Publications

We show how certain long-range models of interacting fermions in d + 1 dimensions are equivalent to gauge theories in D + 1 dimensions in which gauge fields are defined in a dimension (D) larger than the dimension (d) of the fermionic theory to be simulated. For d = 1 it is possible to obtain an exact mapping, providing an expression of the fermionic interaction potential in terms of half-integer powers of the Laplacian. An analogous mapping can be applied to the kinetic term of the bosonized theory. A diagrammatic representation of the theories obtained by dimensional mismatch is presented, and consequences and applications of the established duality are discussed. Finally, by using a perturbative approach, we address the canonical quantization of fermionic theories presenting non-locality in the interaction term to construct the Hamiltonians for the effective theories found by dimensional reduction. We conclude by showing that one can engineer the gauge fields and the dimensional mismatch in order to obtain long-range effective Hamiltonians with 1/r or 1/r 2 potentials as examples.

Angle-resolved photoemission spectroscopy allows one to visualize in momentum space the probability weight maps of electrons subtracted from molecules deposited on a substrate. The interpretation of these maps usually relies on the plane wave approximation through the Fourier transform of single particle orbitals obtained from density functional theory. Here we propose a first-principle many-body approach based on quantum Monte Carlo (QMC) to directly calculate the quasi-particle wave functions (also known as Dyson orbitals) of molecules in momentum space. The comparison between these correlated QMC images and their single particle counterpart highlights features that arise from many-body effects. We test the QMC approach on the linear C2H2, CO2, and N2 molecules, for which only small amplitude remodulations are visible. Then, we consider the case of the pentacene molecule, focusing on the relationship between the momentum space features and the real space quasi-particle orbital. Eventually, we verify the correlation effects present in the metal CuCl42- planar complex.

We study scrambling in connection with multipartite entanglement dynamics in regular and chaotic long-range spin chains, characterized by a well-defined semi-classical limit. For regular dynamics, scrambling and entanglement dynamics are found to be very different: up to the Ehrenfest time, they rise side by side, departing only afterward. Entanglement saturates and becomes extensively multipartite, while scrambling, characterized by the dynamic of the square commutator of initially commuting variables, continues its growth up to the recurrence time. Remarkably, the exponential growth of the latter emerges not only in the chaotic case but also in the regular one, when the dynamics occurs at a dynamical critical point.

The continuous spontaneous localization (CSL) model strives to describe the quantum-to-classical transition from the viewpoint of collapse models. However, its original formulation suffers from a fundamental inconsistency in that it is explicitly energy nonconserving. Fortunately, a dissipative extension to CSL has been recently formulated that solves such an energy-divergence problem. We compare the predictions of the dissipative and nondissipative CSL models when various optomechanical settings are used and contrast such predictions with available experimental data, thus building the corresponding exclusion plots.

We extend the semiclassical picture for the spreading of entanglement and correlations to quantum quenches with several species of quasiparticles that have non-trivial pair correlations in momentum space. These pair correlations are, for example, relevant in inhomogeneous lattice models with a periodically-modulated Hamiltonian parameter. We provide explicit predictions for the spreading of the entanglement entropy in the space-time scaling limit. We also predict the time evolution of one- and two-point functions of the order parameter for quenches within the ordered phase. We test all our predictions against exact numerical results for quenches in the Ising chain with a modulated transverse field and we find perfect agreement.

The modular (or entanglement) Hamiltonian correspondent to the half-space bipartition of a quantum state uniquely characterizes its entanglement properties. However, in the context of lattice models, its explicit form is analytically known only for the two spin chains and certain free theories in one dimension. In this work, we provide a thorough investigation of entanglement Hamiltonians in lattice models obtained via the Bisognano-Wichmann theorem, which provides an explicit functional form for the entanglement Hamiltonian itself in quantum field theory. Our study encompasses a variety of one- and two-dimensional models, supporting diverse quantum phases and critical points, and, most importantly, scanning several universality classes, including Ising, Potts, and Luttinger liquids. We carry out extensive numerical simulations based on the density matrix renormalization group method, exact diagonalization, and quantum Monte Carlo. In particular, we compare the exact entanglement properties and correlation functions to those obtained applying the Bisognano-Wichmann theorem on the lattice. We carry out this comparison on both the eigenvalues and eigenvectors of the entanglement Hamiltonian, and expectation values of correlation functions and order parameters. Our results evidence that as long as the low-energy description of the lattice model is well captured by a Lorentz-invariant quantum field theory, the Bisognano-Wichmann theorem provides a qualitatively and quantitatively accurate description of the lattice entanglement Hamiltonian. The resulting framework paves the way to direct studies of entanglement properties utilizing well-established statistical mechanics methods and experiments.

In this paper we aim at characterizing the effect of stochastic fluctuations on the distribution of the energy exchanged by a quantum system with the external environment under sequences of quantum measurements performed at random times. Both quenched and annealed averages are considered. The information about fluctuations is encoded in the quantum-heat probability density function, or equivalently in its characteristic function, whose general expression for a quantum system with arbitrary Hamiltonian is derived. We prove that, when a stochastic protocol of measurements is applied, the quantum Jarzynski equality is obeyed. Therefore, the fluctuation relation is robust against the presence of randomness in the times intervals between measurements. Then, for the paradigmatic case of a two-level system, we analytically characterize the quantum-heat transfer. Particular attention is devoted to the limit of large number of measurements and to the effects caused by the stochastic fluctuations. The relation with the stochastic Zeno regime is also discussed.

Quantum-enhanced measurements exploit quantum mechanical effects for increasing the sensitivity of measurements of certain physical parameters and have great potential for both fundamental science and concrete applications. Most of the research has so far focused on using highly entangled states, which are, however, difficult to produce and to stabilize for a large number of constituents. In the following alternative mechanisms are reviewed, notably the use of more general quantum correlations such as quantum discord, identical particles, or nontrivial Hamiltonians; the estimation of thermodynamical parameters or parameters characterizing nonequilibrium states; and the use of quantum phase transitions. Both theoretically achievable enhancements and enhanced sensitivities not primarily based on entanglement that have already been demonstrated experimentally and indicate some possible future research directions are described.

Using analytic and numerical approaches, we study the spatiotemporal evolution of a conserved order parameter of a fluid in film geometry, following an instantaneous quench to the critical temperature Tc as well as to supercritical temperatures. The order parameter dynamics is chosen to be governed by model B within mean-field theory and is subject to no-flux boundary conditions as well as to symmetric surface fields at the confining walls. The latter give rise to critical adsorption of the order parameter at both walls and provide the driving force for the non-Trivial time evolution of the order parameter. During the dynamics, the order parameter is locally and globally conserved; thus, at thermal equilibrium, the system represents the canonical ensemble. We furthermore consider the dynamics of the nonequilibrium critical Casimir force, which we obtain based on the generalized force exerted by the order parameter field on the confining walls. We identify various asymptotic regimes concerning the time evolution of the order parameter and the critical Casimir force and we provide, within our approach, exact expressions of the corresponding dynamic scaling functions.

Abstract: Models of spontaneous wave function collapse describe the quantum-to-classical transition by assuming a progressive breakdown of the superposition principle when the mass of the system increases, providing a well-defined phenomenology in terms of a non-linearly and stochastically modified Schrödinger equation, which can be tested experimentally. The most popular of such models is the continuous spontaneous localization (CSL) model: in its original version, the collapse is driven by a white noise, and more recently, generalizations in terms of colored noises, which are more realistic, have been formulated. We will analyze how current non-interferometric tests bound the model, depending on the spectrum of the noise. We will find that low frequency purely mechanical experiments provide the most stable and strongest bounds. Graphical abstract: [Figure not available: see fulltext.].

By using variational Monte Carlo and auxiliary-field quantum Monte Carlo methods, we perform an accurate finite-size scaling of the s-wave superconducting order parameter and the pairing correlations for the negative-U Hubbard model at zero temperature in the square lattice. We show that the twist-averaged boundary conditions (TABCs) are extremely important to control finite-size effects and to achieve smooth and accurate extrapolations to the thermodynamic limit. We also show that TABCs are much more efficient in the grand-canonical ensemble rather than in the standard canonical ensemble with fixed number of electrons. The superconducting order parameter as a function of the doping is presented for several values of |U|/t and is found to be significantly smaller than the mean-field BCS estimate already for moderate couplings. This reduction is understood by a variational ansatz able to describe the low-energy behavior of the superconducting phase by means of a suitably chosen Jastrow factor including long-range density-density correlations.

We study the behaviour of Rényi entropies in a generic thermodynamic macrostate of an integrable model. In the standard quench action approach to quench dynamics, the Rényi entropies may be derived from the overlaps of the initial state with Bethe eigenstates. These overlaps fix the driving term in the thermodynamic Bethe ansatz (TBA) formalism. We show that this driving term can be also reconstructed starting from the macrostate's particle densities. We then compute explicitly the stationary Rényi entropies after the quench from the dimer and the tilted Néel state in XXZ spin chains. For the former state we employ the overlap TBA approach, while for the latter we reconstruct the driving terms from the macrostate. We discuss in full detail the limits that can be analytically handled and we use numerical simulations to check our results against the large time limit of the entanglement entropies.

We study the effect of a thermal environment on the quantum annealing dynamics of a transverse-field Ising chain. The environment is modeled as a single Ohmic bath of quantum harmonic oscillators weakly interacting with the total transverse magnetization of the chain in a translationally invariant manner. We show that the density of defects generated at the end of the annealing process displays a minimum as a function of the annealing time, the so-called optimal working point, only in rather special regions of the bath temperature and coupling strength plane. We discuss the relevance of our results for current and future experimental implementations with quantum annealing hardware.

The large-scale properties of homogeneous states after quantum quenches in integrable systems have been successfully described by a semiclassical picture of moving quasiparticles. Here we consider the generalisation for the entanglement evolution after an inhomogeneous quench in noninteracting systems in the framework of generalised hydrodynamics. We focus on the protocol where two semi-infinite halves are initially prepared in different states and then joined together, showing that a proper generalisation of the quasiparticle picture leads to exact quantitative predictions. If the system is initially prepared in a quasistationary state, we find that the entanglement entropy is additive and it can be computed by means of generalised hydrodynamics. Conversely, additivity is lost when the initial state is not quasistationary; yet the entanglement entropy in the large-scale limit can be exactly predicted in the quasiparticle picture, provided that the initial state is low entangled.

Recently, nonthermal excess noise, compatible with the theoretical prediction provided by collapse models, was measured in a millikelvin nanomechanical cantilever experiment [A. Vinante, Phys. Rev. Lett. 119, 110401 (2017)PRLTAO0031-900710.1103/PhysRevLett.119.110401]. We propose a feasible implementation of the cantilever experiment able to probe such noise. The proposed modification, completely within the grasp of current technology and readily implementable also in other types of mechanical noninterferometric experiments, consists in replacing the homogeneous test mass with one composed of different layers of different materials. This will enhance the action of a possible collapse noise above that given by standard noise sources.

In these lectures, I pedagogically review some recent advances in the study of the non-equilibrium dynamics of isolated quantum systems. In particular I emphasise the role played by the reduced density matrix and by the entanglement entropy in the understanding of the stationary properties after a quantum quench. The idea that the stationary thermodynamic entropy is the entanglement accumulated during the non-equilibrium dynamics is introduced and used to provide quantitative predictions for the time evolution of the entanglement itself. The harmonic chain is studied as an elementary model in which the quench dynamics can be easily and exactly worked out. This example provides a useful playground where general concepts can be simply understood and later applied to more complex and realistic systems.

In this Proceedings we report some recent results on Majorana quasi-particles published in Phys. Rev. Lett. 118, 200404 (2017). We show how angular momentum conservation can stabilise a symmetry-protected quasi-topological phase of matter supporting Majorana quasi-particles as edge modes in one-dimensional cold atom gases. We investigate a number-conserving four-species Hubbard model in the presence of spin-orbit coupling. The latter reduces the global spin symmetry to an angular momentum parity symmetry, which provides an extremely robust protection mechanism that does not rely on any coupling to additional reservoirs. The emergence of Majorana edge modes is elucidated using field theory techniques, and corroborated by density-matrix-renormalization-group simulations. Our results pave the way toward the observation of Majorana edge modes with alkaline-earth-like fermions in optical lattices, where all basic ingredients for our recipe - spin-orbit coupling and strong inter-orbital interactions - have been experimentally realized over the last two years.

The phase diagram of isotropically expanded graphene cannot be correctly predicted by ignoring either electron correlations, or mobile carbons, or the effect of applied stress, as was done so far. We calculate the ground state enthalpy (not just energy) of strained graphene by an accurate off-lattice quantum Monte Carlo correlated ansatz of great variational flexibility. Following undistorted semimetallic graphene at low strain, multideterminant Heitler-London correlations stabilize between ≃8.5% and ≃15% strain an insulating Kekulé-like dimerized (DIM) state. Closer to a crystallized resonating-valence bond than to a Peierls state, the DIM state prevails over the competing antiferromagnetic insulating state favored by density-functional calculations which we conduct in parallel. The DIM stressed graphene insulator, whose gap is predicted to grow in excess of 1 eV before failure near 15% strain, is topological in nature, implying under certain conditions 1D metallic interface states lying in the bulk energy gap.

We study the nonequilibrium evolution of a one-dimensional quantum Ising chain with spatially disordered, time-dependent, transverse fields characterized by white noise correlation dynamics. We establish prethermalization in this model, showing that the quench dynamics of the on-site transverse magnetization first approaches a metastable state unaffected by noise fluctuations, and then relaxes exponentially fast toward an infinite temperature state as a result of the noise. We also consider energy transport in the model, starting from an inhomogeneous state with two domain walls which separate regions characterized by spins with opposite transverse magnetization. We observe at intermediate timescales a phenomenology akin to Anderson localization: energy remains localized within the two domain walls, until the Markovian noise destroys coherence and, accordingly, disorder-induced localization, allowing the system to relax toward the late stages of its nonequilibrium dynamics. We compare our results with the simpler case of a noisy quantum Ising chain without disorder, and we find that the prethermal plateau is a generic property of spin chains with weak noise, while the phenomenon of prethermal Anderson localization is a specific feature arising from the competition of noise and disorder in the real-time transport properties of the system.