Publications

The effectiveness of the variational approach à la Feynman is proved in the spin-boson model, i.e., the simplest realization of the Caldeira-Leggett model able to reveal the quantum phase transition from delocalized to localized states and the quantum dissipation and decoherence effects induced by a heat bath. After exactly eliminating the bath degrees of freedom, we propose a trial, nonlocal in time, interaction between the spin and itself simulating the coupling of the two-level system with the bosonic bath. It stems from a Hamiltonian where the spin is linearly coupled to a finite number of harmonic oscillators whose frequencies and coupling strengths are variationally determined. We show that a very limited number of these fictitious modes is enough to get a remarkable agreement, up to very low temperatures, with the data obtained by using an approximation-free Monte Carlo approach, predicting (1) in the Ohmic regime, a Berezinski-Thouless-Kosterlitz quantum phase transition exhibiting the typical universal jump at the critical value; and (2) in the sub-Ohmic regime (s?0.5), mean-field quantum phase transitions, with logarithmic corrections for s=0.5.

We employ a quantum trajectory approach to characterize synchronization and phase-locking between open quantum systems in nonequilibrium steady states. We exemplify our proposal for the paradigmatic case of two quantum Van der Pol oscillators interacting through dissipative coupling. We show the deep impact of synchronization on the statistics of phase-locking indicators and other correlation measures defined for single trajectories, spotting a link between the presence of synchronization and the emergence of large tails in the probability distribution for the entanglement along trajectories. Our results shed light on fundamental issues regarding quantum synchronization providing methods for its precise quantification.

One of the most significant drawbacks of the all-electron ab initio diffusion Monte Carlo (DMC) is that its computational cost drastically increases with the atomic number (Z), which typically scales with Z∼6. In this study, we introduce a very efficient implementation of the lattice regularized diffusion Monte Carlo (LRDMC), where the conventional time discretization is replaced by its lattice space counterpart. This scheme enables us to conveniently adopt a small lattice space in the vicinity of nuclei, and a large one in the valence region, by which a considerable speedup is achieved, especially for large atomic number Z. Indeed, the computational performances of the improved LRDMC can be theoretically established based on the Thomas-Fermi model for heavy atoms, implying the optimal Z∼5 scaling for all-electron DMC calculations. This improvement enables us to apply the DMC technique even for superheavy elements (Z≥104), such as oganesson (Z=118), which has the highest atomic number of all synthesized elements so far.

We discuss a scheme for macrorealistic theories of the Leggett-Garg form (Leggett and Garg 1985 Phys. Rev. Lett. 54 857). Our scheme is based on a hybrid optomechanical system. It seems reasonable to test these inequalities with an optomechanical system, since in an optomechanical cavity it is possible to create non-classical states of the mirror through a projective measurement on the cavity field. We will present the protocol to generate such non-classicality for a general optomechanical cavity and after we will carry out a theoretical test for one of the possible formulations of these inequalities using a hybrid optomechanical system. Specifically, the inequality will be investigated for an harmonic oscillator coupled to a two-level system, which replaces the light field of the cavity. The aim is to reproduce, with this system, the evolution of a single spin-1/2 for which the inequality is violated; this is achievable through the conditioning of the two-level system which will be used as an ancilla.

The study of critical properties of systems with long-range interactions has attracted, in recent decades, a continuing interest and motivated the development of several analytical and numerical techniques, in particular in connection with spin models. From the point of view of the investigation of their criticality, a special role is played by systems in which the interactions are long-range enough that their universality class is different from the short-range case and, nevertheless, they maintain the extensivity of thermodynamical quantities. Such interactions are often called weak long-range. In this paper we focus on the study of the critical behaviour of spin systems with weak-long range couplings using functional renormalization group, and we review their remarkable properties. For the sake of clarity and self-consistency, we start from classical spin models and we then move to quantum spin systems.

Physical systems made of many interacting quantum particles can often be described by Euler hydrodynamic equations in the limit of long wavelengths and low frequencies. Recently such a classical hydrodynamic framework, now dubbed generalized hydrodynamics (GHD), was found for quantum integrable models in one spatial dimension. Despite its great predictive power, GHD, like any Euler hydrodynamic equation, misses important quantum effects, such as quantum fluctuations leading to nonzero equal-time correlations between fluid cells at different positions. Focusing on the one-dimensional gas of bosons with delta repulsion, and on states of zero entropy, for which quantum fluctuations are larger, we reconstruct such quantum effects by quantizing GHD. The resulting theory of quantum GHD can be viewed as a multicomponent Luttinger liquid theory, with a small set of effective parameters that are fixed by the thermodynamic Bethe ansatz. It describes quantum fluctuations of truly nonequilibrium systems where conventional Luttinger liquid theory fails.

We carry out a comprehensive comparison between the exact modular Hamiltonian and the lattice version of the Bisognano-Wichmann (BW) one in one-dimensional critical quantum spin chains. As a warm-up, we first illustrate how the trace distance provides a more informative mean of comparison between reduced density matrices when compared to any other Schatten n-distance, normalized or not. In particular, as noticed in earlier works, it provides a way to bound other correlation functions in a precise manner, i.e., providing both lower and upper bounds. Additionally, we show that two close reduced density matrices, i.e. with zero trace distance for large sizes, can have very different modular Hamiltonians. This means that, in terms of describing how two states are close to each other, it is more informative to compare their reduced density matrices rather than the corresponding modular Hamiltonians. After setting this framework, we consider the ground states for infinite and periodic XX spin chain and critical Ising chain. We provide robust numerical evidence that the trace distance between the lattice BW reduced density matrix and the exact one goes to zero as `<sup>-2</sup> for large length of the interval `. This provides strong constraints on the difference between the corresponding entanglement entropies and correlation functions. Our results indicate that discretized BW reduced density matrices reproduce exact entanglement entropies and correlation functions of local operators in the limit of large subsystem sizes. Finally, we show that the BW reduced density matrices fall short of reproducing the exact behavior of the logarithmic emptiness formation probability in the ground state of the XX spin chain.

We investigate the effect of dissipation from a thermal environment on topological pumping in the periodically-driven Rice-Mele model. We report that dissipation can improve the robustness of pumping quantisation in a regime of finite driving frequencies. Specifically, in this regime, lowerature dissipative dynamics can lead to a pumped charge that is much closer to the Thouless quantised value, compared to a coherent evolution. We understand this effect in the Floquet framework: dissipation increases the population of a Floquet band which shows a topological winding, where pumping is essentially quantised. This finding is a step towards understanding a potentially very useful resource to exploit in experiments, where dissipation effects are unavoidable. We consider small couplings with the environment and we use a Bloch-Redfield quantum master equation approach for our numerics: comparing these results with an exact MPS numerical treatment we find that the quantum master equation works very well also at low temperature, a quite remarkable fact.

Abstract: We study the quantum many-body dynamics and entropy production triggered by an interaction quench of few dipolar bosons in an external harmonic trap. We solve the time-dependent many-body Schrödinger equation by using an in-principle numerically exact many-body method called the multiconfigurational time-dependent Hartree method for bosons (MCTDHB). We study the dynamical measures with high level of accuracy. We monitor the time evolution of the occupation in the natural orbitals and normalized first- and second-order Glauber’s correlation functions. In particular, we focus on the relaxation dynamics of the Shannon entropy. Comparison with the corresponding results for contact interactions is presented. We observe significant effects coming from the presence of the non-local part of the dipolar interaction. The relaxation process is very fast for dipolar bosons with a clear signature of a truly saturated maximum entropy state. We also discuss the connection between the entropy production and the occurrence of correlations and loss of coherence in the system. We identify the long-time relaxed state as a many-body state retaining only diagonal correlations in the first-order correlation function and building up anti-bunching effect in the second-order correlation function. Graphical abstract: [Figure not available: see fulltext.]

Consistency with the Maxwell equations determines how matter must be coupled to the electromagnetic field (EMF) within the minimal coupling scheme. Specifically, if the Hamiltonian includes just a short-range repulsion among the conduction electrons, as is commonly the case for models of correlated metals, those electrons must be coupled to the full internal EMF, whose longitudinal and transverse components are self-consistently related to the electron charge and current densities through Gauss's and circuital laws, respectively. Since such self-consistency relation is hard to implement when modeling the nonequilibrium dynamics caused by the EMF, as in pump-probe experiments, it is common to replace in model calculations the internal EMF by the external one. Here we show that such replacement may be misleading, especially when the frequency of the external EMF is below the intraband plasma edge.

Vanadium dioxide is one of the most studied strongly correlated materials. Nonetheless, the intertwining between electronic correlation and lattice effects has precluded a comprehensive description of the rutile metal to monoclinic insulator transition, in turn triggering a longstanding "the chicken or the egg"debate about which comes first, the Mott localization or the Peierls distortion. Here, we suggest that this problem is in fact ill posed: The electronic correlations and the lattice vibrations conspire to stabilize the monoclinic insulator, and so they must be both considered to not miss relevant pieces of the VO2 physics. Specifically, we design a minimal model for VO2 that includes all the important physical ingredients: The electronic correlations, the multiorbital character, and the two components of the antiferrodistortive mode that condense in the monoclinic insulator. We solve this model by dynamical mean-field theory within the adiabatic Born-Oppenheimer approximation. Consistently with the first-order character of the metal-insulator transition, the Born-Oppenheimer potential has a rich landscape, with minima corresponding to the undistorted phase and to the four equivalent distorted ones, and which translates into an equally rich thermodynamics that we uncover by the Monte Carlo method. Remarkably, we find that a distorted metal phase intrudes between the low-temperature distorted insulator and high-temperature undistorted metal, which sheds new light on the debated experimental evidence of a monoclinic metallic phase.

We show how to implement a Rydberg-atom quantum simulator to study the nonequilibrium dynamics of an Abelian (1+1)-dimensional lattice gauge theory. The implementation locally codifies the degrees of freedom of a Z3 gauge field, once the matter field is integrated out by means of the Gauss local symmetries. The quantum simulator scheme is based on currently available technology and thus is scalable to considerable lattice sizes. It allows, within experimentally reachable regimes, us to explore different string dynamics and to infer information about the Schwinger U(1) model.

Finding the exact counterdiabatic potential is, in principle, particularly demanding. Following recent progress about variational strategies to approximate the counterdiabatic operator, in this paper we apply this technique to the quantum annealing of the p-spin model. In particular, for p=3 we find a new form of the counterdiabatic potential originating from a cyclic ansatz that allows us to have optimal fidelity even for extremely short dynamics, independently of the size of the system. We compare our results with a nested commutator ansatz, recently proposed in Claeys, Pandey, Sels, and Polkovnikov [Phys. Rev. Lett. 123, 090602 (2019)PRLTAO0031-900710.1103/PhysRevLett.123.090602] for p=1 and p=3. We also analyze generalized p-spin models to get a further insight into our ansatz.

We exploit the knowledge of the entanglement spectrum in the ground state of the gapped XXZ spin chain to derive asymptotic exact results for the full counting statistics of the transverse magnetisation in a large spin block of length ℓ. We found that for a subsystem of even length the full counting statistics is Gaussian, while for odd subsystems it is the sum of two Gaussian distributions. We test our analytic predictions with accurate tensor networks simulations. As a byproduct, we also obtain the symmetry (magnetisation) resolved entanglement entropies.

The quasi-particle picture is a powerful tool to understand the entanglement spreading in many-body quantum systems after a quench. As an input, the structure of the excitations’ pattern of the initial state must be provided, the common choice being pairwise-created excitations. However, several cases exile this simple assumption. In this work we investigate weakly-interacting to free quenches in one dimension. This results in a far richer excitations’ pattern where multiplets with a larger number of particles are excited. We generalize the quasi-particle ansatz to such a wide class of initial states, providing a small-coupling expansion of the Rényi entropies. Our results are in perfect agreement with iTEBD numerical simulations.

We study the continuum limit of the entanglement Hamiltonians of a block of consecutive sites in massless harmonic chains. This block is either in the chain on the infinite line or at the beginning of a chain on the semi-infinite line with Dirichlet boundary conditions imposed at its origin. The entanglement Hamiltonians of the interval predicted by conformal field theory (CFT) for the massless scalar field are obtained in the continuum limit. We also study the corresponding entanglement spectra, and the numerical results for the ratios of the gaps are compatible with the operator content of the boundary CFT of a massless scalar field with Neumann boundary conditions imposed along the boundaries introduced around the entangling points by the regularisation procedure.

Variational wave functions have been a successful tool to investigate the properties of quantum spin liquids. Finding their parent Hamiltonians is of primary interest for the experimental realization of these strongly correlated phases, and for gathering additional insights on their stability. In this work, we systematically reconstruct approximate spin-chain parent Hamiltonians for Jastrow-Gutzwiller wave functions, which share several features with quantum spin liquid wave functions in two dimensions. Firstly, we determine the different phases encoded in the parameter space through their correlation functions and entanglement properties. Secondly, we apply a recently proposed entanglement-guided method to reconstruct parent Hamiltonians to these states, which constrains the search to operators describing relativistic low-energy field theories - as expected for deconfined phases of gauge theories relevant to quantum spin liquids. The quality of the results is discussed using different quantities and comparing to exactly known parent Hamiltonians at specific points in parameter space. Our findings provide guiding principles for experimental Hamiltonian engineering of this class of states.

We study the symmetry resolved entanglement entropies in gapped integrable lattice models. We use the corner transfer matrix to investigate two prototypical gapped systems with a U(1) symmetry: the complex harmonic chain and the XXZ spin-chain. While the former is a free bosonic system, the latter is genuinely interacting. We focus on a subsystem being half of an infinitely long chain. In both models, we obtain exact expressions for the charged moments and for the symmetry resolved entropies. While for the spin chain we found exact equipartition of entanglement (i.e. all the symmetry resolved entropies are the same), this is not the case for the harmonic system where equipartition is effectively recovered only in some limits. Exploiting the gaussianity of the harmonic chain, we also develop an exact correlation matrix approach to the symmetry resolved entanglement that allows us to test numerically our analytic results.

In general quantum operations, or quantum channels cannot be inverted by physical operations, i.e., by completely positive trace-preserving maps. An arbitrary state passing through a quantum channel loses its fidelity with the input. Given a quantum channel E, we discuss the concept of its quasi-inverse as a completely positive trace-preserving map Eqi which when composed with E increases its average input-output fidelity in an optimal way. The channel Eqi comes as close as possible to the inverse of a quantum channel. We give a complete classification of such maps for qubit channels and provide quite a few illustrative examples.

We study the finite-Time dynamics of an initially localized wave packet in the Anderson model on the random regular graph (RRG) and show the presence of a subdiffusion phase coexisting both with ergodic and putative nonergodic phases. The full probability distribution Π(x,t) of a particle to be at some distance x from the initial state at time t is shown to spread subdiffusively over a range of disorder strengths. The comparison of this result with the dynamics of the Anderson model on Zd lattices, d>2, which is subdiffusive only at the critical point implies that the limit d→∞ is highly singular in terms of the dynamics. A detailed analysis of the propagation of Π(x,t) in space-Time (x,t) domain identifies four different regimes determined by the position of a wave front Xfront(t), which moves subdiffusively to the most distant sites Xfront(t)∼tβ with an exponent β<1. Importantly, the Anderson model on the RRG can be considered as proxy of the many-body localization transition (MBL) on the Fock space of a generic interacting system. In the final discussion, we outline possible implications of our findings for MBL.