Quasilocal entanglement across the Mott-Hubbard transition

Bellomia G., Mejuto-Zaera C., The possibility to directly measure, in a cold-atom quantum simulator, the von Neumann entropy and mutual information between a site and its environment opens new perspectives on the characterization of the Mott-Hubbard metal-insulator transition, in the framework of quantum information theory. In this work, we provide an alternative view of the Mott transition in the two-dimensional Hubbard model in terms of rigorous quasilocal measures of entanglement and correlation between two spatially separated electronic orbitals, with no contribution from their environment. A space-resolved analysis of cluster dynamical mean-field theory results elucidates the prominent role of the nearest-neighbor entanglement in probing Mott localization: both its lower and upper bounds sharply increase at the metal-insulator transition. The two-site entanglement beyond nearest neighbors is shown to be quickly damped as the intersite distance is increased. These results ultimately resolve a conundrum of previous analyses based on the single-site von Neumann entropy, which has been found to monotonically decrease when the interaction is increased. The quasilocal two-site entanglement recovers instead the distinctive character of Mott insulators as strongly correlated quantum states, demonstrating its central role in the 2d Hubbard model.

Topological gap opening without symmetry breaking from dynamical quantum correlations

Paoletti F., Fanfarillo L., Topological phase transitions are typically associated with the formation of gapless states. Spontaneous symmetry breaking can lead to a gap opening, thereby obliterating the topological nature of the system. Here we highlight a completely different destiny for a topological transition in the presence of interaction. Solving a Bernevig-Hughes-Zhang model with local interaction, we show that dynamical quantum fluctuations can lead to the opening of a gap without any symmetry breaking. As we vary the interaction and the bare mass of the model, the continuous gapless topological transition turns into a first-order one, associated with the presence of a massive Dirac fermion at the transition point, showing a Gross-Neveu critical behavior near the quantum critical endpoint. We identify the gap opening as a condensed matter analog of the Coleman-Weinberg mechanism of mass generation.

Halide Perovskite Artificial Solids as a New Platform to Simulate Collective Phenomena in Doped Mott Insulators

Milloch A., Filippi U., Franceschini P., Galvani M., Mor S., Pagliara S., Ferrini G., Banfi F., The development of quantum simulators, artificial platforms where the predictions of many-body theories of correlated quantum materials can be tested in a controllable and tunable way, is one of the main challenges of condensed matter physics. Here we introduce artificial lattices made of lead halide perovskite nanocubes as a new platform to simulate and investigate the physics of correlated quantum materials. We demonstrate that optical injection of quantum confined excitons in this system realizes the two main features that ubiquitously pervade the phase diagram of many quantum materials: collective phenomena, in which long-range orders emerge from incoherent fluctuations, and the excitonic Mott transition, which has one-to-one correspondence with the insulator-to-metal transition described by the repulsive Hubbard model in a magnetic field. Our results demonstrate that time-resolved experiments provide a quantum simulator that is able to span a parameter range relevant for a broad class of phenomena, such as superconductivity and charge-density waves.

Collective Excitations of a Strongly Correlated Nonequilibrium Photon Fluid across the Insulator-Superfluid Phase Transition

Caleffi F., We develop a Gutzwiller theory for the nonequilibrium steady states of a strongly interacting photon fluid driven by a non-Markovian incoherent pump. In particular, we explore the collective modes of the system across the out-of-equilibrium insulator-superfluid transition of the system, characterizing the diffusive Goldstone mode in the superfluid phase and the excitation of particles and holes in the insulating one. Observable features in the pump-and-probe optical response of the system are highlighted. Our predictions are experimentally accessible to state-of-the-art circuit-QED devices and open the way for the study of novel driven-dissipative many-body scenarios with no counterparts at equilibrium.

Mott-enhanced exciton condensation in a Hubbard bilayer

Giuli S., Amaricci A., We study the conditions to realize an excitonic condensed phase in an electron-hole bilayer system with local Hubbard-like interactions at half-filling, where we can address the interplay with Mott localization. Using dynamical mean-field theory, we find that an excitonic state is stable in a sizable region of a phase diagram spanned by the intralayer (U) and interlayer (V) interactions. The latter term is expected to favor the excitonic phase which is indeed found in a slice of the phase diagram with V>U. Remarkably, we find that, when U is large enough, the excitonic region extends also for U>V, in contrast with naïve expectations. The extended stability of the excitonic phase can be linked to in-layer Mott localization and interlayer spin correlations. Using a mapping to a model with attractive interlayer coupling, we fully characterize the condensate phase in terms of its superconducting counterpart, thereby addressing its coherence and correlation length.

Massive superfluid vortices and vortex necklaces on a planar annulus

Caldara M., Richaud A., We study a superfluid in a planar annulus hosting vortices with massive cores. An analytical point-vortex model shows that the massive vortices may perform radial oscillations on top of the usual uniform precession of their massless counterpart. Beyond a critical vortex mass, this oscillatory motion becomes unstable and the vortices are driven towards one of the edges. The analogy with the motion of a charged particle in a static electromagnetic field leads to the development of a plasma orbit theory that provides a description of the trajectories which remains accurate even beyond the regime of small radial oscillations. These results are confirmed by the numerical solution of coupled two-component Gross-Pitaevskii equations. The analysis is then extended to a necklace of vortices symmetrically arranged within the annulus.

Time-dependent ghost Gutzwiller nonequilibrium dynamics

Guerci D., We introduce the time-dependent ghost Gutzwiller approximation (TD-gGA), a nonequilibrium extension of the ghost Gutzwiller approximation (gGA), a powerful variational approach which systematically improves on the standard Gutzwiller method by including auxiliary degrees of freedom. We demonstrate the effectiveness of TD-gGA by studying the quench dynamics of the single-band Hubbard model as a function of the number of auxiliary parameters. Our results show that TD-gGA captures the relaxation of local observables, in contrast with the time-dependent Gutzwiller method. This systematic and qualitative improvement leads to an accuracy comparable with time-dependent dynamical mean-field theory which comes at a much lower computational cost. These findings suggest that TD-gGA has the potential to enable extensive and accurate theoretical investigations of multiorbital correlated electron systems in nonequilibrium situations, with potential applications in the field of quantum control, Mott solar cells, and other areas where an accurate account of the nonequilibrium properties of strongly interacting quantum systems is required.

Full view on the dynamics of an impurity coupled to two one-dimensional baths

Stefanini M., We consider a model for the motion of an impurity interacting with two parallel, one-dimensional baths, described as two Tomonaga-Luttinger liquid systems. The impurity is able to move along the baths, and to jump from one to the other. We provide a perturbative expression for the evolution of the system when the impurity is injected in one of the baths, with a given wave packet. We obtain an approximation formally of infinite order in the impurity-bath coupling, which allows us to reproduce the orthogonality catastrophe. We monitor and discuss the dynamics of the impurity and its effect on the baths, in particular for a Gaussian wave packet. Besides the motion of the impurity, we also analyze the dynamics of the bath density and momentum density (i.e., the particle current), and show that it fits an intuitive semiclassical interpretation. We also quantify the correlation that is established between the baths by calculating the interbath, equal-time spatial correlation functions of both bath density and momentum, finding a complex pattern. We show that this pattern contains information on both the impurity motion and on the baths, and that these can be unveiled by taking appropriate "slices"of the time evolution.

Mass-driven vortex collisions in flat superfluids

Richaud A., Lamporesi G., Quantum vortices are often endowed with an effective inertial mass, due, for example, to massive particles in their cores. Such "massive vortices"display new phenomena beyond the standard picture of superfluid vortex dynamics, where mass is neglected. In this work, we demonstrate that massive vortices are allowed to collide, as opposed to their massless counterparts. We propose a scheme to generate controllable, repeatable, deterministic collisional events in pairs of quantum vortices. We demonstrate two mass-driven fundamental processes: (i) the annihilation of two counter-rotating vortices and (ii) the merging of two corotating vortices, thus pointing out new mechanisms supporting incompressible-to-compressible kinetic-energy conversion, as well as doubly quantized vortex stabilization in flat superfluids.

Exciton condensation in strongly correlated quantum spin Hall insulators

Amaricci A., Mazza G., Time-reversal symmetric topological insulators are generically robust with respect to weak local interaction unless symmetry-breaking transitions take place. Using dynamical mean-field theory, we solve an interacting model of quantum spin Hall insulators and show the existence at intermediate coupling of a symmetry-breaking transition to a nontopological insulator characterized by exciton condensation. This transition is of first order. For a larger interaction strength, the insulator evolves into a Mott one. The transition is continuous if magnetic order is prevented, and notably, for any finite Hund's exchange, it progresses through a Mott localization before the condensate coherence is lost. We show that the correlated excitonic state corresponds to a magneto-electric insulator, which allows for direct experimental probing. Finally, we discuss the fate of the helical edge modes across the excitonic transition.

Enhancement of chiral edge currents in (d+1)-dimensional atomic Mott-band hybrid insulators

Ferraretto M., Richaud A., Del Re L., Fallani L., We consider the effect of a local interatomic repulsion on synthetic heterostructures where a discrete synthetic dimension is created by Raman processes on top of SU(N)symmetric two-dimensional lattice systems. At a filling of one fermion per site, increasing the interaction strength, the system is driven towards a Mott state which is adiabatically connected to a band insulator. The chiral currents associated with the synthetic magnetic field increase all the way to the Mott transition, where they reach the maximum value, and they remain finite in the whole insulating state. The transition towards the Mott-band insulator is associated with the opening of a gap within the low-energy quasiparticle peak, while a mean-field picture is recovered deep in the insulating state.

Competing correlated insulators in multiorbital systems coupled to phonons

Scazzola A., Amaricci A., We study the interplay between electron-electron interaction and a Jahn-Teller phonon coupling in a two-orbital Hubbard model. We demonstrate that the e-ph interaction coexists with the Mott localization driven by the Hubbard repulsion U, but it competes with the Hund's coupling J. This interplay leads to two spectacularly different Mott insulators, a standard high-spin Mott insulator with frozen phonons which is stable when the Hund's coupling prevails, and a low-spin Mott-bipolaronic insulator favored by phonons, where the characteristic features of Mott insulators and bipolarons coexist. The two phases are separated by a sharp boundary along which an intriguing intermediate solution emerges as a kind of compromise between the two solutions.

Nematic spectral signatures of the Hund's metal

Fanfarillo L., Valli A., We show, by means of dynamical mean-field theory calculations, that the experimental fingerprints of the nematic order in iron-based superconductors are intrinsically connected with the electronic correlations in the Hund's correlated metallic state and they cannot be accessed via a renormalized quasiparticle picture. In particular, our results show that (i) in a metal in which correlations are dominated by the Hund's coupling the nematic ordering does not produce a rigid energy shift in the photoemission spectra, but a much richer spectral weight redistribution which mirrors the experimental results, and (ii) the nematic ordering is characterized by an orbital-selective coherence induced by the Hund's physics in agreement with the experimental picture.

Mott Quantum Critical Points at Finite Doping

Chatzieleftheriou M., Kowalski A., Berović M., Amaricci A., We demonstrate that a finite-doping quantum critical point (QCP) naturally descends from the existence of a first-order Mott transition in the phase diagram of a strongly correlated material. In a prototypical case of a first-order Mott transition the surface associated with the equation of state for the homogeneous system is "folded"so that in a range of parameters stable metallic and insulating phases exist and are connected by an unstable metallic branch. Here we show that tuning the chemical potential, the zero-temperature equation of state gradually unfolds. Under general conditions, we find that the Mott transition evolves into a first-order transition between two metals, associated with a phase separation region ending in the finite-doping QCP. This scenario is here demonstrated solving a minimal multiorbital Hubbard model relevant for the iron-based superconductors, but its origin - the splitting of the atomic ground state multiplet by a small energy scale, here Hund's coupling - is much more general. A strong analogy with cuprate superconductors is traced.

Flavour-selective localization in interacting lattice fermions

Tusi D., Franchi L., Livi L.F., Baumann K., Benedicto Orenes D., Del Re L., Barfknecht R.E., Zhou T.W., Inguscio M., Cappellini G., A large repulsion between particles in a quantum system can lead to their localization, an effect responsible for the Mott insulator phases in strongly correlated materials. In a system with multiple orbitals, an orbital-selective Mott insulator can form, where electrons in some orbitals are predicted to localize while others remain itinerant. Here we demonstrate a more general version of this phenomenon by observing flavour-selective localization in an atom-based quantum simulator. Our experiment realizes Fermi–Hubbard models with an SU(3) symmetry that can be broken using a tunable coupling between flavours. We observe an enhancement of the localization associated with a selective Mott transition and the emergence of flavour-dependent correlations. Our realization of flavour-selective Mott physics demonstrates the potential of cold atoms to simulate interacting multicomponent materials such as superconductors and topological insulators.

Steady-state quantum Zeno effect of driven-dissipative bosons with dynamical mean-field theory

Seclì M., We study a driven-dissipative Bose-Hubbard model in the presence of two-particle losses and an incoherent single-particle drive on each lattice site, leading to a finite-density stationary state. Using dynamical mean-field theory (DMFT) and an impurity solver based on exact diagonalization of the associated Lindbladian, we investigate the regime of strong two-particle losses. Here a stationary-state quantum Zeno effect emerges, as can be seen in the on-site occupation and spectral function. We show that DMFT captures this effect through its self-consistent bath. We show that, in the deep Zeno regime, the bath structure simplifies, with the occupation of all bath sites except one becoming exponentially suppressed. As a result, an effective dissipative hard-core Bose-Hubbard dimer model emerges, where the auxiliary bath site has single-particle dissipation controlled by the Zeno dissipative scale.

Charge and energy transfer in ac-driven Coulomb-coupled double quantum dots

Ludovico M.F., Abstract: We study the dynamics of charge and energy currents in a Coulomb-coupled double quantum dot system, when only one of the two dots is adiabatically driven by a time-periodic gate that modulates its energy level. Although the Coulomb coupling does not allow for electron transfer between the dots, it enables an exchange of energy between them which induces a time variation of charge in the undriven dot. We describe the effect of electron interactions at low temperature using a time-dependent slave-spin 1 formulation within mean field that efficiently captures the main effects of the strong correlations as well as the dynamical nature of the driving. We find that the currents induced in the undriven dot due to the mutual friction between inter-dot electrons are of the same order as those generated in the adiabatically driven dot. Interestingly, up to 43% of the energy injected by the ac sources can be transferred from the driven dot to the undriven one. We complete our analysis by studying the impact of the Coulomb interaction on the resistance of the quantum dot that is driven by the gate. Graphic abstract: [Figure not available: see fulltext.].

EDIpack: A parallel exact diagonalization package for quantum impurity problems

Amaricci A., Crippa L., Scazzola A., Petocchi F., Mazza G., de Medici L., We present EDIpack, an exact diagonalization package to solve generic quantum impurity problems. The algorithm includes a generalization of the look-up method introduced in Ref. [1] and enables a massively parallel execution of the matrix-vector linear operations required by Lanczos and Arnoldi algorithms. We show that a suitable Fock basis organization is crucial to optimize the inter-processors communication in a distributed memory setup and to reach sub-linear scaling in sufficiently large systems. We discuss the algorithm in details indicating how to deal with multiple orbitals and electron-phonon coupling. Finally, we outline the download, installation and functioning of the package. Program summary: Program title: EDIpack CPC Library link to program files: https://doi.org/10.17632/2hxhw9zjg9.1 Code Ocean capsule: https://codeocean.com/capsule/3537659 Licensing provisions: GPLv3 Programming language: Fortran, Python External dependencies: CMake (>=3.0.0), Scifortran, MPI Nature of problem: The solution of multi-orbital quantum impurity systems at zero or low temperatures, including the effective description of lattice models of strongly correlated electrons, are difficult to determine. Solution method: Use parallel exact diagonalization algorithm to compute the low lying spectrum and evaluate dynamical correlation functions.

Mimicking Multiorbital Systems with SU(N) Atoms: Hund’s Physics and Beyond

Richaud A., Ferraretto M., The physics of many interesting correlated materials can be captured by multiorbital Hubbard models, where conduction electrons feature an additional orbital degree of freedom. The multiorbital characteristic is not a mere complication, but it leads to an immensely richer landscape of physical regimes. One of the key features is the interplay between Hubbard repulsion and Hund’s exchange coupling, which has been shown to lead to orbital-selective correlations and to the existence of correlation-resilient metals (usually called Hund’s metals) defying Mott localization. Here, we show that experimentally available platforms of SU(N)-symmetric ultracold atoms can indeed mimic the rich physics disclosed by multiorbital materials, by exploiting the internal degrees of freedom of multicomponent atoms. We discuss in detail the SU(N) version of interaction-resilient Hund’s metal and some other interesting regimes.

Local versus nonlocal correlation effects in interacting quantum spin Hall insulators

Crippa L., Amaricci A., Adler S., Sangiovanni G., The impact of Coulomb interaction on the electronic properties of a quantum spin Hall insulator is studied using quantum cluster methods, disentangling local from nonlocal effects. We identify different regimes, according to the value of the bare mass term, characterized by drastically different self-energy contributions. For small mass, nonlocal correlations start to be important and eventually dominate over local ones when getting close enough to the zero-mass semimetallic line. For intermediate and large mass, local correlation effects outweigh nonlocal corrections, leading to a first-order topological phase transition, in agreement with previous predictions.