Angelo Valli

Superconductivity and nematicity coexist in the phase diagram of many correlated systems, including iron‐based superconductors. We investigate how Hund‐driven correlations reshape boson‐mediated superconductivity in a multiorbital nematic metal. We find that dynamical correlation effects beyond a quasiparticle‐only description are essential to capture the robustness of superconductivity in the Hund regime. In the nematic phase, Hund correlations simultaneously enhance the orbital differentiation of the superconducting gaps and inhibit the most extreme nematic‐driven orbital polarization and coherence collapse that would otherwise suppress pairing at strong coupling. A controlled cutoff analysis reveals a nontrivial, orbital‐dependent buildup of the gaps, indicating that different frequency windows of the correlated spectrum contribute unevenly to pairing in the nematic Hund regime. This implies that pairing mechanisms with different characteristic boson energies can lead to distinct gap structures and trends.

Strongly correlated physics arises from electron-electron scattering within partially filled orbitals. Organic molecules in open-shell configurations are therefore good candidates to exhibit many-body effects. We focus on electron transport in a two-terminal single-molecule junction setup, in which the molecular bridge consists of an organic radical with a molecular orbital hosting a single unpaired electron [singly occupied molecular orbital (SOMO)]. We perform beyond state-of-the-art numerical simulations combining an description of the chemical environment with quantum field-theoretical techniques that account for many-body effects. The key observation is that the SOMO resonance is prone to splitting, and we identify a electronic scattering rate as the driving many-body mechanism, akin to that of the Mott metal-to-insulator transition. By comparing linear and cyclic radicals, we show that the spatial distribution of the SOMO and its projection on the molecular backbone have dramatic consequences for the transport properties of the junction. We argue that the phenomenon and the underlying microscopic mechanism apply to a broad family of open-shell molecular systems, and can explain puzzling experimental observations such as suppressed conductance in radical junctions.

We study the emergence of complexity in deep random N -qubit T -gate-doped Clifford circuits, as reflected in their spectral properties and in magic generation, characterized by the stabilizer Rényi entropy distribution and the nonstabilizing power of the circuit. For pure (undoped) Clifford circuits, a unique periodic orbit structure in the space of Pauli strings implies peculiar spectral correlations and level statistics with large degeneracies. T -gate doping induces an exponentially fast transition to chaotic behavior, described by random matrix theory. We compare these complexity indicators with magic generation properties of the Clifford + T ensemble, and determine the distribution of magic, as well as the average nonstabilizing power of the quantum circuit ensemble. In the dilute limit, N T ≪ N , magic generation is governed by single-qubit behavior. Magic is generated in approximate quanta, increases approximately linearly with the number of T gates, N T , and displays a discrete distribution for small N T . At N T ≈ N , the distribution becomes quasicontinuous, and for N T ≫ N , it converges to that of Haar-random unitaries, and averages to a finite magic density, m 2 , lim N → ∞ 〈 m 2 〉 Haar = 1 . This is in contrast to the spectral transition, where O ( 1 ) T gates suffice to remove spectral degeneracies and to induce a transition to chaotic behavior in the thermodynamic limit. Magic is therefore a more sensitive indicator of complexity.

We investigate numerically the joint distribution of magic (as described by the stabilizer 2-Rényi entropy M 2 ) and entanglement (as described by the von Neumann entropy S ) in N -qubit Haar-random quantum states. The distribution P N ( M 2 , S ) and the marginals become exponentially localized, and centered around the typical values, M 2 ̃ → N − 2 and S ̃ → N / 2 as N → ∞ . Magic and entanglement fluctuations are, however, found to become exponentially uncorrelated. While the set of stabilizer states grows exponentially with N , they nevertheless form a measure-zero subset of Haar-random states and thus occur with vanishing probability. Typical quantum states are characterized by large magic and entanglement entropy, and uncorrelated magic and entanglement fluctuations. The mutual information of the joint distribution vanishes exponentially as N → ∞ , implying that fluctuations of these two resources are not only uncorrelated but asymptotically independent.

We propose a numerical method to efficiently compute quantum generating functions for a wide class of observables in one-dimensional quantum systems at high temperature. We obtain high-accuracy estimates for the cumulants and reconstruct full counting statistics from the quantum generating functions. We demonstrate its potential on spin S = 1 / 2 anisotropic Heisenberg chain, where we can reach timescales hitherto inaccessible to state-of-the-art classical and quantum simulations. Our results challenge the conjecture of the Kardar-Parisi-Zhang universality for isotropic integrable quantum spin chains.