Publications

The tensor cross interpolation (TCI) algorithm is a rank-revealing algorithm for decomposing low-rank, high-dimensional tensors into tensor trains/matrix product states (MPS). TCI learns a compact MPS representation of the entire object from a tiny training data set. Once obtained, the large existing MPS toolbox provides exponentially fast algorithms for performing a large set of operations. We discuss several improvements and variants of TCI. In particular, we show that replacing the cross interpolation by the partially rank-revealing LU decomposition yields a more stable and more flexible algorithm than the original algorithm. We also present two open source libraries, xfac in Python/C++ and this http URL in Julia, that implement these improved algorithms, and illustrate them on several applications. These include sign-problem-free integration in large dimension, the superhigh-resolution quantics representation of functions, the solution of partial differential equations, the superfast Fourier transform, the computation of partition functions, and the construction of matrix product operators.

We propose exchanging the energy functionals in ground-state DFT with physically equivalent exact force expressions as a new promising route towards approximations to the exchange-correlation potential and energy. In analogy to the usual energy-based procedure, we split the force difference between the interacting and auxiliary Kohn-Sham system into a Hartree, an exchange, and a correlation force. The corresponding scalar potential is obtained by solving a Poisson equation, while an additional transverse part of the force yields a vector potential. These vector potentials obey an exact constraint between the exchange and correlation contribution and can further be related to the atomic-shell structure. Numerically, the force-based local-exchange potential and the corresponding exchange energy compare well with the numerically more involved optimized effective-potential method. Overall, the force-based method has several benefits when compared to the usual energy-based approach and opens a route towards numerically inexpensive non-local and (in the time-dependent case) non-adiabatic approximations.

We report the first ab initio, non-relativistic QED method that couples light and matter self-consistently beyond the electric dipole approximation and without multipolar truncations. This method is based on an extension of the Maxwell-Pauli-Kohn-Sham approach to a full minimal coupling Hamiltonian, where the space- and time-dependent vector potential is coupled to the matter system, and its back-reaction to the radiated fields is generated by the full current density. The implementation in the open-source Octopus code is designed for massively-parallel multiscale simulations considering different grid spacings for the Maxwell and matter subsystems. Here, we show the first applications of this framework to simulate renormalized Cherenkov radiation of an electronic wavepacket, magnetooptical effects with non-chiral light in non-chiral molecular systems, and renormalized plasmonic modes in a nanoplasmonic dimer. We show that in some cases the beyond-dipole effects can not be captured by a multipolar expansion Hamiltonian in the length gauge. Finally, we discuss further opportunities enabled by the framework in the field of twisted light and orbital angular momentum, inelastic light scattering and strong field physics.

We show that in models with the Hatsugai-Kohmoto type of interaction that is local in momentum space thus infinite-range in real space, Kubo formulas neither reproduce the correct thermodynamic susceptibilities, nor yield sensible transport coefficients. Using Kohn's trick to differentiate between metals and insulators by threading a flux in a torus geometry, we uncover the striking property that Hatsugai-Kohmoto models with an interaction-induced gap in the spectrum sustain a current that grows as the linear size at any non-zero flux and which can be either diamagnetic or paramagnetic.

Despite recent numerical evidence, one of the fundamental theoretical mysteries of polaritonic chemistry is how and if collective strong coupling can induce local changes of the electronic structure to modify chemical properties. Here we present non-perturbative analytic results for a model system consisting of an ensemble of N harmonic molecules under vibrational strong coupling (VSC) that alters our present understanding of this fundamental question. By applying the cavity Born-Oppenheimer partitioning on the Pauli-Fierz Hamiltonian in dipole approximation, the dressed many-molecule problem can be solved self-consistently and analytically in the dilute limit. We discover that the electronic molecular polarizabilities are modified even in the case of vanishingly small single-molecule couplings. Consequently, this non-perturbative local polarization mechanism persists even in the large-N limit. In contrast, a perturbative calculation of the polarizabilities leads to a qualitatively erroneous scaling behavior with vanishing effects in the large-N limit. Nevertheless, the exact (self-consistent) polarizabilities can be determined from single-molecule strong coupling simulations instead. Our fundamental theoretical observations demonstrate that hitherto existing collective-scaling arguments are insufficient for polaritonic chemistry and they pave the way for refined single- (or few-) molecule strong-coupling ab-initio simulations of chemical systems under collective strong coupling.

In strongly correlated materials, interacting electrons are entangled and form collective quantum states, resulting in rich low-temperature phase diagrams. Notable examples include cuprate superconductors, in which superconductivity emerges at low doping out of an unusual

While superconductors are conventionally established by attractive interactions, higher-temperature mechanisms for emergent electronic pairing from strong repulsive electron-electron interactions remain under considerable scrutiny. Here, we establish a strong-coupling mechanism for intertwined superconductivity and magnetic order from purely repulsive interactions in a Kondo-like bilayer system, composed of a two-dimensional Mott insulator coupled to a layer of weakly-interacting itinerant electrons. Combining large scale DMRG and Monte Carlo simulations, we find that superconductivity persists and coexists with magnetism over a wide range of interlayer couplings. We classify the resulting rich phase diagram and find 2-rung antiferromagnetic and 4-rung antiferromagnetic order in one-dimensional systems along with a phase separation regime, while finding that superconductivity coexists with either antiferromagnetic or ferromagnetic order in two dimensions. Remarkably, the model permits a rigorous strong-coupling analysis via localized spins coupled to charge-2e bosons through Kugel-Khomskii interactions, capturing the pairing mechanism in the presence of magnetism due to emergent attractive interactions. Our numerical analysis reveals that pairing remains robust well beyond the strong-coupling regime, establishing a new mechanism for superconductivity in coupled weakly- and strongly-interacting electron systems, relevant for infinite-layer nickelates and superconductivity in moire multilayer heterostructures.

Moiré transition metal dichalcogenide (TMD) systems provide a tunable platform for studying electron-correlation driven quantum phases. Such phases have so far been found at rational fillings of the moiré superlattice, and it is believed that lattice commensurability plays a key role in their stability. In this work, we show via magnetotransport measurements on twisted WSe2 that new correlated electronic phases can exist away from commensurability. The first phase is an antiferromagnetic metal that is driven by proximity to the van Hove singularity. The second is a re-entrant magnetic field-driven insulator. This insulator is formed from a small and equal density of electrons and holes with opposite spin projections - an Ising excitonic insulator.

Two dimensional materials subject to long-wavelength modulations have emerged as novel platforms to study topological and correlated quantum phases. In this article, we develop a versatile and computationally inexpensive method to predict the topological properties of materials subjected to a superlattice potential by combining degenerate perturbation theory with the method of symmetry indicators. In the absence of electronic interactions, our analysis provides a systematic rule to find the Chern number of the superlattice-induced miniband starting from the harmonics of the applied potential and a few material-specific coefficients. Our method also applies to anomalous (interaction-generated) bands, for which we derive an efficient algorithm to determine all Chern numbers compatible with a self-consistent solution to the Hartree-Fock equations. Our approach gives a microscopic understanding of the quantum anomalous Hall insulators recently observed in rhombohedral graphene multilayers.

Quantum simulators have the potential to solve quantum many-body problems that are beyond the reach of classical computers, especially when they feature long-range entanglement. To fulfill their prospects, quantum simulators must be fully controllable, allowing for precise tuning of the microscopic physical parameters that define their implementation. We consider Rydberg-atom arrays, a promising platform for quantum simulations. Experimental control of such arrays is limited by the imprecision on the optical tweezers positions when assembling the array, hence introducing uncertainties in the simulated Hamiltonian. In this work, we introduce a scalable approach to Hamiltonian learning using graph neural networks (GNNs). We employ the Density Matrix Renormalization Group (DMRG) to generate ground-state snapshots of the transverse field Ising model realized by the array, for many realizations of the Hamiltonian parameters. Correlation functions reconstructed from these snapshots serve as input data to carry out the training. We demonstrate that our GNN model has a remarkable capacity to extrapolate beyond its training domain, both regarding the size and the shape of the system, yielding an accurate determination of the Hamiltonian parameters with a minimal set of measurements. We prove a theorem establishing a bijective correspondence between the correlation functions and the interaction parameters in the Hamiltonian, which provides a theoretical foundation to our learning algorithm. Our work could open the road to feedback control of the positions of the optical tweezers, hence providing a decisive improvement of analog quantum simulators.