Many-body Correlations Research Articles

Verified quantum information scrambling.

Quantum scrambling is the dispersal of local information into many-body quantum entanglements and correlations distributed throughout an entire system. This concept accompanies the dynamics of thermalization in closed quantum systems, and has recently emerged as a powerful tool for characterizing chaos in black holes1-4. However, the direct experimental measurement of quantum scrambling is difficult, owing to the exponential complexity of ergodic many-body entangled states. One way to characterize quantum scrambling is to measure an out-of-time-ordered correlation function (OTOC); however, because scrambling leads to their decay, OTOCs do not generally discriminate between quantum scrambling and ordinary decoherence. Here we implement a quantum circuit that provides a positive test for the scrambling features of a given unitary process5,6. This approach conditionally teleports a quantum state through the circuit, providing an unambiguous test for whether scrambling has occurred, while simultaneously measuring an OTOC. We engineer quantum scrambling processes through a tunable three-qubit unitary operation as part of a seven-qubit circuit on an ion trap quantum computer. Measured teleportation fidelities are typically about 80 per cent, and enable us to experimentally bound the scrambling-induced decay of the corresponding OTOC measurement.

Quantum coherence, many-body correlations, and non-thermal effects for autonomous thermal machines

One of the principal objectives of quantum thermodynamics is to explore quantum effects and their potential beneficial role in thermodynamic tasks like work extraction or refrigeration. So far, even though several papers have already shown that quantum effect could indeed bring quantum advantages, a global and deeper understanding is still lacking. Here, we extend previous models of autonomous machines to include quantum batteries made of arbitrary systems of discrete spectrum. We establish their actual efficiency, which allows us to derive an efficiency upper bound, called maximal achievable efficiency, shown to be always achievable, in contrast with previous upper bounds based only on the Second Law. Such maximal achievable efficiency can be expressed simply in term of the apparent temperature of the quantum battery. This important result appears to be a powerful tool to understand how quantum features like coherence but also many-body correlations and non-thermal population distribution can be harnessed to increase the efficiency of thermal machines.

Nonadditivity of the Adsorption Energies of Linear Acenes on Au(111): Molecular Anisotropy and Many-Body Effects.

Adsorption energies of chemisorbed molecules on inorganic solids usually scale linearly with molecular size and are well described by additive scaling laws. However, much less is known about scaling laws for physisorbed molecules. Our temperature-programmed desorption experiments demonstrate that the adsorption energy of acenes (benzene to pentacene) on the Au(111) surface in the limit of low coverage is highly nonadditive with respect to the molecular size. For pentacene, the deviation from an additive scaling of the adsorption energy amounts to as much as 0.7 eV. Our first-principles calculations explain the observed nonadditive behavior in terms of anisotropy of molecular polarization stemming from many-body electronic correlations. The observed nonadditivity of the adsorption energy has implications for surface-mediated intermolecular interactions and the ensuing on-surface self-assembly. Thus, future coverage-dependent studies should aim to gain insights into the impact of these complex interactions on the self-assembly of π-conjugated organic molecules on metal surfaces.

Morphometric Approach to Many-Body Correlations in Hard Spheres.

We model the thermodynamics of local structures within the hard sphere liquid at arbitrary volume fractions through the morphometric calculation of n-body correlations. We calculate absolute free energies of local geometric motifs in excellent quantitative agreement with molecular dynamics simulations across the liquid and supercooled liquid regimes. We find a bimodality in the density library of states where fivefold symmetric structures appear lower in free energy than fourfold symmetric structures and from a single reaction path predict a dynamical barrier which scales linearly in the compressibility factor. The method provides a new route to assess changes in the free energy landscape at volume fractions dynamically inaccessible to conventional techniques.

Modeling micro-heterogeneity in mixtures: The role of many body correlations.

A two-component interaction model is introduced herein, which allows us to describe macroscopic miscibility with various modes of tunable micro-segregation, ranging from phase separation to micro-segregation, and is in excellent agreement with structural quantities obtained from simulations and the liquid state hypernetted-chain like integral equation theory. The model is based on the conjecture that the many-body correlation bridge function term in the closure relation can be divided into one part representing the segregation effects, which are modeled herein, and the usual part representing random many body fluctuations. Furthermore, the model allows us to fully neglect these second contributions, thus increasing the agreement between the simulations and the theory. The analysis of the retained part of the many body correlations gives important clues about how to model the many body bridge functions for more realistic systems exhibiting micro-segregation, such as aqueous mixtures.

Dropping an impurity into a Chern insulator: A polaron view on topological matter

We investigate the properties of an impurity particle interacting with a Fermi gas in a Chern-insulating state. The interaction leads to the formation of an exotic polaron, which consists of a coherent superposition of the topologically trivial impurity and the surrounding topological cloud. We characterize this intriguing topologically composite object by calculating its transverse (Hall) conductivity, using diagrammatic as well as variational methods. The ``polaronic Hall conductivity,'' i.e., the transverse drag exerted by the dressing cloud on the impurity, is shown to exhibit a sharp jump from zero to a finite value whenever the surrounding cloud enters a topologically nontrivial state. In this way, the polaron partially inherits the topological properties of the Chern insulator through genuine interaction effects. This is also analyzed at the microscopic level of wave functions, by identifying a ``composite Berry curvature'' for the polaron, which closely mimics the Berry curvature of the Chern insulator's band structure. Finally, we discuss how this interplay between topology and many-body correlations can be studied in cold-atom experiments, using available technologies.

Dynamical vertex approximation for the attractive Hubbard model

In this work, we adapt the formalism of the dynamical vertex approximation (D$\Gamma$A), a diagrammatic approach including many-body correlations beyond the dynamical mean-field theory, to the case of attractive onsite interactions. We start by exploiting the ladder approximation of the D$\Gamma$A scheme, in order to derive the corresponding equations for the non-local 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 D$\Gamma$A 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 non-local correlations on the single-particle properties.

Configurational Entropy in Multicomponent Alloys: Matrix Formulation from Ab Initio Based Hamiltonian and Application to the FCC Cr-Fe-Mn-Ni System.

Configuration entropy is believed to stabilize disordered solid solution phases in multicomponent systems at elevated temperatures over intermetallic compounds by lowering the Gibbs free energy. Traditionally, the increment of configuration entropy with temperature was computed by time-consuming thermodynamic integration methods. In this work, a new formalism based on a hybrid combination of the Cluster Expansion (CE) Hamiltonian and Monte Carlo simulations is developed to predict the configuration entropy as a function of temperature from multi-body cluster probability in a multi-component system with arbitrary average composition. The multi-body probabilities are worked out by explicit inversion and direct product of a matrix formulation within orthonomal sets of point functions in the clusters obtained from symmetry independent correlation functions. The matrix quantities are determined from semi canonical Monte Carlo simulations with Effective Cluster Interactions (ECIs) derived from Density Functional Theory (DFT) calculations. The formalism is applied to analyze the 4-body cluster probabilities for the quaternary system Cr-Fe-Mn-Ni as a function of temperature and alloy concentration. It is shown that, for two specific compositions (CrFeMnNi and CrFeMnNi), the high value of probabilities for Cr-Fe-Fe-Fe and Mn-Mn-Ni-Ni are strongly correlated with the presence of the ordered phases L1-CrFe and L1-MnNi, respectively. These results are in an excellent agreement with predictions of these ground state structures by ab initio calculations. The general formalism is used to investigate the configuration entropy as a function of temperature and for 285 different alloy compositions. It is found that our matrix formulation of cluster probabilities provides an efficient tool to compute configuration entropy in multi-component alloys in a comparison with the result obtained by the thermodynamic integration method. At high temperatures, it is shown that many-body cluster correlations still play an important role in understanding the configuration entropy before reaching the solid solution limit of high-entroy alloys (HEAs).

Representing local atomic environment using descriptors based on local correlations.

Statistical learning of material properties is an emerging topic of research and has been tremendously successful in areas such as representing complex energy landscapes as well as in technologically relevant areas, like identification of better catalysts and electronic materials. However, analysis of large data sets to efficiently learn characteristic features of a complex energy landscape, for example, depends on the ability of descriptors to effectively screen different local atomic environments. Thus, discovering appropriate descriptors of bulk or defect properties and the functional dependence of such properties on these descriptors remains a difficult and tedious process. To this end, we develop a framework to generate descriptors based on many-body correlations that can effectively capture intrinsic geometric features of the local environment of an atom. These descriptors are based on the spectrum of two-body, three-body, four-body, and higher order correlations between an atom and its neighbors and are evaluated by calculating the corresponding two-body, three-body, and four-body overlap integrals. They are invariant to global translation, global rotation, reflection, and permutations of atomic indices. By systematically testing the ability to capture the local atomic environment, it is shown that the local correlation descriptors are able to successfully reconstruct structures containing 10-25 atoms which was previously not possible.

Incorporating Brueckner-Hartree-Fock correlations in energy density functionals

Recently, a microscopically motivated nuclear energy density functional was derived by applying the density matrix expansion to the Hartree-Fock (HF) energy obtained from long-range chiral effective field theory two- and three-nucleon interactions. However, the HF approach cannot account for all many-body correlations. One class of correlations is included by Brueckner-Hartree-Fock (BHF) theory, which gives an improved definition of the one-body HF potential by replacing the interaction by a reaction matrix $G$. In this paper, we find that the difference between the $G$-matrix and the nucleon-nucleon potential $V_{\mathrm{NN}}$ can be well accounted for by a truncated series of contact terms. This is consistent with renormalization group decoupling generating a series of counterterms as short-distance physics is integrated out. The coefficients $C_{n}$ of the power series expansion $\sum C_{n}q^{n}$ for the counterterms are examined for two potentials at different renormalization group resolutions and at a range of densities. The success of this expansion for $G-V_{\mathrm{NN}}$ means we can apply the density matrix expansion at the HF level with low-momentum interactions and density-dependent zero-range interactions to model BHF correlations.

Shattered time: can a dissipative time crystal survive many-body correlations?

We investigate the emergence of a time crystal (TC) in a driven dissipative many-body spin array. In this system the interplay between incoherent spin pumping and collective emission stabilizes a synchronized non-equilibrium steady state which in the thermodynamic limit features a self-generated time-periodic pattern imposed by collective elastic interactions. In contrast to prior realizations where the time symmetry is already broken by an external drive, here it is only spontaneously broken by the elastic exchange interactions and manifest in the two-time correlation spectrum. Employing a combination of exact numerical calculations and a second-order cumulant expansion, we investigate the impact of many-body correlations on the TC formation and establish a connection between the regime where it is stable and where the system features a slow growth rate of the mutual information. This observation allows us to conclude that the TC studied here is an emergent semi-classical out-of-equilibrium state of matter. We also confirm the rigidity of the TC to single-particle dephasing. Finally, we discuss an experimental implementation using long lived dipoles in an optical cavity.

Extracting many-body color charge correlators in the proton from exclusive DIS at large Bjorken x

We construct a general QCD light front formalism to compute many-body color charge correlators in the proton. These form factors can be extracted from deeply inelastic scattering measurements of exclusive final states in analogy to electromagnetic form factors extracted in elastic electron scattering experiments. Particularly noteworthy is the potential to extract a novel Odderon form factor, either indirectly from exclusive $J/\Psi$ measurements, or directly from exclusive measurements of the $\eta_c$ or tensor mesons at large Bjorken x. Besides the intrinsic information conveyed by these color charge correlators on the spatio-temporal tomography at the sub-femtoscopic scale at large x, the corresponding cumulants extend the domain of validity of McLerran-Venugopalan type weight functionals from small x and large nuclei to nucleons and light nuclei at large $x$, as well as to non-zero momentum transfer. This may significantly reduce nonperturbative systematic uncertainties in the initial conditions for QCD evolution equations at small $x$ and could be of strong relevance for the phenomenology of present and future collider experiments.

Hund-Enhanced Electronic Compressibility in FeSe and its Correlation with T_{c}.

We compute the compressibility of the conduction electrons in both bulk orthorhombic FeSe and monolayer FeSe on a SrTiO_{3} substrate, including dynamical electronic correlations within slave-spin mean-field + density-functional theory. Results show a zone of enhancement of the electronic compressibility crossing the interaction-doping phase diagram of these compounds in accord with previous simulations on iron pnictides and in general with the phenomenology of Hund's metals. Interestingly, at ambient pressure FeSe is found slightly away from the zone with enhanced compressibility but moved right into it with hydrostatic pressure, while in monolayer FeSe the stronger enhancement region is realized on the electron-doped side. These findings correlate positively with the enhancement of superconductivity seen in experiments, and support the possibility that Hund's induced many-body correlations boost superconductive pairing when the system is at the frontier of the normal- to Hund's metal crossover.

Microscopic optical potentials for calcium isotopes

We construct nucleonic microscopic optical potentials by combining the Green's function approach with the coupled-cluster method for $\rm{^{40}Ca}$ and $\rm{^{48}Ca}$. For the computation of the ground-state of $\rm{^{40}Ca}$ and $\rm{^{48}Ca}$, we use the coupled-cluster method in the singles-and-doubles approximation, while for the A = $\pm 1$ nuclei we use particle-attached/removed equation-of-motion method truncated at two-particle-one-hole and one-particle-two-hole excitations, respectively. Our calculations are based on the chiral nucleon-nucleon and three-nucleon interaction $\rm{NNLO_{sat}}$, which reproduces the charge radii of $^{40}$Ca and $^{48}$Ca, and the chiral nucleon-nucleon interaction $\rm{NNLO_{opt}}$. In all cases considered here, we observe that the overall form of the neutron scattering cross section is reproduced for both interactions, but the imaginary part of the potential, which reflects the loss of flux in the elastic channel, is negligible. The latter points to neglected many-body correlations that would appear beyond the coupled-cluster truncation level considered in this work. We show that, by artificially increasing the parameter $\eta$ in the Green's function, practical results can be further improved.

Realistic shell-model calculations for p -shell nuclei including contributions of a chiral three-body force

In this paper we present an evolution of our derivation of the shell-model effective Hamiltonian, namely introducing effects of three-body contributions. More precisely, we consider a three-body potential at next-to-next-to-leading order in chiral perturbation theory, and the induced three-body forces that arise from many-body correlations among valence nucleons. The first one is included, in the derivation of the effective Hamiltonian for one- and two-valence nucleon-systems, at first order in the many-body perturbation theory. Namely, we include only the three-body interaction between one or two valence nucleons and those belonging to the core. For nuclei with more than two valence particles, both induced - turned on by the two-body potential - and genuine three-body forces come into play. Since it is difficult to perform shell-model calculations with three-body forces, these contributions are estimated for the ground-state energy only. In order to establish the reliability of our approximations, we focus attention on nuclei belonging to the p shell, aiming to benchmark our calculations against those performed with the ab initio no-core shell-model. The obtained results are satisfactory, and pave the way to the application of our approach to nuclear systems with heavier masses.

Many-body correlations brought to light in absorption spectra of diluted magnetic semiconductors

Diluted magnetic semiconductors are materials well known to exhibit strong correlations which typically manifest in carrier-mediated magnetic ordering. In this Rapid Communication, we show that the interaction between excitons and magnetic impurities in these materials is even strong enough to cause a significant deviation from the bare exciton picture in linear absorption spectra of quantum well nanostructures. It is found that exciton-impurity correlations induce a characteristic fingerprint in the form of an additional feature close to the exciton resonance in combination with a shift of the main exciton line of up to a few meV. We trace back these features to the form of the self-energy and demonstrate that reliable values of the average correlation energy per exciton can be extracted directly from the spectra. Since the only requirement for our findings is sufficiently strong correlations, the results can be generalized to other strongly correlated systems.

Nonlocal electron correlations in an itinerant ferromagnet

Our understanding of the properties of ferromagnetic materials, widely used in spintronic devices, is fundamentally based on their electronic band structure. However, even for the most simple elemental ferromagnets, electron correlations are prevalent, requiring descriptions of their electronic structure beyond the simple picture of independent quasi-particles. Here, we give evidence that in itinerant ferromagnets like cobalt these electron correlations are of nonlocal origin, manifested in a complex self-energy Σσ(E,k) that disperses as function of spin σ, energy E, and momentum vector k. Together with one-step photoemission calculations, our experiments allow us to quantify the dispersive behaviour of the complex self-energy over the whole Brillouin zone. At the same time we observe regions of anomalously large “waterfall”-like band renormalization, previously only attributed to strong electron correlations in high-TC superconductors, making itinerant ferromagnets a paradigmatic test case for the interplay between band structure, magnetism, and many-body correlations.

Number-Phase Fluctuations in Isolated Superconductors

We improve the Bardeen-Cooper-Schrieffer wave function with a fixed particle number so as to incorporate many-body correlations beyond the mean-field treatment. It is shown that the correlations lower the ground-state energy far more than Cooper-pair condensation in the weak-coupling region. Moreover, they naturally bring a superposition over the number of condensed particles. Thus, Cooper-pair condensation is special among the various bound-state formations of quantum mechanics in that number fluctuations are necessarily present in the condensate through the dynamical exchange of particles with the non-condensate reservoir. On the basis of this result, we propose $\varDelta N_{\rm con}\cdot \varDelta \phi\gtrsim 1$ as the uncertainty relation relevant to the number-phase fluctuations in superconductors and superfluids, where the number of condensed particles $N_{\rm con}$ is used instead of the total particle number $N$. The formula implies that a macroscopic phase $\phi$ can be established even in number-fixed superconductors and superfluids since $\varDelta N_{\rm con}\gg 1$.

Many-body correlations in shell model effective interactions derived by ab initio methods and the Vlow-k approach**Supported by National Natural Science Foundation of China (11505056, U1732138, 11605054, 11790325, 11305108, 11575290, 11675148, 11747312, 11775316) and the Outstanding Young Talent Research Fund of Zhengzhou University (1521317002)

We investigate many-body correlations caused by two- and three-body (2-, 3bd) forces. Shell-model effective interactions derived from ab initio methods (coupled-cluster method, no-core shell model) are adopted. Vlow-k potentials, based on many-body perturbation theory, are also tested, especially for their cut-off dependence. We compare the central, tensor and spin-orbit interactions from microscopic theory to the fitted interactions. After the inclusion of the three-body force, the matrix elements become fairly close to those fitted directly to experimental data. Calculations of neutron-rich oxygen isotopes are performed, to clarify the effects of 3bd forces, tensor, and spin-orbit interactions on the nuclear binding and excitation energies. We find that the 3bd force can influence the binding energies greatly, which also determines the drip line position, while its effect on excitation energies is not very pronounced. The spin-orbit force, which is part of the 2bd force, can affect the shell structure explicitly, at least for neutron-rich systems.

Structural and Collective Dynamics of Bi50Zn50 of binary metallic glass

In the present paper, structural properties, collective dynamics and elastic properties have been studied of Bi50Zn50 liquid metallic glass at a wide range of temperatures. Ashcroft and Langreth binary structure factor have been used to study for static structure factor and pair correlation function for present alloy. The collective excitation has been studied for longitudinal and transverses phonon modes based on our well-established model potential along with Hubbard and Beeby (HB) approach. These frequencies are expressed in terms of many-body correlation functions of atoms as well as of interatomic potential. The important ingredients in the present study are the pair-potential and pair-correlation functions. The local field correlation functions due to Hartree (H) and Farid et al (F) are employed to investigate the influence of the screening effects on the vibrational dynamics of Bi50Zn50 liquid metallic glass. The results for bulk modulus (BT), modulus of rigidity (G), Poisson’s ratio (ξ), Young’s modulus (Y), Debye temperature (ƟD), the propagation velocity of elastic waves and dispersion curves are reported. Good agreement with the experiment is observed for the structure factors and elastic properties results are consistent and confirm the applicability of model potential and self-consistent phonon theory for such studies.