Publications

We report a quantum Monte Carlo study, on a very simple but nevertheless very instructive model system of four hydrogen atoms, recently proposed in Gasperich et al. [J. Chem. Phys. 147, 074106 (2017)]. We find that the Jastrow correlated Antisymmetrized Geminal Power (JAGP) is able to recover most of the correlation energy even when the geometry is symmetric and the hydrogens lie on the edges of a perfect square. Under such conditions, the diradical character of the molecule ground state prevents a single determinant Ansatz to achieve an acceptable accuracy, whereas the JAGP performs very well for all geometries. Remarkably, this is obtained with a similar computational effort. Moreover, we find that the Jastrow factor is fundamental in promoting the correct resonances among several configurations in the JAGP, which cannot show up in the pure Antisymmetrized Geminal Power (AGP). We also show the extremely fast convergence of this approach in the extension of the basis set. Remarkably, only the simultaneous optimization of the Jastrow and the AGP part of our variational Ansatz is able to recover an almost perfect nodal surface, yielding therefore state of the art energies, almost converged in the complete basis set limit, when the so called diffusion Monte Carlo is applied.

The discovery of novel entanglement patterns in quantum many-body systems is a prominent research direction in contemporary physics. Here we provide the example of a spin chain with random and inhomogeneous couplings that in the ground state exhibits a very unusual area-law violation. In the clean limit, i.e. without disorder, the model is the rainbow chain and has volume law entanglement. We show that, in the presence of disorder, the entanglement entropy exhibits a power-law growth with the subsystem size, with an exponent 1/2. By employing the strong disorder renormalization group (SDRG) framework, we show that this exponent is related to the survival probability of certain random walks. The ground state of the model exhibits extended regions of short-range singlets (that we term 'bubble' regions) as well as rare long range singlet ('rainbow' regions). Crucially, while the probability of extended rainbow regions decays exponentially with their size, that of the bubble regions is power law. We provide strong numerical evidence for the correctness of SDRG results by exploiting the free-fermion solution of the model. Finally, we investigate the role of interactions by considering the random inhomogeneous XXZ spin chain. Within the SDRG framework and in the strong inhomogeneous limit, we show that the above area-law violation takes place only at the free-fermion point of phase diagram. This point divides two extended regions, which exhibit volume-law and area-law entanglement, respectively.

By employing unbiased numerical methods, we show that pulse irradiation can induce unconventional superconductivity even in the Mott insulator of the Hubbard model. The superconductivity found here in the photoexcited state is due to the η-pairing mechanism, characterized by staggered pair-density-wave oscillations in the off-diagonal long-range correlation, and is absent in the ground-state phase diagram; i.e., it is induced neither by a change of the effective interaction of the Hubbard model nor by simple photocarrier doping. Because of the selection rule, we show that the nonlinear optical response is essential to increase the number of η pairs and thus enhance the superconducting correlation in the photoexcited state. Our finding demonstrates that nonequilibrium many-body dynamics is an alternative pathway to access a new exotic quantum state that is absent in the ground-state phase diagram, and also provides an alternative mechanism for enhancing superconductivity.

Critical points and phase transitions are characterized by diverging susceptibilities, reflecting the tendency of the system toward spontaneous symmetry breaking. Equilibrium statistical mechanics bounds these instabilities to occur at zero frequency, giving rise to static order parameters. In this work we argue that a prototype model of correlated driven-dissipative lattice bosons, of direct relevance for upcoming generation of circuit QED arrays experiments, exhibits a susceptibility sharply diverging at a finite nonzero frequency, which is an emerging scale set by interactions and nonequilibrium effects. In the broken-symmetry phase the corresponding macroscopic order parameter becomes nonstationary and oscillates in time without damping, thus breaking continuous time-translational symmetry. Our work, connecting breaking of time translational invariance to divergent finite frequency susceptibilities, which are of direct physical relevance, could potentially be extended to study other time-domain instabilities in nonequilibrium quantum systems, including Floquet time crystals and quantum synchronization.

We discuss and qualify the connection between two separate phenomena in the physics of nanoscale friction, general in nature and relevant to experiments. The first is thermally assisted lubricity (TAL), i.e., the low-velocity regime where a nanosized dry slider exhibits a viscouslike friction despite corrugations that would otherwise imply hard stick-slip friction. The second is the occurrence of negative dissipated work (NDW) events in sampling the work probability distribution. The abundance, or scarcity due to insufficient sampling, of these NDW events implies experimental fulfillment or violation of the celebrated Jarzynski equality (JE) of nonequilibrium statistical mechanics. We show, both analytically and in simulations of the one-dimensional point slider Prandtl-Tomlinson model, that a general crossover can be individuated as the total frictional work per cycle crosses kBT. Below such crossover, the TAL regime holds, the dissipation is essentially linear, and the numerical validation for the JE is feasible (i.e., does not require an exponentially large sampling size). Above it, the dissipation profile departs from linearity and gains its hard stick-slip features, and the mandatory sampling for the JE becomes exponentially large. In addition, we derive a parameter-free formula expressing the linear velocity coefficient of viscous friction, correcting previous empirically parameterized expressions. With due caution, the connection between friction and work tails can be extended beyond a single degree of freedom to more complex sliders, thus inviting realistic crosscheck experiments. Of importance for experimental nanofriction will be the search for NDW tails in the sliding behavior of trapped cold ions, and alternatively checking for TAL in the sliding pattern of dragged colloid monolayers as well as in forced protein unwinding.

L functions based on Dirichlet characters are natural generalizations of the Riemann function: they both have series representations and satisfy an Euler product representation, i.e. an infinite product taken over prime numbers. In this paper we address the generalized Riemann hypothesis relative to the non-trivial complex zeros of the Dirichlet L functions by studying the possibility to enlarge the original domain of convergence of their Euler product. The feasibility of this analytic continuation is ruled by the asymptotic behavior in N of the series involving Dirichlet characters modulo q on primes p n . Although deterministic, these series have pronounced stochastic features which make them analogous to random time series. We show that the B N 's satisfy various normal law probability distributions. The study of their large asymptotic behavior poses an interesting problem of statistical physics equivalent to the single Brownian trajectory problem, here addressed by defining an appropriate ensemble involving intervals of primes. For non-principal characters, we show that the series B N present a universal diffusive random walk behavior in view of the Dirichlet theorem on the equidistribution of reduced residue classes modulo q and the Lemke Oliver-Soundararajan conjecture on the distribution of pairs of residues on consecutive primes. This purely diffusive behavior of B N implies that the domain of convergence of the infinite product representation of the Dirichlet L-functions for non-principal characters can be extended from down to , without encountering any zeros before reaching this critical line.

Simulated quantum annealing (SQA) is a classical computational strategy that emulates a quantum annealing (QA) dynamics through a path-integral Monte Carlo whose parameters are changed during the simulation. Here we apply SQA to the one-dimensional transverse field Ising chain, where previous works have shown that, in the presence of disorder, a coherent QA provides a quadratic speedup with respect to classical simulated annealing, with a density of Kibble-Zurek defects decaying as ρKZQA∼(log10τ)-2 as opposed to ρKZSA∼(log10τ)-1, τ being the total annealing time, while for the ordered case both give the same power law ρKZQA≈ρKZSA∼τ-1/2. We show that the dynamics of SQA, while correctly capturing the Kibble-Zurek scaling τ-1/2 for the ordered case, is unable to reproduce the QA dynamics in the disordered case at intermediate τ. We analyze and discuss several issues related to the choice of the Monte Carlo moves (local or global in space), the time-continuum limit needed to eliminate the Trotter-discretization error, and the long autocorrelation times shown by a local-in-space Monte Carlo dynamics for large disordered samples.

We have developed an application and implemented parallel algorithms in order to provide a computational framework suitable for massively parallel supercomputers to study the unitary dynamics of quantum systems. We use renowned parallel libraries such as PETSc/SLEPc combined with high-performance computing approaches in order to overcome the large memory requirements to be able to study systems whose Hilbert space dimension comprises over 9 billion independent quantum states. Moreover, we provide descriptions of the parallel approach used for the three most important stages of the simulation: handling the Hilbert subspace basis, constructing a matrix representation for a generic Hamiltonian operator and the time evolution of the system by means of the Krylov subspace methods. We employ our setup to study the evolution of quasidisordered and clean many-body systems, focussing on the return probability and related dynamical exponents: the large system sizes accessible provide novel insights into their thermalization properties. Program summary: Program Title: DSQMKryST Program Files doi: http://dx.doi.org/10.17632/f6vty3wkwj.1 Licensing provisions: BSD 3-clause Programming language: C++ Supplementary material: https://github.com/mbrenesn/DSQMKryST External routines/libraries: PETSc (https://www.mcs.anl.gov/petsc/), SLEPc (http://slepc.upv.es), Boost C++ (http://www.boost.org) Nature of problem: Unitary dynamics of quantum mechanical many-body systems Solution method: Krylov subspace techniques (Arnoldi procedure) with a massively parallel, distributed memory approach

We present an analog of the phenomenon of orthogonality catastrophe in quantum many-body systems subject to a local dissipative impurity. We show that the fidelity F(t), giving a measure for distance of the time-evolved state from the initial one, displays a universal scaling form F(t)?tθe-γt, when the system supports long-range correlations, in a fashion reminiscent of traditional instances of orthogonality catastrophe in condensed matter. An exponential falloff at rate γ signals the onset of environmental decoherence, which is critically slowed down by the additional algebraic contribution to the fidelity. This picture is derived within a second-order cumulant expansion suited for Liouvillian dynamics, and substantiated for the one-dimensional transverse field quantum Ising model subject to a local dephasing jump operator, as well as for XY and XX quantum spin chains, and for the two-dimensional Bose gas deep in the superfluid phase with local particle heating. Our results hint that local sources of dissipation can be used to inspect real-time correlations and to induce a delay of decoherence in open quantum many-body systems.

In this work, we adapt the formalism of the dynamical vertex approximation (DΓA), a diagrammatic approach including many-body correlations beyond the dynamical mean-field theory, to the case of attractive on-site interactions. We start by exploiting the ladder approximation of the DΓA scheme, in order to derive the corresponding equations for the nonlocal self-energy and vertex functions of the attractive Hubbard model. Second, we prove the validity of our derivation by showing that the results obtained in the particle-hole symmetric case fully preserve the exact mapping between the attractive and the repulsive models. It will be shown how this property can be related to the structure of the ladders, which makes our derivation applicable for any approximation scheme based on ladder diagrams. Finally, we apply our DΓA algorithm to the attractive Hubbard model in three dimensions, for different fillings and interaction values. Specifically, we focus on the parameters region in the proximity of the second-order transition to the superconducting and charge-density wave phases, respectively, and calculate (i) their phase-diagrams, (ii) their critical behavior, as well as (iii) the effects of the strong nonlocal correlations on the single-particle properties.

A fundamental pillar of quantum mechanics concerns indistinguishable quantum particles. In three dimensions they may be classified into fermions or bosons, having, respectively, antisymmetric or symmetric wave functions under particle exchange. One of the numerous manifestations of this quantum statistics is the tendency of fermions (bosons) to antibunch (bunch). In a two-particle scattering experiment with two possible outgoing channels [C. K. Hong, Z. Y. Ou, and L. Mandel, Phys. Rev. Lett. 59, 2044 (1987)PRLTAO0031-900710.1103/PhysRevLett.59.2044], the probability of the two particles to arrive each at a different terminal is enhanced (with respect to classical particles) for fermions, and reduced for bosons. Here we show that by entangling the particles with an external degree of freedom, we can engineer quantum statistical transmutation, which may cause fermions to bunch. Our analysis may have consequences on the observed fractional statistics of anyons, including non-Abelian statistics, with serious implications for quantum computing operations in the presence of external degrees of freedom.

We study the nonequilibrium phase diagram and the dynamical phase transitions occurring during the prethermalization of nonintegrable quantum spin chains, subject to either quantum quenches or linear ramps of a relevant control parameter. We consider spin systems in which long-range ferromagnetic interactions compete with short-range, integrability-breaking terms. We capture the prethermal stages of the nonequilibrium evolution via a time-dependent spin-wave expansion at leading order in the spin-wave density. In order to access regimes with strong integrability breaking, instead, we perform numerical simulations based on the time-dependent variational principle with matrix product states. By investigating a large class of quantum spin models, we demonstrate that nonequilibrium fluctuations can significantly affect the dynamics near critical points of the phase diagram, resulting in a chaotic evolution of the collective order parameter, akin to the dynamics of a classical particle in a multiple-well potential subject to quantum friction. We also elucidate the signature of this novel dynamical phase on the time-dependent correlation functions of the local order parameter. We finally establish a connection with the notion of dynamical quantum phase transition associated with a possible nonanalytic behavior of the return probability amplitude, or Loschmidt echo, showing that the latter displays cusps whenever the order parameter vanishes during its real-time evolution.

We study the transport properties of a one-dimensional spinful Fermi gas, after a junction of two semi-infinite subsystems held at different temperatures. The ensuing dynamics is studied by analyzing the space-time profiles of local observables emerging at large distances x and times t, as a function of ζ=x/t. At equilibrium, the system displays two distinct species of quasiparticles, naturally associated with different physical degrees of freedom. By employing the generalized hydrodynamic approach, we show that when the temperatures are finite no notion of separation can be attributed to the quasiparticles. In this case, the profiles can not be qualitatively distinguished by those associated to quasiparticles of a single species that can form bound states. On the contrary, signatures of separation emerge in the low-temperature regime, where two distinct characteristic velocities appear. In this regime, we analytically show that the profiles display a piecewise constant form and can be understood in terms of two decoupled Luttinger liquids.

We numerically simulate a Harper-Hofstadter model equipped with broadband optical gain, with the goal of extracting those general features of the lasing regime resulting from the chirality of the edge modes. We find ultraslow relaxation times well above threshold and, depending on the shape of the amplifying region, the opening of a convective instability region in which the competition between the two chiral edge modes emerges more clearly.

We address an informational puzzle that appears with a non-Markovian open qubit dynamics: namely the fact that, while, according to the existing witnesses of information flows, a single qubit affected by that dissipative dynamics does not show information returning to it from its environment, instead two qubits do show such information when evolving independently under the same dynamics. We solve the puzzle by adding the so-called quasi-entropies to the possible witnesses of information flows.

The phase of an optical field inside a linear amplifier is widely known to diffuse with a diffusion coefficient that is inversely proportional to the photon number. The same process occurs in lasers which limits its intrinsic linewidth and makes the phase uncertainty difficult to calculate. The most commonly used simplification is to assume a narrow photon-number distribution for the optical field (which we call the small-noise approximation). For coherent light, this condition is determined by the average photon number. The small-noise approximation relies on (i) the input to have a good signal-to-noise ratio, and (ii) that such a signal-to-noise ratio can be maintained throughout the amplification process. Here we ask: For a coherent input, how many photons must be present in the input to a quantum linear amplifier for the phase noise at the output to be amenable to a small-noise analysis? We address these questions by showing how the phase uncertainty can be obtained without recourse to the small-noise approximation. It is shown that for an ideal linear amplifier (i.e. an amplifier most favourable to the small-noise approximation), the small-noise approximation breaks down with only a few photons on average. Interestingly, when the input strength is increased to tens of photons, the small-noise approximation can be seen to perform much better and the process of phase diffusion permits a small-noise analysis. This demarcates the limit of the small-noise assumption in linear amplifiers as such an assumption is less true for a nonideal amplifier.

Wave function collapse models assume that the Schrödinger equation is not entirely right, and must be supplemented with extra terms, which cause the (random) collapse of the wave function. In some of these models, the collapse is linked to gravity. We review the most popular gravitational wave function collapse models, with an emphasis on their conceptual status, stage of development, comparison with experiments, and open questions.

Collapse models implement a progressive loss of quantum coherence when the mass and the complexity of quantum systems increase. We will review such models and the current attempts to test their predicted loss of quantum coherence.

We estimate the output phase uncertainty of linear amplifiers in a practical regime (weak input, ideal amplification, and large gain) without the small-noise assumption. Furthermore, the small-noise assumption is shown to fail in this regime.