We develop a generalization of the ghost-rotationally-invariant slave-boson (ghost-RISB) method that incorporates local phonon modes coupled to arbitrary on-site electronic degrees of freedom, enabling a nonperturbative treatment of electron-electron and electron-phonon interactions within an efficient variational framework. The method extends the ghost-orbital construction to capture dynamical self-energy effects and phonon-induced renormalizations beyond static slave-boson approaches. Benchmarking against dynamical mean-field theory (DMFT) results for the Hubbard-Holstein model, we find excellent quantitative agreement for electron quasiparticle weights and phonon properties across a wide range of coupling strengths, and it captures accurately the competition between electron-electron and electron-phonon interactions. We show that the inclusion of the ghost orbitals is crucial to accurately describe the regime of low-frequency, strongly dynamical, phonons. The extended ghost-RISB achieves this accuracy at a fraction of the computational cost of DMFT, due to its self-consistency rooted in static observables instead of dynamical ones, enabling rapid exploration of correlated electron-phonon phase diagrams. We exploit this advantage to characterize the most demanding regime of strong coupling and adiabatic phonons. Our analysis shows a suppression of the superconducting order parameter, which is interpreted as a Franck-Condon-like reduction of the overlap between the phonon wavefunctions associated with empty and doubly-occupied sites in the bipolaronic regime.

We study a two-orbital Hubbard-Kanamori model, which has been originally proposed for iron-based superconductors, using variational Monte Carlo. We span the nonmagnetic sector at both hole-doping and electron-doping, with respect to the half-filled case n=2. We report the presence of a superconductive region with a s^± symmetry only when the half-filled system is in a Mott state, while orbital selectivity is absent. These results are qualitatively different from what was reported in the three-orbital Hubbard-Kanamori model, where a more extended superconductive region was observed with a concomitant development of orbital selectivity, and they are to some extent more reminiscent of the single-band Hubbard model.

We characterize the Hall response of non-interacting fermionic M-leg ladders in the presence of an artificial magnetic flux, that can be realized in one-dimensional optical lattices supplemented with a synthetic dimension. We focus on the Hall imbalance, which can be directly measured in experiments with ultracold fermionic atoms. At relatively large synthetic flux we find a dependence of the density that contrasts with previously reported density-independent behavior. In particular, the Hall imbalance can be significantly enhanced in the limit of small density of particles (or holes), or it can vanish and change sign at specific fluxes, which we obtain analytically in the large inter-leg coupling regime. This behavior is explained in terms of Lifshitz transitions of the band structure, where the number of Fermi points changes as a function of the flux and density. Finally, we explore the connection between these transitions and the so-called Meissner-vortex transition for fermionic ladders by computing the site-resolved leg and rung currents and discussing the similarities and differences with the bosonic counterpart.

We study the non-stabilizerness (quantum magic) content of the Hubbard dimer, an analytically solvable, yet completely non-trivial, model of strongly correlated fermions. We can access zero- and finite-temperature properties as well as the time evolution in a quantum quench protocol. We evaluate local and nonlocal non-stabilizerness using both the robustness of magic and the stabilizer Renyi entropy, demonstrating how the latter often fails in detecting the mixed stabilizer states that are typically found in this kind of systems. Finally, we compare the non-stabilizerness with other genuine resources of quantum-state complexity, i.e., the fermionic non-Gaussianity and the superselected two-site entanglement. Our findings corroborate the notion of non-stabilizerness as a fundamentally different quantum resource, able to give profound insights that are missed by more traditional information-theoretic quantities.

When a superconductor is placed in contact with a normal material, Cooper pairs penetrate the latter and induce superconductivity via the proximity effect. Despite its central role in quantum materials, superconducting devices and topological platforms, a predictive first-principles description of the proximity effect at realistic interfaces has remained computationally prohibitive so far. Here, we fill this gap by developing a Green's-function framework based on real-space dynamical embedding that enables first-principles simulations of superconducting proximity in mesoscopic systems. We show that the proximity effect admits a transparent diagrammatic formulation in terms of normal and anomalous embedding self-energies, which disentangle and quantify the distinct renormalization mechanisms generated by coupling to a superconducting bath. By combining this formalism with recursive schemes, we compute local spectral functions and proximity lengths extending over hundreds of nanometers into the bulk without resorting to thick interface slabs. We deploy the approach on tight-binding models (Qi-Hughes-Zhang and Fu-Kane-Mele), where we analyze mixed-parity superconductivity in topological insulators proximitized by s-wave superconductors, and on first-principles simulations of NbSe_2/CrBr_3 heterostructures based on density-functional theory and maximally-localized Wannier functions, the latter enabling direct comparison with scanning tunneling spectroscopy experiments. Our work provides a scalable and conceptually unified framework that bridges microscopic electronic structure and mesoscale proximity physics, enabling predictive atomistic simulations of superconducting interfaces.

The prototypical Mott-Hubbard insulator LaVO3 undergoes a structural phase transition accompanied by the onset of spin and orbital ordering below 140 K. By combining ultrafast optical pump-probe spectroscopy and two-dimensional electronic spectroscopy, we investigate the interplay between fluctuations of the local spin and orbital order parameter and the lifetime of high-energy electron-hole excitations. Specifically, we demonstrate that the pump-induced perturbation of the order parameter leads to a change of the Hubbard exciton decoherence time and, consequently, of its homogeneous linewidth. Dynamical mean-field theory calculations confirm that the exciton scattering rate is crucially affected by the degree of order of the spin and orbital lattices in LaVO3. Our results demonstrate that multi-dimensional ultrafast optical spectroscopy can be used to track the dynamics of the order parameter, thus opening new routes in the study of correlated quantum materials characterized by intertwined orders.

We demonstrate that the local nonfreeness, an unbiased measure of correlation between electrons at a single lattice site, can be computed as the mutual information between local natural spin orbitals. This leads us to prove a general result: local electron correlations in Hubbard-type models that conserve the orbital-and spin-resolved electron number are fully classical since the local reduced density matrix is separable in the natural basis and no quantum correlations beyond entanglement are present. Finally, we compare different theoretical descriptions of magnetic and nonmagnetic states, showing that local classical correlations are drastically influenced by nonlocal processes. These results confirm the relation between local classical correlations within an open system and nonlocal entanglement and they provide a clear path for the study of the relationship between traditional quantum resources and the nonfreeness in terms of experimentally accessible quantities.

We investigate a minimal two-orbital Hubbard model with intra- and inter-orbital nearest-neighbor hopping t and t̃, as well as intra- and inter-orbital density-density interactions U and U' by means of variational ansätze based on Jastrow-Slater wave functions within quantum Monte Carlo techniques. To focus on the electronic mechanisms of superconductivity, we restrict the variational ansätze to uniform nonmagnetic states with an explicit pairing amplitude and compute the pairing correlations as a function of filling and model parameters. At U/t=10, superconducting correlations are highly enhanced by the presence of inter-orbital terms, U' and t̃. For t̃=0, a finite value of U' effectively screens the intra-orbital repulsion U, producing a shift in the superconducting dome. Consequently, inter-orbital repulsion yields a sizable increase in electron pairing compared to the single-orbital baseline. Furthermore, introducing a finite t̃ provides an additional boost to superconducting correlations, an effect driven by the simultaneous presence of flat and broad bands in the electronic structure.

We propose quantum simulation experiments of the Kondo impurity problem using cold alkaline-earth(-like) atoms (AEAs) in a combination of optical lattice and optical tweezer potentials. Within an ab initio model for atomic interactions in the optical potentials, we analyze hallmark signatures of the Kondo effect in a variety of observables accessible in cold-atom quantum simulators. We identify additional terms not part of the textbook Kondo problem, mostly ignored in previous works and giving rise to a direct competition between spin and charge correlations, strongly suppressing Kondo physics. We show that the Kondo effect can be restored by locally adjusting the chemical potential on the impurity site, and we identify realistic parameter regimes and preparation protocols suited to current experiments with AEA arrays. Our work paves the way for quantum simulations of the Kondo problem and offers insights into Kondo physics in unconventional regimes.

Cold-atom experiments based on alkali-like atoms provide us with a tool to experimentally realize Hubbard models with a large number N of components. The value of N can be seen as a new handle to tune the properties of the system, leading to new physics both in the case of fully SU(N) symmetric systems, or in the presence of controlled symmetry breaking. We focus on the Mott transition at global half filling and we characterize local correlations between particles through the inter-flavor mutual information, an experimentally accessible quantity that rigorously measures the distance from the closest gaussian state, unveiling features that cannot be accessed by conventional probes of Mottness. We prove that these correlations are fully independent from local entanglement and quantum discord, and, using Dynamical Mean-Field Theory, we show that the SU(4) system has significantly smaller correlations than the SU(2) counterpart. In the atomic limit we prove that increasing N further decreases the strength of the correlations. This suggests that a controlled reduction of the symmetry, reducing the number of effective components, can be used to enhance the degree of correlation. We confirm this scenario solving the model for N=4 and gradually breaking the symmetry via a Raman field, revealing an evolution from the SU(4) to the SU(2) Mott transition as the symmetry-breaking term increases, with a sudden recovery of the large correlations of the SU(2) model at weak Raman coupling in the Mott state. By further exploring the interplay between energy repulsion and the Raman field, we obtain a rich phase diagram with three different phases – a metal, a band insulator, and a Mott insulator – all coexisting at a single tricritical point.

Altermagnetism, a new phase of collinear spin-order sharing similarities with antiferromagnets and ferromagnets, has introduced a new guiding principle for spintronic/thermoelectric applications due to its direction-dependent magnetic properties. Fulfilling the promise to exploit altermagnetism for device design depends on identifying materials with tuneable transport properties. The search for intrinsic altermagnets has so far focused on the role of anisotropy in the crystallographic symmetries and in the bandstructure. Here, we present a different mechanism that approaches this goal by leveraging the interplay between a Hubbard local repulsion and the itinerant magnetism given by the presence of van Hove singularities. We show that altermagnetism is stable for a broad range of interactions and dopings and we focus on tunability of the spin-charge conversion ratio.

We study a three-orbital Hubbard-Kanamori model relevant for iron-based superconductors using variational wave functions explicitly including spatial correlations and electron pairing. We span the nonmagnetic sector from filling n=4, which is representative of undoped iron-based superconductors, to n=3, where a Mott insulating state with each orbital at half filling is found. In the strong-coupling regime, when the electron density is increased, we find a spontaneous differentiation between the occupation of d_xz and d_yz orbitals, leading to an orbital-selective state with a nematic character that becomes stronger at increasing density. One of these orbitals stays half-filled for all densities while the other one hosts (together with the d_xy orbital) the excess of electron density. Most importantly, in this regime long-range pairing correlations appear in the orbital with the largest occupation. Our results highlight a strong link between orbital-selective correlations, nematicity, and superconductivity, which requires the presence of a significant Hund's coupling.

We present a next-generation version of EDIpack, a flexible, high-performance numerical library using Lanczos-based exact diagonalization to solve generic quantum impurity problems, such as those introduced in Dynamical Mean-Field Theory to describe extended strongly correlated materials. This new release efficiently solves impurity problems allowing for different broken-symmetry solutions, including superconductivity, featuring local spin-orbit coupling and/or electron-phonon coupling. It provides quick access to dynamical correlation functions on the entire complex frequency plane at zero and low-temperatures. The modular architecture of the software not only provides Fortran APIs but also includes bindings to C/C++, interfaces with Python and Julia or with TRIQS and w2dynamics research platforms, thus ensuring unprecedented level of inter-operability. The outlook includes further extensions to study quantum materials and cold atoms quantum simulators, as well as quantum information applications.

We study a two-orbital attractive Hubbard model with a repulsive Hund's exchange coupling J as an idealized model for a two-band superconductor. This framework is motivated by systems where strong isotropic electron-phonon coupling drives the on-site Hubbard repulsion U to negative while leaving the exchange term unaffected. We solve the model at zero temperature and half filling using dynamical mean-field theory, focusing on the intraorbital singlet superconducting phase and discarding other possible instabilities, such as interorbital pairing and charge-density wave ordering. Already at J = 0, the two-orbital model features a superconductor-insulator transition as |U | grows, in contrast to the single-orbital case, which remains superconducting for any U < 0. We find that a finite J strengthens the effect of the attractive U, both in the normal state and, even more significantly, in the superconducting state. However, this pushes the system towards an effectively stronger coupling and hence to a faster transition to the insulating state. Similar to the Mott transition in the repulsive model, the superconductor-insulator transition here is marked by a vanishing quasiparticle weight Z. This leads to a scenario that recalls strongly correlated superconductivity close to a Mott transition, where pairing is enhanced but phase coherence is rapidly lost, even though the present model is dominated by attractive interactions.

Nonadiabatic effects in the electron-phonon coupling are important whenever the ratio between the phononic and the electronic energy scales, the adiabatic ratio, is non negligible. For superconducting systems, this gives rise to additional diagrams in the superconducting self-energy, the vertex and cross corrections. In this work we explore these corrections in a two-dimensional single-band system through the crossover between the weak-coupling BCS and strong-coupling Bose-Einstein regimes. By focusing on the pseudogap phase, we identify the parameter range in which the pairing amplitude is amplified by nonadiabatic effects and map them throughout the BCS-BEC crossover. These effects become stronger as the system is driven deeply in the crossover regime, for phonon frequencies of the order of the hopping energy and for large enough electron-phonon coupling. Finally, we provide the phase space regions in which the effects of nonadiabaticity are more relevant for unconventional superconductors.

Accurate and reliable algorithms to solve complex impurity problems are instrumental to a routine use of quantum embedding methods for material discovery. In this context, we employ an efficient selected configuration-interaction impurity solver to investigate the role of bath discretization-specifically, bath size and parametrization-in Hamiltonian-based cluster dynamical mean-field theory (CDMFT) for the one- and twoorbital Hubbard models. We consider two- and four-site clusters for the single-orbital model and a two-site cluster for the two-orbital model. Our results demonstrate that, for small bath sizes, the choice of parametrization can significantly influence the solution, highlighting the importance of systematic convergence checks. Comparing different bath parametrizations not only reveals the robustness of a given solution but can also provide insights into the nature of different solutions and potential instabilities of the paramagnetic state. We present an extensive analysis of the zero-temperature Mott transition of the paramagnetic half-filled single-band Hubbard model, benchmarking our findings against previous literature. We find that, for the single-band model the dependence on parametrization is weak for the largest bath sizes accessible with ASCI, while a tendency towards a nematic solution can be seen when the bath size is small. Building on this, we extend our study to the multiband regime, where we present a systematic analysis at zero temperature for two orbitals and a two-site cluster. This setup allows us to assess the effect of nearest-neighbor dynamical correlations on the multi-orbital Mott transition. In this case, some quantitative dependence on the parametrization is retained for the two-orbital model, for instance in the value of the critical interaction for a Mott transition.

Quantum vortices are commonly described as funnel-like objects around which the superfluid swirls, and their motion is typically modeled in terms of massless particles. Here we show that in Fermi superfluids the normal component confined in the vortex core provides the vortex with a finite inertial mass. This inertia imparts an unambiguous signature to the dynamic behavior of vortices, specifically manifesting as small-amplitude transverse oscillations which remarkably follow the prediction of a simple point-like model supplemented by an effective mass. We demonstrate this phenomenon through large-scale time-dependent simulations of Fermi superfluids across a wide range of interaction parameters, at both zero and finite temperatures, and for various initial conditions. Our findings pave the way for the exploration of inertial effects in superfluid vortex dynamics.

The possibility to directly measure, in a cold-atom quantum simulator, the von Neumann entropy and mutual information between a site and its environment opens new perspectives on the characterization of the Mott-Hubbard metal-insulator transition, in the framework of quantum information theory. In this work we provide an alternative view of the Mott transition in the two-dimensional Hubbard model in terms of rigorous quasilocal measures of entanglement and correlation between two spatially separated electronic orbitals, with no contribution from their environment. A space-resolved analysis of cluster dynamical mean-field theory results elucidates the prominent role of the nearest-neighbor entanglement in probing Mott localization: both its lower and upper bounds sharply increase at the metal-insulator transition. The two-site entanglement beyond nearest neighbors is shown to be quickly damped as the inter-site distance is increased. These results ultimately resolve a conundrum of previous analyses based on the single-site von Neumann entropy, which has been found to monotonically decrease when the interaction is increased. The quasilocal two-site entanglement recovers instead the distinctive character of Mott insulators as strongly correlated quantum states, demonstrating its central role in the $2d$ Hubbard model.

Topological phase transitions are typically associated with the formation of gapless states. Spontaneous symmetry breaking can lead to a gap opening, thereby obliterating the topological nature of the system. Here we highlight a completely different destiny for a topological transition in the presence of interaction. Solving a Bernevig-Hughes-Zhang model with local interaction, we show that dynamical quantum fluctuations can lead to the opening of a gap without any symmetry breaking. As we vary the interaction and the bare mass of the model, the continuous gapless topological transition turns into a first-order one, associated with the presence of a massive Dirac fermion at the transition point, showing a Gross-Neveu critical behavior near the quantum critical endpoint. We identify the gap opening as a condensed matter analog of the Coleman-Weinberg mechanism of mass generation.

We characterize the dynamical instability responsible for the breakdown of regular rows and necklaces of quantized vortices that appear at the interface between two superfluids in relative motion. Making use of a generalized point-vortex model, we identify several mechanisms leading to the suppression of this instability. They include a non-zero mass of the vortex cores, dissipative processes resulting from the interaction between the vortices and the excitations of the superfluid, and the proximity of the vortex array to the sample boundaries. We show that massive vortex cores not only have a mitigating effect on the dynamical instability, but also change the associated scaling law and affect the direction along which it develops. The predictions of our massive and dissipative point-vortex model are eventually compared against recent experimental measurements of the maximum instability growth rate relevant to vortex necklaces in a cold-atom platform.