Publications

The properties of a strongly correlated many-body quantum system, from the presence of topological order to the onset of quantum criticality, leave a footprint in its entanglement spectrum. The entanglement spectrum is composed by the eigenvalues of the density matrix representing a subsystem of the whole original system, but its direct measurement has remained elusive due to the lack of direct experimental probes. Here we show that the entanglement spectrum of the ground state of a broad class of Hamiltonians becomes directly accessible via the quantum simulation and spectroscopy of a suitably constructed entanglement Hamiltonian, building on the Bisognano–Wichmann theorem of axiomatic quantum field theory. This theorem gives an explicit physical construction of the entanglement Hamiltonian, identified as the Hamiltonian of the many-body system of interest with spatially varying couplings. On this basis, we propose a scalable recipe for the measurement of a system’s entanglement spectrum via spectroscopy of the corresponding Bisognano–Wichmann Hamiltonian realized in synthetic quantum systems, including atoms in optical lattices and trapped ions. We illustrate and benchmark this scenario on a variety of models, spanning phenomena as diverse as conformal field theories, topological order and quantum phase transitions.

We study the holographic entanglement entropy of spatial regions having arbitrary shapes in the AdS4/BCFT3 correspondence with static gravitational backgrounds, focusing on the subleading term with respect to the area law term in its expansion as the UV cutoff vanishes. An analytic expression depending on the unit vector normal to the minimal area surface anchored to the entangling curve is obtained. When the bulk spacetime is a part of AdS4, this formula becomes the Willmore functional with a proper boundary term evaluated on the minimal surface viewed as a submanifold of a three dimensional flat Euclidean space with boundary. For some smooth domains, the analytic expressions of the finite term are reproduced, including the case of a disk disjoint from a boundary which is either flat or circular. When the spatial region contains corners adjacent to the boundary, the subleading term is a logarithmic divergence whose coefficient is determined by a corner function that is known analytically, and this result is also recovered. A numerical approach is employed to construct extremal surfaces anchored to entangling curves with arbitrary shapes. This analysis is used both to check some analytic results and to find numerically the finite term of the holographic entanglement entropy for some ellipses at finite distance from a flat boundary.

The continuous spontaneous localization (CSL) model is the best known and studied among collapse models, which modify quantum mechanics and identify the fundamental reasons behind the unobservability of quantum superpositions at the macroscopic scale. Albeit several tests were performed during the last decade, up to date the CSL parameter space still exhibits a vast unexplored region. Here, we study and propose an unattempted non-interferometric test aimed to fill this gap. We show that the angular momentum diffusion predicted by CSL heavily constrains the parametric values of the model when applied to a macroscopic object.

We analyze a simple implementation of an absorption refrigerator, a system that requires heat and not work to achieve refrigeration, based on two Coulomb-coupled single-electron systems. We analytically determine the general condition to achieve cooling-by-heating, and we determine the system parameters that simultaneously maximize the cooling power and cooling coefficient of performance (COP) finding that the system displays a particularly simple COP that can reach Carnot's upper limit. We also find that the cooling power can be indirectly determined by measuring a charge current. Analyzing the system as an autonomous Maxwell demon, we find that the highest efficiencies for information creation and consumption can be achieved, and we relate the COP to these efficiencies. Finally, we propose two possible experimental setups based on quantum dots or metallic islands that implement the nontrivial cooling condition. Using realistic parameters, we show that these systems, which resemble existing experimental setups, can develop an observable cooling power.

We investigate the emergence of antiferromagnetic ordering and its effect on the helical edge states in a quantum spin Hall insulator, in the presence of strong Coulomb interaction. Using dynamical mean-field theory, we show that the breakdown of lattice translational symmetry favors the formation of magnetic ordering with nontrivial spatial modulation. The onset of a nonuniform magnetization enables the coexistence of spin-ordered and topologically nontrivial states. An unambiguous signature of the persistence of the topological bulk property is the survival of bona fide edge states. We show that the penetration of the magnetic order is accompanied by the progressive reconstruction of gapless states in subperipheral layers, redefining the actual topological boundary within the system.

We investigate a semimetal-superconductor phase transition of two-dimensional Dirac electrons at zero temperature by large-scale and essentially unbiased quantum Monte Carlo simulations for the half-filled attractive Hubbard model on the triangular lattice, in the presence of alternating magnetic π flux, that is introduced to construct two Dirac points in the one-particle bands at the Fermi level. This phase transition is expected to describe quantum criticality of the chiral XY class in the framework of the Gross-Neveu model, where, in the ordered phase, the U(1) symmetry is spontaneously broken and a mass gap opens in the excitation spectrum. We compute the order parameter of the s-wave superconductivity and estimate the quasiparticle weight from the long-distance behavior of the single-particle Green's function. These calculations allow us to obtain the critical exponents of this transition in a reliable and accurate way. Our estimate for the critical exponents is in good agreement with those obtained for a transition to a Kekulé valence bond solid, where an emergent U(1) symmetry is proposed [Z.-X. Li, Nat. Commun. 8, 314 (2017)2041-172310.1038/s41467-017-00167-6].

Figure 6 has a typographical error in the key: The labels corresponding to RWA and without the RWA are wrongly switched. The caption as well as all the rest of the paper are nevertheless correct and unaffected by this error. We show the exact figure here below with its original caption from the paper. (Figure Presented).

In this work we introduce boundary time crystals. Here continuous time-translation symmetry breaking occurs only in a macroscopic fraction of a many-body quantum system. After introducing their definition and properties, we analyze in detail a solvable model where an accurate scaling analysis can be performed. The existence of the boundary time crystals is intimately connected to the emergence of a time-periodic steady state in the thermodynamic limit of a many-body open quantum system. We also discuss connections to quantum synchronization.

We study the electronic thermal drag in two different Coulomb-coupled systems, the first one composed of two Coulomb-blockaded metallic islands and the second one consisting of two parallel quantum wires. The two conductors of each system are electrically isolated and placed in the two circuits (the drive and the drag) of a four-electrode setup. The systems are biased, either by a temperature ΔT or a voltage V difference, on the drive circuit, while no biases are present on the drag circuit. In the case of a pair of metallic islands we use a master equation approach to determine the general properties of the dragged heat current Idrag(h), accounting also for cotunneling contributions and the presence of large biases. Analytic results are obtained in the sequential tunneling regime for small biases, finding, in particular, that Idrag(h) is quadratic in ΔT or V and nonmonotonic as a function of the interisland coupling. Finally, by replacing one of the electrodes in the drag circuit with a superconductor, we find that heat can be extracted from the other normal electrode. In the case of the two interacting quantum wires, using the Luttinger liquid theory and the bosonization technique, we derive an analytic expression for the thermal transresistivity ρ12(h), in the weak-coupling limit and at low temperatures. ρ12(h) turns out to be proportional to the electrical transresistivity, in such a way that their ratio (a kind of Wiedemann-Franz law) is proportional to T3. We find that ρ12(h) is proportional to T for low temperatures and decreases like 1/T for intermediate temperatures or like 1/T3 for high temperatures. We complete our analyses by performing numerical simulations that confirm the above results and allow us to access the strong-coupling regime.

We study by dynamical mean-field theory the ground state of a quarter-filled Hubbard model of two bands with different bandwidths. At half-filling, this model is known to display an orbital selective Mott transition, with the narrower band undergoing Mott localization while the wider one being still itinerant. At quarter-filling, the physical behavior is different and to some extent reversed. The interaction generates an effective crystal field splitting, absent in the Hamiltonian, that tends to empty the narrower band in favor of the wider one, which also become more correlated than the former at odds with the orbital selective paradigm. Upon increasing the interaction, the depletion of the narrower band can continue till it empties completely and the system undergoes a topological Lifshitz transition into a half-filled single-band metal that eventually turns insulating. Alternatively, when the two bandwidths are not too different, a first order Mott transition intervenes before the Lifshitz's one. The properties of the Mott insulator are significantly affected by the interplay between spin and orbital degrees of freedom.

We address the phenomenon of statistical orthogonality catastrophe in insulating disordered systems. In more detail, we analyse the response of a system of non-interacting fermions to a local perturbation induced by an impurity. By inspecting the overlap between the pre- and post-quench many-body ground states we fully characterise the emergent statistics of orthogonality events as a function of both the impurity position and the coupling strength. We consider two well-known one-dimensional models, namely the Anderson and Aubry-André insulators, highlighting the arising differences. Particularly, in the Aubry-André model the highly correlated nature of the quasi-periodic potential produces unexpected features in how the orthogonality catastrophe occurs. We provide a quantitative explanation of such features via a simple, effective model. We further discuss the incommensurate ratio approximation and suggest a viable experimental verification in terms of charge transfer statistics and interferometric experiments using quantum probes.

We study the dynamics of Fermi-Pasta-Ulam (FPU) chains with both harmonic and anharmonic power-law long-range interactions. We show that the dynamics is described in the continuum limit by a Generalized Fractional Boussinesq differential Equation (GFBE), whose derivation is performed in full detail. We also discuss a version of the model where couplings are alternating in sign.

In this article, we provide an overview of the scientific contributions of Frank W. J. Hekking to the fields of mesoscopic electron transport and superconductivity as well as atomic gases. Frank Hekking passed away in May 2017. We hope that the present review gives a faithful testimony of his scientific legacy.

We study the emergent dynamics resulting from the infinite volume limit of the mean-field dissipative dynamics of quantum spin chains with clustering, but not time-invariant states. We focus upon three algebras of spin operators: the commutative algebra of mean-field operators, the quasi-local algebra of microscopic, local operators and the collective algebra of fluctuation operators. In the infinite volume limit, mean-field operators behave as time-dependent, commuting scalar macroscopic averages while quasi-local operators, despite the dissipative underlying dynamics, evolve unitarily in a typical non-Markovian fashion. Instead, the algebra of collective fluctuations, which is of bosonic type with time-dependent canonical commutation relations, undergoes a time-evolution that retains the dissipative character of the underlying microscopic dynamics and exhibits non-linear features. These latter disappear by extending the time-evolution to a larger algebra where it is represented by a continuous one-parameter semigroup of completely positive maps. The corresponding generator is not of Lindblad form and displays mixed quantum-classical features, thus indicating that peculiar hybrid systems may naturally emerge at the level of quantum fluctuations in many-body quantum systems endowed with non time-invariant states.

The interplay between the Kondo effect and magnetic ordering driven by the Ruderman-Kittel-Kasuya-Yosida interaction is studied within the two-dimensional Hubbard-Kondo lattice model. In addition to the antiferromagnetic exchange interaction J between the localized spins and the conduction electrons, this model also contains the local repulsion U between the conduction electrons. We use variational cluster approximation to investigate the competition between the antiferromagnetic phase, the Kondo singlet phase, and a ferrimagnetic phase on square lattice. At half-filling, the Néel antiferromagnetic phase dominates from small to moderate J and UJ, and the Kondo singlet elsewhere. Sufficiently away from half-filling, the antiferromagnetic phase first gives way to a ferrimagnetic phase (in which the localized spins order ferromagnetically, and the conduction electrons do likewise, but the two mutually align antiferromagnetically), and then to the Kondo singlet phase.

A typical working condition in the study of quantum quenches is that the initial state produces a distribution of quasiparticle excitations with an opposite-momentum-pair structure. In this work we investigate the dynamical and stationary properties of the entanglement entropy after a quench from initial states which do not have such structure: instead of pairs of excitations they generate ν-plets of correlated excitations with . Our study is carried out focusing on a system of non-interacting fermions on the lattice. We study the time evolution of the entanglement entropy showing that the standard semiclassical formula is not applicable. We propose a suitable generalisation which correctly describes the entanglement entropy evolution and perfectly matches numerical data. We finally consider the relation between the thermodynamic entropy of the stationary state and the diagonal entropy, showing that when there is no pair structure their ratio depends on the details of the initial state and lies generically between 1/2 and 1.

Using the Dirichlet theorem on the equidistribution of residue classes modulo q and the Lemke Oliver-Soundararajan conjecture on the distribution of pairs of residues on consecutive primes, we show that the domain of convergence of the infinite product of Dirichlet L-functions of non-principal characters can be extended from down to , without encountering any zeros before reaching this critical line. The possibility of doing so can be traced back to a universal diffusive random walk behavior of a series C N over the primes which underlies the convergence of the infinite product of the Dirichlet functions. The series C N presents several aspects in common with stochastic time series and its control requires to address a problem similar to the single Brownian trajectory problem in statistical mechanics. In the case of the Dirichlet functions of non principal characters, we show that this problem can be solved in terms of a self-averaging procedure based on an ensemble of block variables computed on extended intervals of primes. Those intervals, called inertial intervals, ensure the ergodicity and stationarity of the time series underlying the quantity C N. The infinity of primes also ensures the absence of rare events which would have been responsible for a different scaling behavior than the universal law of the random walks.

One of the major goals of quantum thermodynamics is the characterization of irreversibility and its consequences in quantum processes. Here, we discuss how entropy production provides a quantification of the irreversibility in open quantum systems through the quantum fluctuation theorem. We start by introducing a two-time quantum measurement scheme, in which the dynamical evolution between the measurements is described by a completely positive, trace-preserving (CPTP) quantum map (forward process). By inverting the measurement scheme and applying the time-reversed version of the quantum map, we can study how this backward process differs from the forward one. When the CPTP map is unital, we show that the stochastic quantum entropy production is a function only of the probabilities to get the initial measurement outcomes in correspondence of the forward and backward processes. For bipartite open quantum systems we also prove that the mean value of the stochastic quantum entropy production is sub-additive with respect to the bipartition (except for product states). Hence, we find a method to detect correlations between the subsystems. Our main result is the proposal of an efficient protocol to determine and reconstruct the characteristic functions of the stochastic entropy production for each subsystem. This procedure enables to reconstruct even others thermodynamical quantities, such as the work distribution of the composite system and the corresponding internal energy. Efficiency and possible extensions of the protocol are also discussed. Finally, we show how our findings might be experimentally tested by exploiting the state of-the-art trapped-ion platforms.

The dynamical spin structure factor is computed within a variational framework to study the one-dimensional J1-J2 Heisenberg model. Starting from Gutzwiller-projected fermionic wave functions, the low-energy spectrum is constructed from two-spinon excitations. The direct comparison with Lanczos calculations on small clusters demonstrates the excellent description of both gapless and gapped (dimerized) phases, including incommensurate structures for J2/J1>0.5. Calculations on large clusters show how the intensity evolves when increasing the frustrating ratio and give an unprecedented accurate characterization of the dynamical properties of (nonintegrable) frustrated spin models.

A quantum system exhibits off-diagonal long-range order (ODLRO) when the largest eigenvalue λ0 of the one-body-density matrix scales as λ0 ∼ N, where N is the total number of particles. Putting λ0 ∼ N^C to define the scaling exponent C, then C = 1 corresponds to ODLRO and C = 0 to the single-particle occupation of the density matrix orbitals. When 0 < C <1, C can be used to quantify deviations from ODLRO. In this paper we study the exponent C in a variety of one-dimensional bosonic and anyonic quantum systems at T = 0. For the 1D Lieb-Liniger Bose gas we find that for small interactions C is close to 1, implying a mesoscopic condensation, i.e., a value of the zero temperature "condensate" fraction λ0/N appreciable at finite values of N (as the ones in experiments with 1D ultracold atoms). 1D anyons provide the possibility to fully interpolate between C = 1 and 0. The behaviour of C for these systems is found to be non-monotonic both with respect to the coupling constant and the statistical parameter.