Publications

We study the models of Kafri et al. (KTM) and Tilloy and Diósi (TD), both of which implement gravity between quantum systems through a continuous measurement and feedback mechanism. The first model is for two particles, moving in one dimension, where the Newtonian potential is linearized. The second is applicable to any quantum system, within the context of Newtonian gravity. We address the issue of how to generalize the KTM model for an arbitrary finite number of particles. We find that the most straightforward generalizations are either inconsistent or are ruled out by experimental evidence. We also show that the TD model does not reduce to the KTM model under the approximations, which define the latter model. We then argue that under the simplest conditions, the TD model is the only viable implementation of a full-Newtonian interaction through a continuous measurement and feedback mechanism.

Quantum scars are nonthermal eigenstates characterized by low entanglement entropy, initially detected in systems subject to nearest-neighbor Rydberg blockade, the so-called PXP model. While most of these special eigenstates elude an analytical description and seem to hybridize with nearby thermal eigenstates for large systems, some of them can be written as matrix product states with size-independent bond dimension. We study the response of these exact quantum scars to perturbations by analyzing the scaling of the fidelity susceptibility with system size. We find that some of them are anomalously stable at first order in perturbation theory, in sharp contrast to the eigenstate thermalization hypothesis. However, this stability seems to break down when all orders are taken into account. We further investigate models with larger blockade radius and find a set of exact quantum scars that we write down analytically and compare with the PXP exact eigenstates. We show that they exhibit the same robustness against perturbations at first order.

We report a successful application of the ab initio quantum Monte Carlo (QMC) framework to a phonon dispersion calculation. A full phonon dispersion of diamond is successfully calculated at the variational Monte Carlo (VMC) level, based on the frozen-phonon technique. The VMC-phonon dispersion is in good agreement with the experimental results, giving renormalized harmonic optical frequencies very close to the experimental values, and improving upon previous density functional theory estimates. Key to success for the QMC approach is the statistical error reduction in the atomic force evaluation. We show that this can be achieved by using well conditioned atomic basis sets and by explicitly removing the basis-set redundancy, which reduces the statistical error of forces by up to two orders of magnitude by combining it with the so-called space-warp transformation algorithm. This leads to affordable and accurate QMC-phonons calculations, which are up to 104 times more efficient than a bare force treatment, and paves the way to new applications, particularly in correlated materials, where phonons have been poorly reproduced so far.

Despite being relevant to better understand the properties of honeycomblike systems, as graphene-based compounds, the electron-phonon interaction is commonly disregarded in theoretical approaches. That is, the effects of phonon fields on interacting Dirac electrons is an open issue, in particular when investigating long-range ordering. Thus, here we perform unbiased quantum Monte Carlo simulations to examine the Hubbard-Holstein model (HHM) in the half-filled honeycomb lattice. By performing careful finite-size scaling analysis, we identify semimetal-to-insulator quantum critical points, and determine the behavior of the antiferromagnetic and charge-density wave phase transitions. We have, therefore, established the ground state phase diagram of the HHM for intermediate interaction strength, determining its behavior for different phonon frequencies. Our findings provide quantitative and qualitative descriptions of the model at intermediate coupling strengths, and may shed light on the emergence of many-body properties in honeycomblike systems.

We study the dynamics of a two-level impurity embedded in a two-dimensional Bose-Hubbard (BH) model at zero temperature from an open quantum system perspective. Results for the decoherence across the whole phase diagram are presented, with a focus on the critical region close to the transition between superfluid and Mott insulator. In particular we show how the decoherence and the deviation from a Markovian behaviour are sensitive to whether the transition is crossed at commensurate or incommensurate densities. The role of the spectrum of the BH environment and its non-Gaussian statistics, beyond the standard independent boson model, is highlighted. Our analysis resorts on a recently developed method (2020 Phys. Rev. Res. 2 033276) - closely related to slave boson approaches - that enables us to capture the correlations across the whole phase diagram. This semi-analytical method provides us with a deep insight into the physics of the spin decoherence in the superfluid and Mott phases as well as close to the phase transitions.

Recent advances in levitated optomechanics provide new perspectives for the use of rotational degrees of freedom for the development of quantum technologies as well as for testing fundamental physics. As for the translational case, their use, especially in the quantum regime, is limited by environmental noises, the characterization of which is fundamental in order to assess, control, and minimize their effect, in particular decoherence. Here, we present a general perturbative approach to compute decoherence for a quantum system in a superposition of its rotational degrees of freedom. The specific cases of the dipole-dipole and quadrupole-quadrupole interactions are solved explicitly, and we show that the rotational degrees of freedom decohere on a time scale that can be longer than the translational one.

We study the massless Dirac field on the line in the presence of a point-like defect characterised by a unitary scattering matrix, that allows both reflection and transmission. Considering this system in its ground state, we derive the modular Hamiltonians of the subregion given by the union of two disjoint equal intervals at the same distance from the defect. The absence of energy dissipation at the defect implies the existence of two phases, where either the vector or the axial symmetry is preserved. Besides a local term, the densities of the modular Hamiltonians contain also a sum of scattering dependent bi-local terms, which involve two conjugate points generated by the reflection and the transmission. The modular flows of each component of the Dirac field mix the trajectory passing through a given initial point with the ones passing through its reflected and transmitted conjugate points. We derive the two-point correlation functions along the modular flows in both phases and show that they satisfy the Kubo-Martin-Schwinger condition. The entanglement entropies are also computed, finding that they do not depend on the scattering matrix.

We study the modular Hamiltonians of an interval for the massless Dirac fermion on the half-line. The most general boundary conditions ensuring the global energy conservation lead to consider two phases, where either the vector or the axial symmetry is preserved. In these two phases we derive the corresponding modular Hamiltonian in explicit form. Its density involves a bi-local term localised in two points of the interval, one conjugate to the other. The associated modular flows are also established. Depending on the phase, they mix fields with different chirality or charge that follow different modular trajectories. Accordingly, the modular flow preserves either the vector or the axial symmetry. We compute the two-point correlation functions along the modular flow and show that they satisfy the Kubo-Martin-Schwinger condition in both phases. The entanglement entropies are also derived.

We show that four-dimensional systems may exhibit a topological phase transition analogous to the well-known Berezinskii-Kosterlitz-Thouless vortex unbinding transition in two-dimensional systems. We study a suitable generalization of the sine-Gordon model in four dimensions and the renormalization group flow equation of its couplings, showing that the critical value of the frequency is the square of the corresponding value in 2D. The value of the anomalous dimension at the critical point is determined (η=1/32) and a conjecture for the universal jump of the superfluid stiffness (4/π2) presented.

Addressing the role of quantum coherence in the interplay between the different matter constituents (electrons, phonons and spin) is a critical step towards understanding transition metal oxides and designing complex materials with new functionalities. Here we use coherent vibrational control of on-site d–d electronic transitions in a model edge-sharing insulating transition metal oxide (CuGeO3) to single out the effects of vibrational coherence in electron–phonon coupling. By comparing time-domain experiments based on high- and low-photon-energy ultrashort laser excitation pulses with a fully quantum description of phonon-assisted absorption, we could distinguish the processes associated with incoherent thermal lattice fluctuations from those driven by the coherent motion of the atoms. In particular, while thermal fluctuations of the phonon bath uniformly increase the electronic absorption, the resonant excitation of phonon modes also results in light-induced transparency that is coherently controlled by the vibrational motion.

We introduce and realize demons that follow a customary gambling strategy to stop a nonequilibrium process at stochastic times. We derive second-law-like inequalities for the average work done in the presence of gambling, and universal stopping-time fluctuation relations for classical and quantum nonstationary stochastic processes. We test experimentally our results in a single-electron box, where an electrostatic potential drives the dynamics of individual electrons tunneling into a metallic island. We also discuss the role of coherence in gambling demons measuring quantum jump trajectories.

The identification of universal properties from minimally processed data sets is one goal of machine learning techniques applied to statistical physics. Here, we study how the minimum number of variables needed to accurately describe the important features of a data set - the intrinsic dimension (Id) - behaves in the vicinity of phase transitions. We employ state-of-the-art nearest-neighbors-based Id estimators to compute the Id of raw Monte Carlo thermal configurations across different phase transitions: first-order, second-order, and Berezinskii-Kosterlitz-Thouless. For all the considered cases, we find that the Id uniquely characterizes the transition regime. The finite-size analysis of the Id allows us to not only identify critical points with an accuracy comparable to methods that rely on a priori identification of order parameters but also to determine the corresponding (critical) exponent ν in the case of continuous transitions. For the case of topological transitions, this analysis overcomes the reported limitations affecting other unsupervised learning methods. Our work reveals how raw data sets display unique signatures of universal behavior in the absence of any dimensional reduction scheme and suggest direct parallelism between conventional order parameters in real space and the intrinsic dimension in the data space.

For a solid lattice, we rederive the continuous spontaneous localization (CSL) noise total energy gain of a test mass starting from a Lindblad formulation, and from a similar starting point rederive the geometry factor governing center of mass energy gain. We then suggest that the geometry factor can be used as a way to distinguish between low temperature cantilever motion saturation arising from CSL noise, and saturation arising from thermal leakage.

We derive the self-consistent harmonic approximation for the 2D XY model with non-local interactions. The resulting equation for the variational couplings holds for any form of the spin-spin coupling as well as for any dimension. Our analysis is then specialized to power-law couplings decaying with the distance r as in order to investigate the robustness, at finite σ, of the Berezinskii-Kosterlitz-Thouless (BKT) transition, which occurs in the short-range limit σ → ∞. We propose an ansatz for the functional form of the variational couplings and show that for any σ > 2 the BKT mechanism occurs. The present investigation provides an upper bound σ ∗ = 2 for the critical threshold σ ∗ above which the traditional BKT transition persists in spite of the non-local nature of the couplings.

Critical Casimir forces emerge between objects, such as colloidal particles, whenever their surfaces spatially confine the fluctuations of the order parameter of a critical liquid used as a solvent. These forces act at short but microscopically large distances between these objects, reaching often hundreds of nanometers. Keeping colloids at such distances is a major experimental challenge, which can be addressed by the means of optical tweezers. Here, we review how optical tweezers have been successfully used to quantitatively study critical Casimir forces acting on particles in suspensions. As we will see, the use of optical tweezers to experimentally study critical Casimir forces can play a crucial role in developing nano-technologies, representing an innovative way to realize self-assembled devices at the nano- and microscale.

A generically observed mechanism that drives the self-organization of living systems is interaction via chemical signals among the individual elements - which may represent cells, bacteria, or even enzymes. Here we propose an unconventional mechanism for such interactions, in the context of chemotaxis, which originates from the polarity of the particles and which generalizes the well-known Keller-Segel interaction term. We study the resulting large-scale dynamical properties of a system of such chemotactic particles using the exact stochastic formulation of Dean and Kawasaki along with dynamical renormalization group analysis of the critical state of the system. At this critical point, an emergent "Galilean"symmetry is identified, which allows us to obtain the dynamical scaling exponents exactly. These exponents reveal superdiffusive density fluctuations and non-Poissonian number fluctuations. We expect our results to shed light on how molecular regulation of chemotactic circuits can determine large-scale behavior of cell colonies and tissues.

The periodically driven O(N) model is studied near the critical line separating a disordered paramagnetic phase from a period doubled phase, the latter being an example of a Floquet time crystal. The time evolution of one-point and two-point correlation functions are obtained within the Gaussian approximation and perturbatively in the drive amplitude. The correlations are found to show not only period doubling, but also power-law decays at large spatial distances. These features are compared with the undriven O(N) model, within the Gaussian approximation, in the vicinity of the paramagnetic-ferromagnetic critical point. The algebraic decays in space are found to be qualitatively different in the driven and the undriven cases. In particular, the spatiotemporal order of the Floquet time crystal leads to position-momentum and momentum-momentum correlation functions which are more long-ranged in the driven than in the undriven model. The light-cone dynamics associated with the correlation functions is also qualitatively different as the critical line of the Floquet time crystal shows a light cone with two distinct velocities, with the ratio of these two velocities scaling as the square-root of the dimensionless drive amplitude. The Floquet unitary, which describes the time evolution due to a complete cycle of the drive, is constructed for modes with small momenta compared to the drive frequency, but having a generic relationship with the square-root of the drive amplitude. At intermediate momenta, which are large compared to the square-root of the drive amplitude, the Floquet unitary is found to simply rotate the modes. On the other hand, at momenta which are small compared to the square-root of the drive amplitude, the Floquet unitary is found to primarily squeeze the modes, to an extent which increases upon increasing the wavelength of the modes, with a power-law dependence on it.

We study the symmetry resolved entanglement entropies in one-dimensional systems with boundaries. We provide some general results for conformal invariant theories and then move to a semi-infinite chain of free fermions. We consider both an interval starting from the boundary and away from it. We derive exact formulas for the charged and symmetry resolved entropies based on theorems and conjectures about the spectra of Toeplitz+Hankel matrices. En route to characterise the interval away from the boundary, we prove a general relation between the eigenvalues of Toeplitz+Hankel matrices and block Toeplitz ones. An important aspect is that the saddle-point approximation from charged to symmetry resolved entropies introduces algebraic corrections to the scaling that are much more severe than in systems without boundaries.

The time evolution of the entanglement entropy is a key concept to understand the structure of a nonequilibrium quantum state. In a large class of models, such evolution can be understood in terms of a semiclassical picture of moving quasiparticles spreading the entanglement throughout the system. However, it is not yet known how the entanglement splits between the sectors of an internal local symmetry of a quantum many-body system. Here, guided by the examples of conformal field theories and free-fermion chains, we show that the quasiparticle picture can be adapted to this goal, leading to a general conjecture for the charged entropies whose Fourier transform gives the desired symmetry-resolved entanglement Sn(q). We point out two physically relevant effects that should be easily observed in atomic experiments: a delay time for the onset of Sn(q) which grows linearly with |Δq| (the difference between the charge q and its mean value) and an effective equipartition when |Δq| is much smaller than the subsystem size.

In this paper, we study the driven-dissipative p-spin models for p≥2. In thermodynamic limit, the equation of motion is derived by using a semiclassical approach. The long-time asymptotic states are obtained analytically, which exhibit multistability in some regions of the parameter space. The steady state is unique as the number of spins is finite. But the thermodynamic limit of the steady-state magnetization displays nonanalytic behavior somewhere inside the semiclassical multistable region. We find both the first-order and continuous dissipative phase transitions. As the number of spins increases, both the Liouvillian gap and magnetization variance vanish according to a power law at the continuous transition. At the first-order transition, the gap vanishes exponentially accompanied by a jump of magnetization in thermodynamic limit. The properties of transitions depend on the symmetry and semiclassical multistability, being qualitatively different among p=2, odd p (p≥3), and even p (p≥4).