Publications

In this work, we report potential energy surfaces (PESs) of the sodium dimer calculated by variational (VMC) and lattice-regularized diffusion Monte Carlo (LRDMC). The VMC calculation is accurate for determining the equilibrium distance and the qualitative shape of the experimental PES. Remarkably, after the application of the LRDMC projection to this single determinant ansatz, namely, the Jastrow Antisymmetrized Geminal Power (JAGP), chemical accuracy (∼1 kcal/mol) is reached in the binding energy, and the obtained equilibrium internuclear distance and harmonic vibrational frequency are in very good agreement with the experimental ones. This outcome is crucially dependent on the quality of the optimization used to determine the best possible trial function within the chosen ansatz. The strategy adopted in this work is to minimize the variational energy by initializing the trial function with the density functional theory (DFT) single determinant ansatz expanded exactly in the same atomic basis used for the corresponding VMC and LRDMC calculations. This atomic basis is reshaped ad-hoc for QMC calculations. Indeed, we multiply the standard Gaussian-type atomic orbitals by a one-body Jastrow factor, satisfying, in this way, the electron-ion cusp conditions. In order to achieve these important advantages, we have defined a very efficient DFT algorithm in the mentioned basis, by estimating the corresponding matrix elements on a mesh, and by using a much finer mesh grid in the vicinity of nuclei.

The laws of thermodynamics require any initial macroscopic inhomogeneity in extended many-body systems to be smoothed out by the time evolution through the activation of transport processes. In generic quantum systems, transport is expected to be governed by a diffusion law, whereas a sufficiently strong quenched disorder can suppress it completely due to many-body localization of quantum excitations. Here, we show that the confinement of quasiparticles can also suppress transport even if the dynamics are generated by nondisordered Hamiltonians. We demonstrate this in the quantum Ising chain with transverse and longitudinal magnetic fields, prepared in a paradigmatic state with a domain wall and thus with a spatially varying energy density. We perform extensive numerical simulations of the dynamics which turn out to be in excellent agreement with an effective analytical description valid within both weak and strong confinement regimes. Our results show that the energy flow from "hot" to "cold" regions of the chain is suppressed for all accessible times. We argue that this phenomenon is general, as it relies solely on the emergence of confinement of excitations.

Collapse models describe phenomenologically the quantum-to-classical transition by adding suitable nonlinear and stochastic terms to the Schrödinger equation, thus (slightly) modifying the dynamics of quantum systems. Experimental bounds on the collapse parameters have been derived from various experiments involving a plethora of different systems, from single atoms to gravitational wave detectors. Here, we give a comprehensive treatment of the continuous spontaneous localization (CSL) model, the most studied among collapse models, for Fermi liquids. We consider both the white and non-white noise case. Application to various astrophysical sources is presented.

Multiorbital Hubbard models host strongly correlated "Hund's metals" even for interactions much stronger than the bandwidth. We characterize this interaction-resilient metal as a mixed-valence state. In particular, it can be pictured as a bridge between two strongly correlated insulators: a high-spin Mott insulator and a charge-disproportionated insulator which is stabilized by a very large Hund's coupling. This picture is confirmed comparing models with negative and positive Hund's coupling for different fillings. Our results provide a characterization of the Hund's metal state and connect its presence with charge disproportionation, which has indeed been observed in chromates and proposed to play a role in iron-based superconductors.

We show that a hierarchy of topological phases in one dimension - a topological Devil's staircase - can emerge at fractional filling fractions in interacting systems, whose single-particle band structure describes a topological or a crystalline topological insulator. Focusing on a specific example in the BDI class, we present a field-theoretical argument based on bosonization that indicates how the system, as a function of the filling fraction, hosts a series of density waves. Subsequently, based on a numerical investigation of the low-lying energy spectrum, Wilczek-Zee phases, and entanglement spectra, we show that they are symmetry protected topological phases. In sharp contrast to the non-interacting limit, these topological density waves do not follow the bulk-edge correspondence, as their edge modes are gapped. We then discuss how these results are immediately applicable to models in the AIII class, and to crystalline topological insulators protected by inversion symmetry. Our findings are immediately relevant to cold atom experiments with alkaline-earth atoms in optical lattices, where the band structure properties we exploit have been recently realized.

We study the dynamical behavior of doped electronic systems subject to a global ramp of the repulsive Hubbard interaction. We start with formulating a real-time generalization of the fluctuation-exchange approximation. Implementing this numerically, we investigate the weak-coupling regime of the Hubbard model both in the electron-doped and hole-doped regimes. The results show that both local and nonlocal (momentum-dependent) observables evolve toward a thermal state, although the temperature of the final state depends on the ramp duration and the band filling. We further reveal a momentum-dependent relaxation rate of the distribution function in doped systems and trace back its physical origin to the anisotropic self-energies in the momentum space.

We introduce a method for the search of parent Hamiltonians of input wave functions based on the structure of their reduced density matrix. The two key elements of our recipe are an ansatz on the relation between the reduced density matrix and parent Hamiltonian that is exact at the field theory level, and a minimization procedure on the space of relative entropies, which is particularly convenient due to its convexity. As examples, we show how our method correctly reconstructs the parent Hamiltonian correspondent to several nontrivial ground state wave functions, including conformal and symmetry-protected-topological phases, and quantum critical points of two-dimensional antiferromagnets described by strongly coupled field theories. Our results show the entanglement structure of ground state wave functions considerably simplifies the search for parent Hamiltonians.

In this work we study the unitary time-evolutions of quantum systems defined on infinite-dimensional separable time-dependent Hilbert spaces. Two possible cases are considered: a quantum system defined on a stochastic interval and another one defined on a Hilbert space with stochastic integration measure (stochastic time-dependent scalar product). The formulations of the two problems and a comparison with the general theory of open quantum systems are discussed. Possible physical applications of the situations considered are analyzed.

We study the dynamics of nonlinear photonic lattices driven by two-photon parametric processes. By means of matrix-product-state-based calculations, we show that a quantum many-body state with long-range hidden order can be generated from the vacuum. Although this order resembles that characterizing the Haldane insulator, our system is far from equilibrium due to the drive and photon loss. A possible explanation highlighting the role of the symmetry of the drive and the effect of photon loss is discussed. An implementation based on superconducting circuits is proposed and analyzed.

We develop a systematic method to calculate the trace distance between two reduced density matrices in 1+1 dimensional quantum field theories. The approach exploits the path integral representation of the reduced density matrices and an ad hoc replica trick. We then extensively apply this method to the calculation of the distance between reduced density matrices of one interval of length in eigenstates of conformal field theories. When the interval is short, using the operator product expansion of twist operators, we obtain a universal form for the leading order in of the trace distance. We compute the trace distances among the reduced density matrices of several low lying states in two-dimensional free massless boson and fermion theories. We compare our analytic conformal results with numerical calculations in XX and Ising spin chains finding perfect agreement.

We investigate the effects of critical Casimir forces and demixing, on the dynamics of a pair of optically trapped particles dispersed in the bulk of a critical binary mixure in proximity of its critical point.

Within the ground-state auxiliary-field quantum Monte Carlo technique, we introduce discrete Hubbard-Stratonovich transformations (HSTs) that are also suitable for spatially inhomogeneous trial functions. The discrete auxiliary fields introduced here are coupled to local spin or charge operators fluctuating around their Hartree-Fock values. The formalism can be considered a generalization of the discrete HSTs by J. E. Hirsch [Phys. Rev. B 28, 4059 (1983)PRBMDO0163-182910.1103/PhysRevB.28.4059] or a compactification of the shifted-contour auxiliary-field Monte Carlo formalism by N. Rom et al. [Chem. Phys. Lett. 270, 382 (1997)CHPLBC0009-261410.1016/S0009-2614(97)00370-9]. An improvement of the acceptance ratio is found for a real auxiliary field, while an improvement of the average sign is found for a purely imaginary auxiliary field. Efficiencies of the different HSTs are tested in the single-band Hubbard model at and away from half filling by studying the staggered magnetization and energy expectation values, respectively.

We perform direct thermovoltage measurements in a single-electron transistor, using on-chip local thermometers, in both the linear and nonlinear regimes. Using a model which accounts for cotunneling, we find excellent agreement with the experimental data with no free parameters even when the temperature difference is larger than the average temperature (far-from-linear regime). This allows us to confirm the sensitivity of the thermovoltage on cotunneling and to find that in the nonlinear regime the temperature of the metallic island is a crucial parameter. Surprisingly, the metallic island tends to overheat even at zero net charge current, resulting in a reduction of the thermovoltage.

We show that long-range ferromagnetic interactions in quantum spin chains can induce spatial quasilocalization of topological magnetic defects, i.e., domain walls, even in the absence of quenched disorder. Utilizing matrix-product-states numerical techniques, we study the nonequilibrium evolution of initial states with one or more domain walls under the effect of a transverse field in variable-range quantum Ising chains. Upon increasing the range of these interactions, we demonstrate the occurrence of a sharp transition characterized by the suppression of spatial diffusion of the excitations during the accessible time scale: the excess energy density remains localized around the initial position of the domain walls. This quasilocalization is accurately reproduced by an effective semiclassical model, which elucidates the crucial role that long-range interactions play in this phenomenon. The predictions of this Rapid Communication can be tested in current experiments with trapped ions.

An unbiased zeroerature auxiliary-field quantum Monte Carlo method is employed to analyze the nature of the semimetallic phase of the two-dimensional Hubbard model on the honeycomb lattice at half filling. It is shown that the quasiparticle weight Z of the massless Dirac fermions at the Fermi level, which characterizes the coherence of zero-energy single-particle excitations, can be evaluated in terms of the long-distance equal-time single-particle Green's function. If this quantity remains finite in the thermodynamic limit, the low-energy single-particle excitations of the correlated semimetallic phase are described by a Fermi-liquid-type single-particle Green's function. Based on the unprecedentedly large-scale numerical simulations on finite-size clusters containing more than 10 000 sites, we show that the quasiparticle weight remains finite in the semimetallic phase below a critical interaction strength. This is also supported by the long-distance algebraic behavior (∼r-2, where r is distance) of the equal-time single-particle Green's function that is expected for the Fermi liquid. Our result thus provides a numerical confirmation of Fermi-liquid theory in two-dimensional correlated metals.

We investigate a model of hard-core bosons with infinitely repulsive nearest- and next-nearest-neighbor interactions in one dimension, introduced by Fendley, Sengupta, and Sachdev [Phys. Rev. B 69, 075106 (2004)PRBMDO1098-012110.1103/PhysRevB.69.075106]. Using a combination of exact diagonalization, tensor network, and quantum Monte Carlo simulations, we show how an intermediate incommensurate phase separates a crystalline and a disordered phase. We base our analysis on a variety of diagnostics, including entanglement measures, fidelity susceptibility, correlation functions, and spectral properties. According to theoretical expectations, the disordered-to-incommensurate-phase transition point is compatible with Berezinskii-Kosterlitz-Thouless universal behavior. The second transition is instead nonrelativistic, with dynamical critical exponent z>1. For the sake of comparison, we illustrate how some of the techniques applied here work at the Potts critical point present in the phase diagram of the model for finite next-nearest-neighbor repulsion. This latter application also allows us to quantitatively estimate which system sizes are needed to match the conformal field theory spectra with experiments performing level spectroscopy.

We study energy transport in disordered XXZ spin-1/2 chains driven to nonequilibrium configurations by thermal reservoirs of different temperatures at the boundaries, using large-scale matrix product simulations. In particular we discuss the transition between diffusive and subdiffusive transport in sectors of zero and finite magnetization at high temperature. At large anisotropies we find that diffusive energy transport prevails over a large range of disorder strengths, which is in contrast to spin transport that is subdiffusive in the same regime for weak disorder. However, at finite magnetization both energy and spin currents decay as a function of the system size with the same exponent. We conclude that diffusion of energy is much more pervasive than that of magnetization in these disordered spin-1/2 systems, and occurs across a significant range of the interaction-disorder parameter phase space. We support the existence of this asymmetry, reminiscent of that in the clean limit, by an analytical estimation of diffusion constants for weak disorder.

We construct a class of period-n-tupling discrete time crystals based on Zn clock variables, for all the integers n. We consider two classes of systems where this phenomenology occurs: disordered models with short-range interactions and fully connected models. In the case of short-range models, we provide a complete classification of time-crystal phases for generic n. For the specific cases of n=3 and n=4, we study in detail the dynamics by means of exact diagonalization. In both cases, through an extensive analysis of the Floquet spectrum, we are able to fully map the phase diagram. In the case of infinite-range models, the mapping onto an effective bosonic Hamiltonian allows us to investigate the scaling to the thermodynamic limit. After a general discussion of the problem, we focus on n=3 and n=4, representative examples of the generic behavior. Remarkably, for n=4 we find clear evidence of a crystal-to-crystal transition between period n-tupling and period n/2-tupling.

Conformal field theories in curved backgrounds have been used to describe inhomogeneous one-dimensional systems, such as quantum gases in trapping potentials and non-equilibrium spin chains. This approach provided, in a elegant and simple fashion, non-trivial analytic predictions for quantities, such as the entanglement entropy, that are not accessible through other methods. Here, we generalise this approach to low-lying excited states, focusing on the entanglement and relative entropies in an inhomogeneous free-fermionic system. Our most important finding is that the universal scaling function characterising these entanglement measurements is the same as the one for homogeneous systems, but expressed in terms of a different variable. This new scaling variable is a non-trivial function of the subsystem length and system's inhomogeneity that is easily written in terms of the curved metric. We test our predictions against exact numerical calculations in the free Fermi gas trapped by a harmonic potential, finding perfect agreement.

We investigate the ground state phase diagram of square ice — a U(1) lattice gauge theory in two spatial dimensions — using gauge invariant tensor network techniques. By correlation function, Wilson loop, and entanglement diagnostics, we characterize its phases and the transitions between them, finding good agreement with previous studies. We study the entanglement properties of string excitations on top of the ground state, and provide direct evidence of the fact that the latter are described by a conformal field theory. Our results pave the way to the application of tensor network methods to confining, two-dimensional lattice gauge theories, to investigate their phase diagrams and low-lying excitations.