Publications

The study of spins and particles on graphs has broad applications, from the dynamics of interacting systems on networks to combinatorial problems. Here, we study the large-nlimit of theO(n) model on graphs, which is considerably more challenging than on regular lattices, as the loss of translational invariance gives rise to an infinite set of saddle point constraints in the thermodynamic limit. We show that the free energy at low and high temperatureTis determined by the spectrum of two fundamental graph-theoretic objects: the Laplacian matrix at lowTand the Adjacency matrix at highT. Their interplay is studied across several classes of graphs. For regular lattices the two coincide. We obtain an exact solution on trees, where the Lagrange multipliers interestingly depend solely on the number of nearest neighbors. We further contrast these classical results with those for a quantum spin model on an exemplary tree. For decorated lattices, the singular part of the free energy is governed by the Laplacian spectrum, whereas this is true for the full free energy only in the zero-temperature limit. Finally, we discuss a bipartite fully connected graph to highlight the importance of a finite coordination number in these results.

The requirement of complete positivity is very often regarded as a fundamental consistency condition for the description of open quantum dynamics. We critically examine this requirement and discuss both its physical motivations and its limitations. We analyse proposals based on restricting the domain of non-completely positive maps to subsets of compatible initial states. Using isotropic states as a concrete example, we show that such domain restrictions become increasingly severe with growing system dimension, revealing an intrinsic weakness of the compatibility-based approach.

We study the out-of-equilibrium dynamics of entanglement fluctuations in the ν=1 quantum symmetric simple exclusion process, a free-fermion chain with hopping amplitudes that are stochastic in time but homogeneous in space. Previous work showed that the average entanglement growth after a quantum quench can be explained in terms of pairs of entangled quasiparticles performing random walks, leading to diffusive entanglement spreading. By incorporating the noise-induced statistical correlations between the quasiparticles, we extend this description to the full-time probability distribution of the entanglement entropy. Our generalized quasiparticle picture allows us to compute the average time evolution of a generic function of the reduced density matrix of a subsystem. We also apply our result to the entanglement asymmetry. This allows us to investigate the restoration of particle-number symmetry in the dynamics from initial states with no well-defined particle number. Regarding the possible existence of the quantum Mpemba effect, our analysis indicates that its occurrence is an extremely fine-tuned phenomenon, requiring very specific conditions and therefore being rather difficult to observe in practice.

We study the entanglement Hamiltonian of an interval for the free massless Dirac field in an inhomogeneous background on a finite segment and in the ground state. We consider a class of metrics that are Weyl equivalent to the flat metric through a Weyl factor that depends only on the spatial coordinate, with the same boundary condition imposed at both endpoints of the segment. The explicit form of the entanglement Hamiltonian is written as the sum of a local and a bilocal term. The weight function of the local term allows us to study a contour function for the entanglement entropies. For the model obtained from the continuum limit of the rainbow chain, the analytic expressions are compared with exact numerical results from the lattice, showing an excellent agreement.

We develop a unified theory of weakly probed differential observables for currents and noise in transport experiments. Our findings uncover a set of universal transport relations between thermoelectric and noise properties of a system probed through a tunnel contact, with the Wiedemann-Franz law being just one example of such universality between charge and heat currents. We apply this theory to various quantum systems, including multichannel Kondo, quantum Hall and Sachdev-Ye-Kitaev quantum dots, resonant impurity, and two-stage Kondo models and demonstrate that each of the microscopic theories is characterized by a set of universal relations connecting conductance and thermoelectrics with noise. Violations of these relations indicate additional energy scales emerging in a system.

We propose a novel, feedback-free method to cancel the effects of dephasing in the dynamics of open quantum systems. The protocol makes use of the coupling with an auxiliary system when they are both subjected to the same noisy dynamics in such a way that their interaction leads to cancellation of the noise on the system itself. This requires tuning the strength of the coupling between the main and auxiliary systems as well as the ability to prepare the auxiliary system in a Fock state, which solely depends on the coupling strength. We investigate the protocol’s efficiency to protect NOON states against dephasing in setups such as tweezer arrays of cold atoms. We show that the protocol’s efficiency is robust against fluctuations of the optimal parameters and, remarkably, that it is independent of the temporal features of the noise. Therefore, it could be applied to cancel both Markovian and non-Markovian dephasing noise, reaching regimes where error-correction protocols become inefficient.

Free fermionic Gaussian, also known as matchgate, random circuits exhibit atypical behavior compared to generic interacting systems. They produce anomalously slow entanglement growth, characterized by diffusive scaling S(t)∼√t, and evolve into volume-law entangled states at late times, S∼N, which are highly unstable under measurements. Here, we investigate how doping such circuits with non-Gaussian resources (gates) restores entanglement structures of typical dynamics. We demonstrate that ballistic entanglement growth S(t)∼t is recovered after injecting an extensive total amount of non-Gaussian gates, which also restores Kardar-Parisi-Zhang fluctuations. When the evolution is perturbed with measurements, we uncover a measurement-induced phase transition between an area-law and a power-law entangled phase, S∼N^α, with α controlled by the doping. A genuine volume-law entangled phase is recovered only when non-Gaussian gates are injected at an extensive rate. Our findings bridge the dynamics of free and interacting fermionic systems, identifying non-Gaussianity as a key resource driving the emergence of nonintegrable behavior.

We investigate the critical behavior of the one-dimensional Ising model with long-range interactions using the functional renormalization group in the local potential approximation (LPA), and compare our findings with Dyson’s hierarchical model (DHM). While the DHM lacks translational invariance, it admits a field-theoretical description closely resembling the LPA, up to minor but nontrivial differences. After reviewing the real-space renormalization group approach to the DHM, we demonstrate a remarkable agreement in the critical exponent ν between the two methods across the entire range of power-law decays 1/2 < σ < 1. We further benchmark our results against Monte Carlo simulations and analytical expansions near the upper boundary of the nontrivial regime, 1

We analyze the validity of the Cutler-Mott relations outside the Landau Fermi-liquid concept. We consider a two-site charge Kondo circuit as a paradigmatic example of a system possessing both Fermi- and non-Fermi-liquid properties. It is shown that the generalized Cutler-Mott-like relations derived in the paper hold in both operating regimes of the charge Kondo quantum circuit, describing a smooth crossover between low- and high-temperature regimes. We discuss the applicability of the generalized Cutler-Mott relations for computing a figure of merit for the non-Fermi-liquid quantum simulators.

We investigate quantum work statistics within the standard two-point measurement scheme in continuously monitored quantum systems, including the effects of generalized unitary evolution, possibly controlled by quantum circuit models, and multiple generalized measurements as well as postselection of no-click trajectories. We derive an explicit expression for the work generating function that naturally incorporates non-Hermitian dynamics arising from quantum jump processes and reveals deviations from the standard Jarzynski equality due to measurement-induced asymmetries. We illustrate our theoretical framework by analyzing a one-dimensional transverse-field Ising model under local spin monitoring. In this model, increased measurement strength projects the system onto the no-click state, leading to a suppression of energy fluctuations and measurement-induced energy saturation, reminiscent of the quantum Zeno effect. Moreover, we find signatures of the measurement-induced transition observed in the no-click limit in the moments of the work distribution.

Hund's metals are strongly correlated systems in which the intra-atomic exchange coupling, known as Hund's coupling, governs electronic properties. By favouring aligned spins in partially filled orbitals, Hund's coupling enhances correlations without leading to full Mott localisation, driving orbital selectivity and suppressing coherence energy scales. In this review, we explore how Hund-driven correlations influence emergent orders. We emphasise the indirect role of Hund's coupling, which can amplify instabilities mediated by spin or orbital fluctuations by modifying both the low-energy electronic spectral weight entering susceptibilities and pairing kernels and the instabilities' effective interaction vertex. We highlight FeSe and Sr (Formula presented.) RuO (Formula presented.) as key materials where Hund-driven mechanisms influence nematic and superconducting behaviour, raising questions about the respective roles of coherent and incoherent electrons and the impact of orbital anisotropy. Finally, we identify open challenges and outline future directions for understanding the interplay between Hund's metals and emergent orders. This review provides a comprehensive framework for understanding Hund's metals and their relevance to broader questions in strongly correlated electron systems.

We study particle and energy transport in an open quantum system consisting of a three-harmonic oscillator chain coupled to thermal baths at different temperatures placed at the ends of the chain. We consider the exact dynamics of the open chain and its so-called local and global Markovian approximations. By comparing them, we show that, while all three yield a divergence-like continuity equation for the probability flow, the energy flow exhibits instead a distinct behavior. The exact dynamics and the local one preserve a standard divergence form for the energy transport, whereas the global open dynamics, due to the rotating wave approximation (RWA), introduces non-divergence sink/source terms. These terms also affect the continuity equation in the case of a master equation obtained through a time-coarse-graining method whereby RWA is avoided through a time-zoom parameter Δt. In such a scenario, sink and source contributions are always present for each Δt>0. While in the limit Δt→+∞ one recovers the global dissipative dynamics, sink and source terms instead vanish when Δt→0, restoring the divergence structure of the exact dynamics. Our results underscore how the choice of the dissipative Markovian approximation to an open system dynamics critically influences the energy transport descriptions, with implications for discriminating among them and thus, ultimately, for the correct modeling of the time-evolution of open quantum many-body systems.

Lagrangians can differ by a total derivative without altering the equations of motion, thus encoding the same physics. This is true both classically and quantum mechanically. We show, however, that in the context of open quantum systems, two Lagrangians that differ by a total derivative can lead to inequivalent reduced dynamics. While these Lagrangians are connected via unitary transformations at the level of the global system-plus-environment description, the equivalence breaks down after tracing out the environment. We argue that only those Lagrangians for which the canonical and mechanical momenta of the system coincide lead to operationally meaningful dynamics. Applying this insight to quantum electrodynamics (QED), we derive the master equation for bremsstrahlung due to an accelerated nonrelativistic electron upto second order in the interaction. The resulting reduced dynamics predicts decoherence in the position basis and closely matches the Caldeira-Leggett form, thus resolving previous discrepancies in the literature. Our findings have implications for both QED and gravitational decoherence, where similar ambiguities arise.

We introduce an efficient method to quantify nonstabilizerness in fermionic Gaussian states, overcoming the long-standing challenge posed by their extensive entanglement. Using a perfect sampling scheme based on an underlying determinantal point process, we compute the Stabilizer Rényi Entropies (SREs) for systems with hundreds of qubits. Benchmarking on random Gaussian states with and without particle conservation, we reveal an extensive leading behavior equal to that of Haar random states, with logarithmic subleading corrections. We support these findings with analytical calculations for a set of related quantities, the participation entropies in the computational (or Fock) basis, for which we derive an exact formula. We also investigate the time evolution of non-stabilizerness in a random unitary circuit with Gaussian gates, observing that it converges in a time that scales logarithmically with the system size. Applying the sampling algorithm to a two-dimensional free-fermionic topological model, we uncover a sharp transition in non-stabilizerness at the phase boundaries, highlighting the power of our approach in exploring different phases of quantum many-body systems, even in higher dimensions.

We investigate fluctuations of electric and heat currents, along with their cross-correlations, in a two-channel charge Kondo circuit driven by either a voltage bias or a temperature gradient applied across the weak link. The ratios of voltage-driven electric/heat noise to the applied voltage V exhibit oscillations with the gate voltage N, resembling the behavior of the thermoelectric coefficient GT. In contrast, the ratios of temperature-driven electric/heat noise to the temperature difference ∆T vary with N in a manner analogous to the thermal coefficient GH or the electric conductance G. The mixed noise, which is defined as the correlation function between electric and heat currents, displays behavior opposite that of the above noises. The logarithmic temperature dependence of these noises signals non-Fermi-liquid behavior, while their oscillations with gate voltage reflect the roles of particle-hole and time-reversal symmetries in thermoelectric transport. Our results demonstrate that the fundamental relations linking voltage- and temperature-induced noises to thermoelectric transport across a tunnel junction persist beyond the Fermi-liquid paradigm.

Understanding the interplay between nonstabilizerness and entanglement is crucial for uncovering the fundamental origins of quantum complexity. Recent studies have proposed entanglement spectral quantities, such as antiflatness of the entanglement spectrum and entanglement capacity, as effective complexity measures, establishing direct connections to stabilizer Rényi entropies. In this work, we systematically investigate quantum complexity across a diverse range of spin models, analyzing how entanglement structure and nonstabilizerness serve as distinctive signatures of quantum phases. By studying entanglement spectra and stabilizer entropy measures, we demonstrate that these quantities consistently differentiate between distinct phases of matter. Specifically, we provide a detailed analysis of spin chains including the XXZ model, the transverse-field XY model, its extension with Dzyaloshinskii-Moriya interactions, as well as the Cluster Ising and Cluster XY models. Our findings reveal that entanglement spectral properties and magic-based measures serve as intertwined, robust indicators of quantum phase transitions, highlighting their significance in characterizing quantum complexity in many-body systems.

We investigate the dynamics of nonstabilizerness-also known as "magic"-in monitored quantum circuits composed of random Clifford unitaries and local measurements. For measurements in the computational basis, we derive an analytical model for dynamics of the stabilizer nullity, showing that it decays in quantized steps and requires exponentially many measurements to vanish, which reveals the strong protection through Clifford scrambling. On the other hand, for measurements performed in rotated non-Clifford bases, measurements can both create and destroy nonstabilizerness. Here, the dynamics leads to a steady state with nontrivial nonstabilizerness, independent of the initial state. We find that Haar-random states equilibrate in constant time, whereas stabilizer states exhibit linear-in-size relaxation time. While the stabilizer nullity is insensitive to the rotation angle, stabilizer Rényi entropies expose a richer structure in their dynamics. Our results uncover sharp distinctions between coarse and fine-grained nonstabilizerness diagnostics and demonstrate how measurements can both suppress and sustain quantum computational resources.

Stability and efficiency are mutually exclusive in a thermodynamic process, e.g., in a thermal machine. Any effort to reduce the fluctuations of a certain output quantity is necessarily accompanied by an increase of entropy production, therefore lowering its efficiency. This interplay is beautifully captured by the so-called thermodynamic uncertainty relations (TURs), which set a lower bound on the relative uncertainty of a current for a given rate of entropy production. Their status in hybrid normal-superconducting (N-S) devices has remained unsettled. We show that, in the subgap regime, departures from the normal quantum TUR are governed by macroscopic superconducting coherence quantified by the pair amplitude, and that introducing a dephasing probe suppresses this coherence and restores the bound. We further derive a hybrid quantum TUR that is general for two-terminal N-S junctions in the Andreev regime: the inequality is never violated, is saturated only at vanishing current, and is related to the normal quantum bound under the replacement e→2e. For N-S quantum dot and Cooper-pair-splitter systems, we compute current and noise and show that deviations from the normal bound track the pair amplitude on the central region. The results establish a direct link between superconducting macroscopic coherence and nonequilibrium fluctuations and supply a general bound for the Andreev regime.