagnons and establish a methodology to probe these modes at the atomic scale, opening avenues for electrically tunable spintronics.

cond-mat.mtrl-sci↗

arXiv2026

Tensor network solvers for ultra-large tight-binding Hamiltonians: algorithms and applications

Understanding quantum materials at meso and even macroscopic scales requires tight-binding calculations on system sizes where explicit matrix representations become prohibitively costly. This represents a major bottleneck to rationalize phenomena in moiré and super-moiré heterostructures and quasicrystals. Here, we present a unified tensor-network methodology to solve tight-binding problems at exceptionally large scales, by mapping a system of $N = 2^L$ sites onto a many-body problem of $L$ pseudospin sites, which is subsequently solved with tensor network algorithms. For Hamiltonians with compressible real-space structure, the tensor network bond dimension remains modest, typically of order a few tens, independent of $N$. Tensor network representations of arbitrary hopping functions including long-range, spatially modulated, and twisted-layer couplings are built with quantics tensor cross interpolation, and all physical observables are evaluated entirely with tensor network algebra without explicit matrix storage or diagonalization. We demonstrate applications to spectral functions, momentum-space spectra via the tensor-network quantum Fourier transform, real-space topological invariants, real-time dynamics, correlation induced symmetry breaking with self-consistent mean-field calculations, non-Hermitian phenomena, and excitonic many-body physics. Our methodology enables routinely solving systems with billions of sites, by leveraging the tensor network compressibility of real-space structures, and establishing a flexible framework to study quantum matter at ultra-large length scales. The methodology is implemented in the open-source Julia package TensorBinding.

cond-mat.str-el↗

arXiv2026

Tensor network approach to momentum-resolved spectroscopy in non-periodic super-moiré systems

Computing spectral functions in large, non-periodic super-moiré systems remains an open problem due to the exceptionally large system size that must be considered. Here, we establish a tensor network methodology that allows computing momentum-resolved spectral functions of non-interacting and interacting super-moiré systems at an atomistic level. Our methodology relies on encoding an exponentially large tight-binding problem as an auxiliary quantum many-body problem, solved with a many-body kernel polynomial tensor network algorithm combined with a quantum Fourier transform tensor network. We demonstrate the method for one and two-dimensional super-moiré systems, including super-moiré with non-uniform strain, interactions treated at the mean-field level, and quasicrystalline super-moiré patterns. Furthermore, we demonstrate that our methodology allows us to compute momentum-resolved spectral functions restricted to selected regions of a super-moiré, enabling direct imaging of position-dependent electronic structure and minigaps in super-moiré systems with non-uniform strain. Our results establish a powerful methodology to compute momentum-resolved spectral functions in exceptionally large super-moiré systems, providing a tool to directly model quantum twisting microscope experiments in twisted van der Waals heterostructures.

cond-mat.str-el↗

arXiv2025

Self-consistent tensor network method for correlated super-moiré matter beyond one billion sites

Moiré and super-moiré materials provide exceptional platforms to engineer exotic correlated quantum matter. The vast number of sites required to model moiré systems in real space remains a formidable challenge due to the immense computational resources required. Super-moiré materials push this requirement to the limit, where millions or even billions of sites need to be considered, a requirement beyond the capabilities of conventional methods for interacting systems. Here, we establish a methodology that allows solving correlated states in systems reaching a billion sites, that exploits tensor-network representations of real-space Hamiltonians and self-consistent real-space mean-field equations. Our method combines a tensor-network kernel polynomial method with quantics tensor cross interpolation algorithm, enabling us to solve exponentially large models, including those whose single particle Hamiltonian is too large to be stored explicitly. We demonstrate our methodology with super-moiré systems featuring spatially modulated hoppings, many-body interactions and domain walls, showing that it allows access to self-consistent symmetry broken states and spectral functions of real-space models reaching a billion sites. Our methodology provides a strategy to solve exceptionally large interacting problems, providing a widely applicable strategy to compute correlated super-moiré quantum matter.

cond-mat.str-el↗

arXiv2025

Tensor network method for real-space topology in quasicrystal Chern mosaics

Computing topological invariants in two-dimensional quasicrystals and super-moire matter is a remarkable open challenge, due to the absence of translational symmetry and the colossal number of sites inherent to these systems. Here, we establish a method to compute local topological invariants of exceptionally large systems using tensor networks, enabling the computation of invariants for Hamiltonians with hundreds of millions of sites, several orders of magnitude above the capabilities of conventional methodologies. Our approach leverages a tensor-network representation of the density matrix using a Chebyshev tensor network algorithm, enabling large-scale calculations of topological markers in quasicrystalline and moire systems. We demonstrate our methodology with two-dimensional quasicrystals featuring $C_8$ and $C_{10}$ rotational symmetries and mosaics of Chern phases. Our work establishes a powerful method to compute topological phases in exceptionally large-scale topological systems, providing the required tool to rationalize generic supe-moire and quasicrystalline topological matter.

cond-mat.str-el↗

arXiv2024

Electric field control of moiré skyrmion phases in twisted multiferroic NiI$_2$ bilayers

Twisted magnetic van der Waals materials provide a flexible platform to engineer new forms of unconventional magnetism. Here we demonstrate the emergence of electrically tunable topological moiré magnetism in twisted bilayers of the spin-spiral multiferroic NiI$_2$. We establish a rich phase diagram featuring uniform spiral phases, a variety of $kπ$-skyrmion lattices, and nematic spin textures ordered at the moiré scale. The emergence of these phases is driven by the local stacking and the resulting modulated frustration in the spin spiral stemming from the moiré pattern. Notably, when the spin-spiral wavelength is commensurate with the moiré length scale by an integer $k$, multi-walled skyrmions become pinned to the moiré pattern. We show that the strong magnetoelectric coupling displayed by the moiré multiferroic allows the electric control of the $kπ$-skyrmion lattices by an out-of-plane electric field, which couples to the moiré-induced electric polarization. While adiabatic changes in the electric field preserve the topology of the spin configurations, abrupt variations can trigger transitions between different skyrmion lattice ground states. Our results establish a highly tunable platform for skyrmionics based on twisted van der Waals multiferroics, potentially enabling a new generation of ultrathin topologically-protected spintronic devices.

cond-mat.str-el↗