Publications

Nonstabilizerness, also colloquially referred to as magic, is a resource for advantage in quantum computing and lies in the access to non-Clifford operations. Developing a comprehensive understanding of how nonstabilizerness can be quantified and how it relates to other quantum resources is crucial for studying and characterizing the origin of quantum complexity. In this work, we establish a direct connection between nonstabilizerness and entanglement spectrum flatness for a pure quantum state. We show that this connection can be exploited to efficiently probe nonstabilizerness even in the presence of noise. Our results reveal a direct connection between nonstabilizerness and entanglement response, and define a clear experimental protocol to probe nonstabilizerness in cold atom and solid-state platforms.

We construct an integrable physical model of a single particle scattering with impurities spread on a circle. The S-matrices of the scattering with the impurities are such that the quantized energies of this system, coming from the Bethe Ansatz equations, correspond to the imaginary parts of the non-trivial zeros of the the Riemann ζ(s) function along the axis of the complex s-plane. A simple and natural generalization of the original scattering problem leads instead to Bethe Ansatz equations whose solutions are the non-trivial zeros of the Dirichlet L-functions again along the axis. The conjecture that all the non-trivial zeros of these functions are aligned along this axis of the complex s-plane is known as the Generalised Riemann Hypothesis (GRH). In the language of the scattering problem analysed in this paper the validity of the GRH is equivalent to the completeness of the Bethe Ansatz equations. Moreover the idea that the validity of the GRH requires both the duality equation (i.e. the mapping s → 1 – s) and the Euler product representation of the Dirichlet L-functions finds additional and novel support from the physical scattering model analysed in this paper. This is further illustrated by an explicit counterexample provided by the solutions of the Bethe Ansatz equations which employ the Davenport-Heilbronn function, i.e. a function whose completion satisfies the duality equation χ(s) = χ(1 – s) but that does not have an Euler product representation. In this case, even though there are infinitely many solutions of the Bethe Ansatz equations along the axis, there are also infinitely many pairs of solutions away from this axis and symmetrically placed with respect to it.

We study the thermalization of the transverse field Ising chain with a power law decaying interaction ∼ 1/rα following a global quantum quench of the transverse field in two different dynamical regimes. The thermalization behavior is quantified by comparing the full probability distribution function (PDF) of the evolving states with the corresponding thermal state given by the canonical Gibbs ensemble (CGE). To this end, we used the matrix product state (MPS)-based Time Dependent Variational Principle (TDVP) algorithm to simulate both real time evolution following a global quantum quench and the finite temperature density operator. We observe that thermalization is strongly suppressed in the region with strong confinement for all interaction strengths α, whereas thermalization occurs in the region with weak confinement.

We study the 1D antiferromagnetic spin-1 Heisenberg XXX model with external magnetic field B and single-ion anisotropy D on finite chains. We determine the nearest and non-nearest neighbor logarithmic entanglement LN. Our main result is the disappearance of LN both for nearest and non-nearest neighbor (next-nearest and next-next-nearest) sites at zero temperature and for low-temperature states. Such disappearance occurs at a critical value of B and D. The resulting phase diagram for the behavior of LN is discussed in the B−D plane, including a separating line – ending in a triple point – where the energy density is independent on the size. Finally, results for LN at finite temperature as a function of B and D are presented and commented.

We compute the form factors of the order and disorder operators, together with those of the stress-energy tensor, of a two-dimensional three-state Potts model with vacancies along its thermal deformation at the critical point. At criticality, the model is described by the non-diagonal partition function of the unitary minimal model M 6 , 7 of conformal field theories and is accompanied by an internal S 3 symmetry. The off-critical thermal deformation is an integrable massive theory that is still invariant under S 3. The presence of infinitely many conserved quantities, whose spin spectrum is related to the exceptional Lie algebra E 6, allows us to determine the analytic S-matrix, the exact mass spectrum and the matrix elements of local operators of this model in an exact non-perturbative way. We use the spectral representation series of the correlators and the fast convergence of these series to compute several universal ratios of the renormalization group.

Following a theoretical proposal on multi-impurity charge Kondo circuits [T. K. T. Nguyen and M. N. Kiselev, Phys. Rev. B 97, 085403 (2018)2469-995010.1103/PhysRevB.97.085403] and the experimental breakthrough in fabrication of the two-site Kondo simulator [W. Pouse, Nat. Phys. 19, 492 (2023)10.1038/s41567-022-01905-4] we investigate a thermoelectric transport through a double-dot charge Kondo quantum nanodevice in the strong coupling operational regime. We focus on the fingerprints of the non-Fermi liquid and its manifestation in the charge and heat quantum transport. We construct a full-fledged quantitative theory describing crossovers between different regimes of the multichannel charge Kondo quantum circuits and discuss possible experimental realizations of the theory.

We study the time evolution of the Rényi entanglement entropies following a quantum quench in a two-dimensional (2D) free fermion system. By employing dimensional reduction, we effectively transform the 2D problem into decoupled chains, a technique applicable when the system exhibits translational invariance in one direction. Various initial configurations are examined, revealing that the behavior of entanglement entropies can often be explained by adapting the one-dimensional quasiparticle picture. However, intriguingly, for specific initial states the entanglement entropy saturates to a finite value without the reduced density matrix converging to a stationary state. We discuss the conditions necessary for a stationary state to exist and delve into the necessary modifications to the quasiparticle picture when such a state is absent.

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 intersite 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.

Topology plays a fundamental role in our understanding of many-body physics, from vortices and solitons in classical field theory to phases and excitations in quantum matter. Topological phenomena are intimately connected to the distribution of information content that, differently from ordinary matter, is now governed by nonlocal degrees of freedom. However, a precise characterization of how topological effects govern the complexity of a many-body state, i.e., its partition function, is presently unclear. In this paper, we show how topology and complexity are directly intertwined concepts in the context of classical statistical mechanics. We concretely present a theory that shows how the Kolmogorov complexity of a classical partition function sampling carries unique, distinctive features depending on the presence of topological excitations in the system. We confront two-dimensional Ising, Heisenberg, and XY models on several topologies and study the corresponding samplings as high-dimensional manifolds in configuration space, quantifying their complexity via the intrinsic dimension. While for the Ising and Heisenberg models the intrinsic dimension is independent of the real-space topology, for the XY model it depends crucially on temperature: across the Berezkinskii-Kosterlitz-Thouless (BKT) transition, complexity becomes topology dependent. In the BKT phase, it displays a characteristic dependence on the homology of the real-space manifold, and, for g-torii, it follows a scaling that is solely genus dependent. We argue that this behavior is intimately connected to the emergence of an order parameter in data space, the conditional connectivity, which displays scaling behavior. Our approach paves the way for an understanding of topological phenomena emergent from many-body interactions from the perspective of Kolmogorov complexity.

Entanglement asymmetry is a novel quantity that, using entanglement methods, measures how much a symmetry is broken in a part of an extended quantum system. So far, it has only been used to characterise the breaking of continuous Abelian symmetries. In this paper, we extend the concept to cyclic Z N groups. As an application, we consider the XY spin chain, in which the ground state spontaneously breaks the Z 2 spin parity symmetry in the ferromagnetic phase. We thoroughly investigate the non-equilibrium dynamics of this symmetry after a global quantum quench, generalising known results for the standard order parameter.

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.

Quantum simulators offer powerful means to investigate strongly correlated quantum matter. However, interpreting measurement outcomes in such systems poses significant challenges. Here, we present a theoretical framework for information extraction in synthetic quantum matter, illustrated for the case of a quantum quench in a spinor Bose-Einstein condensate experiment. Employing nonparametric unsupervised learning tools that provide different measures of information content, we demonstrate a theory-agnostic approach to identify dominant degrees of freedom. This enables us to rank operators according to their relevance, akin to effective field theory. To characterize the corresponding effective description, we then explore the intrinsic dimension of data sets as a measure of the complexity of the dynamics. This reveals a simplification of the data structure, which correlates with the emergence of time-dependent universal behavior in the studied system. Our assumption-free approach can be immediately applied in a variety of experimental platforms.

Interspersing unitary dynamics with local measurements results in measurement-induced phases and transitions in many-body quantum systems. When the evolution is driven by a local Hamiltonian, two types of transitions have been observed, characterized by an abrupt change in the system size scaling of entanglement entropy. The critical point separates the strongly monitored area-law phase from a volume law or a subextensive, typically logarithmiclike, one at low measurement rates. Identifying the key ingredients responsible for the entanglement scaling in the weakly monitored phase is the key purpose of this work. For this purpose, we consider prototypical one-dimensional spin chains with local monitoring featuring the presence/absence of U(1) symmetry, integrability, and interactions. Using exact numerical methods, the system sizes studied reveal that the presence of interaction is always correlated to a volume law weakly monitored phase. In contrast, noninteracting systems present subextensive scaling of entanglement. Other characteristics, namely integrability or U(1) symmetry, do not play a role in the character of the entanglement phase.

We theoretically analyse an autonomous clock comprising a nanoelectromechanical system, which undergoes self-oscillations driven by electron tunnelling. The periodic mechanical motion behaves as the clockwork, similar to the swinging of a pendulum, while induced oscillations in the electrical current can be used to read out the ticks. We simulate the dynamics of the system in the quasi-adiabatic limit of slow mechanical motion, allowing us to infer statistical properties of the clock’s ticks from the current auto-correlation function. The distribution of individual ticks exhibits a tradeoff between accuracy, resolution, and dissipation, as expected from previous literature. Going beyond the distribution of individual ticks, we investigate how clock accuracy varies over different integration times by computing the Allan variance. We observe non-monotonic features in the Allan variance as a function of time and applied voltage, which can be explained by the presence of temporal correlations between ticks. These correlations are shown to yield a precision advantage for timekeeping over the timescales that the correlations persist. Our results illustrate the non-trivial features of the tick series produced by nanoscale clocks, and pave the way for experimental investigation of clock thermodynamics using nanoelectromechanical systems.

The dynamics of a quantum system, undergoing unitary evolution and continuous monitoring, can be described in term of quantum trajectories. Although the averaged state fully characterizes expectation values, the entire ensemble of stochastic trajectories goes beyond simple linear observables, keeping a more attentive description of the entire dynamics. Here we go beyond the Lindblad dynamics and study the probability distribution of the expectation value of a given observable over the possible quantum trajectories. The measurements are applied to the entire system, having the effect of projecting the system into a product state. We develop an analytical tool to evaluate this probability distribution at any time t. We illustrate our approach by analyzing two paradigmatic examples: a single qubit subjected to magnetization measurements, and a free hopping particle subjected to position measurements.

We study the Rényi entanglement entropies along the massless renormalisation group flow that connects the tricritical and critical Ising field theories. Similarly to the massive integrable field theories, we derive a set of bootstrap equations, from which we can analytically calculate the twist field form factors in a recursive way. Additionally, we also obtain them as a non-trivial ‘roaming limit’ of the sinh-Gordon theory. Then the Rényi entanglement entropies are obtained as expansions in terms of the form factors of these branch point twist fields. We find that the form factor expansion of the entanglement entropy along the flow organises in two different kind of terms. Those that couple particles with the same chirality, and reproduce the entropy of the infrared Ising theory, and those that couple particles with different chirality, which provide the ultraviolet contributions. The massless flow under study possesses a global ℤ2 spin-flip symmetry. We further consider the composite twist fields associated to this group, which enter in the study of the symmetry resolution of the entanglement. We derive analytical expressions for their form factors both from the bootstrap equations and from the roaming limit of the sinh-Gordon theory.

We investigate how entanglement in the mixed state of a quantum field theory can be described using the cross-computable norm or realignment (CCNR) criterion, employing a recently introduced negativity. We study its symmetry resolution for two disjoint intervals in the ground state of the massless Dirac fermion field theory, extending previous results for the case of adjacent intervals. By applying the replica trick, this problem boils down to computing the charged moments of the realignment matrix. We show that, for two disjoint intervals, they correspond to the partition function of the theory on a torus with a non-contractible charged loop. This confers a great advantage compared to the negativity based on the partial transposition, for which the Riemann surfaces generated by the replica trick have higher genus. This result empowers us to carry out the replica limit, yielding analytic expressions for the symmetry-resolved CCNR negativity. Furthermore, these expressions provide also the symmetry decomposition of other related quantities such as the operator entanglement of the reduced density matrix or the reflected entropy.

The presence of gauge symmetry in 1+1 dimensions is known to be redundant, since it does not imply the existence of dynamical gauge bosons. As a consequence, in the continuum, the Abelian-Higgs model (i.e., the theory of bosonic matter interacting with photons) just possesses a single phase, as the higher-dimensional Higgs and Coulomb phases are connected via nonperturbative effects. However, recent research published in Phys. Rev. Lett. 128, 090601 (2022)0031-900710.1103/PhysRevLett.128.090601 has revealed an unexpected phase transition when the system is discretized on the lattice. This transition is described by a conformal field theory with a central charge of c=3/2. In this paper, we aim to characterize the two components of this c=3/2 theory - namely the free Majorana fermionic and bosonic parts - through equilibrium and out-of-equilibrium spectral analyses.

Although different architectures of quantum perceptrons have been recently put forward, the capabilities of such quantum devices versus their classical counterparts remain debated. Here, we consider random patterns and targets independently distributed with biased probabilities and investigate the storage capacity of a continuous quantum perceptron model that admits a classical limit, thus facilitating the comparison of performances. Such a more general context extends a previous study of the quantum storage capacity where using statistical mechanics techniques in the limit of a large number of inputs, it was proved that no quantum advantages are to be expected concerning the storage properties. This outcome is due to the fuzziness inevitably introduced by the intrinsic stochasticity of quantum devices. We strengthen such an indication by showing that the possibility of indefinitely enhancing the storage capacity for highly correlated patterns, as it occurs in a classical setting, is instead prevented at the quantum level.

In this chapter, we review recent advances in the theoretical, numerical, and experimental studies of critical Casimir forces in soft matter, with particular emphasis on their relevance for the structures of colloidal suspensions and on their dynamics. Distinct from other interactions which act in soft matter, such as electrostatic and van der Waals forces, critical Casimir forces are effective interactions characterized by the possibility to control reversibly their strength via minute temperature changes, while their attractive or repulsive character is conveniently determined via surface treatments or by structuring the involved surfaces. These features make critical Casimir forces excellent candidates for controlling the equilibrium and dynamical properties of individual colloids or colloidal dispersions as well as for possible applications in micro-mechanical systems. In the past 25 years, a number of theoretical and experimental studies have been devoted to investigate these forces primarily under thermal equilibrium conditions, while their dynamical and non-equilibrium behavior is a largely unexplored subject open for future investigations.