Properties Of Many-body Systems Research Articles

Adaptive variational quantum eigensolvers for highly excited states

Highly excited states of quantum many-body systems are central objects in the study of quantum dynamics and thermalization that challenge classical computational methods due to their volume-law entanglement content. In this work, we explore the potential of variational quantum algorithms to approximate such states. We propose an adaptive variational algorithm, adaptive VQE-X, that self-generates a variational ansatz for arbitrary eigenstates of a many-body Hamiltonian $H$ by attempting to minimize the energy variance with respect to $H$. We benchmark the method by applying it to an Ising spin chain with integrable and nonintegrable regimes, where we calculate various quantities of interest, including the total energy, magnetization density, and entanglement entropy. We also compare the performance of adaptive VQE-X to an adaptive variant of the folded-spectrum method. For both methods, we find a strong dependence of the algorithm's performance on the choice of operator pool used for the adaptive construction of the ansatz. In particular, an operator pool including long-range two-body gates accelerates the convergence of both algorithms in the nonintegrable regime. We also study the scaling of the number of variational parameters with system size, finding that an exponentially large number of parameters may be necessary to approximate individual highly excited states. Nevertheless, we argue that these methods lay a foundation for the use of quantum algorithms to study finite-energy-density properties of many-body systems.

Pairwise tomography networks for many-body quantum systems

We introduce the concept of pairwise tomography networks to characterise quantum properties in many-body systems and demonstrate an efficient protocol to measure them experimentally. Pairwise tomography networks are generators of multiplex networks where each layer represents the graph of a relevant quantifier such as, e.g., concurrence, quantum discord, purity, quantum mutual information, or classical correlations. We propose a measurement scheme to perform two-qubit tomography of all pairs showing exponential improvement in the number of qubits $N$ with respect to previously existing methods. We illustrate the usefulness of our approach by means of several examples revealing its potential impact to quantum computation, communication and simulation. We perform a proof-of-principle experiment demonstrating pairwise tomography networks of $W$ states on IBM Q devices.

Practical approach for beryllium atomic clusters: TD-DFT potential energy surfaces from equilibrium to dissociation for excited states of 2s → 2p

To shed light on the spectroscopic energy-smearing mechanism of the recently developed technique for multi-element analysis (e.g., forensic tests on artworks), which is called plume laser-induced fluorescence, practically computer simulations need to be accurate and fast enough for generating wide-range excited-state potential energy surfaces (PESs) from equilibrium to dissociation of large (non-equilibrated) atomic clusters. Currently, all the very high-level post-Hartree–Fock theories (e.g., coupled-cluster theory) are computationally too expensive for this purpose (e.g., taking at least ~ 23 years). After considering the extensive applications of time-dependent density-functional theory (TD-DFT) in computing the optical properties of many-body systems, we wonder how TD-DFT performs in the wide-range-PES generations because no such TD-DFT application is found by us in the literature (perhaps due to its insufficient static/non-dynamical correlation energy). In this work, we carried out TD-DFT calculations on beryllium atomic clusters from Be1 to Be50 (in contrast to open-shell H2 or Li2 system, we think the individual closed-shell Be systems at the dissociation limit could help TD-DFT to describe the static/non-dynamical correlation. For example, it is usually considered that Be2 has zero non-dynamical correlation energy in the literature) with and without Tamm–Dancoff approximation (TDA). Electronic excited-state properties (e.g., PES, equilibrium position, dissociation energy, fork intersection) associated with 2s → 2p are systematically investigated at a total of 48 levels of TD-DFT. Our calculations are thoroughly benchmarked against experimental results and (very) high-level theoretical values. In short, we find that for accurate simulations, it is necessary to use diffuse basis sets and the TDA approximation. TD-DFT with the small basis set 3-21+G* took ~ 2 min to finish a single-point excitation energy calculation on a linear Be50 (a toy model), while the large basis set 6-311+G(2df,2p) took 30 min. By contrast, a couple-cluster theory EOM-CCSD with 6-311+G(2df,2p) took 2.5 h to do the same but merely for a smaller linear Be10. In general, we suggest that TD-DFT:TDA with 3-21+G* should be practically fast and accurate enough for emulating our desired wide-range excited-state PESs of large Be atomic clusters (including conical intersection points of close energies) in the future studies. Nevertheless, benchmarking work on (much) larger sizes of Be clusters will always be more desirable whenever its computational costs at very high level of theories becomes more tractable.

Radiative heat transfer in fractal structures

The radiative properties of most structures are intimately connected to the way in which their constituents are ordered on the nano-scale. We have proposed a new representation for radiative heat transfer formalism in many-body systems. In this representation, we explain why collective effects depend on the morphology of structures, and how the arrangement of nanoparticles and their material affects the thermal properties in many-body systems. We investigated the radiative heat transfer problem in fractal (i.e., scale invariant) structures. In order to show the effect of the structure morphology on the collective properties, the radiative heat transfer and radiative cooling are studied and the results are compared for fractal and non-fractal structures. It is shown that fractal arranged nanoparticles display complex radiative behavior related to their scaling properties. we showed that, in contrast to non-fractal structures, heat flux in fractals is not of large-range character. By using the fractal dimension as a means to describe the structure morphology, we present a universal scaling behavior that quantitatively links the structure radiative cooling to the structure gyration radius.

Derivation of effective field theories

A general self-consistency approach allows for a thorough treatment of the corrections to the mean-field approximation (MFA). The natural extension of standard MFA with the help of a cumulant expansion leads to a point of view on the effective field theories. The proposed approach can be used for a systematic treatment of fluctuation effects of various length scales and, perhaps, for the development of a coarse-graining procedure. We outline and justify our method by some preliminary calculations. Results are given for the critical temperature and the Landau parameters of the phi(4) theory--the field counterpart of the Ising model. An important unresolved problem of the modern theory of phase transitions--the problem for the calculation of the true critical temperature--is considered within the framework of the present approach. A comprehensive description of the ground-state properties of many-body systems is also demonstrated.

Universal properties of conformal quantum many-body systems

Universal properties of many-body systems in conformal quantum mechanics in arbitrary dimensions are presented. Specially, a general structure of discrete energy spectra and eigenstates is found. Finally, a simple construction of a universal time operator conjugated to a conformal Hermitian or a PT-invariant Hamiltonian is proposed.

蛋白質フォールディングのダイナミックス : 主成分空間におけるエルゴード性

Using a novel method for determining the time scale for the self‐averaging of properties of many body systems, the effective ergodic behavior of a coarse‐grained protein model was investigated in terms of both the chemical characters and the principal components. The ergodic behavior was examined in detail with a focus on the time scale needed to obtain effective ergodicity.

Cumulant approach and coupled-cluster method for many-particle systems

Cumulants represent a natural language for expressing macroscopic properties of many-body systems. The most important property of cumulants is that of size consistency, i.e. a cumulant expression for an extensive variable scales with the size of the system, independent of possible further approximations used in the evaluation procedure. Cumulants can be considered as a generalization of linked diagrams known from diagrammatic technique of many-body theory. In this paper we outline a recently introduced method based on cumulants in order to derive expressions for zero-temperature properties of many-particle systems, i.e. the ground-state energy, static expectation values and dynamical correlation functions. This cumulant formalism allows one to describe weakly and strongly correlated systems along the same lines. We show that the coupled-cluster method known from quantum chemistry can be derived from our cumulant approach. Finally, we demonstrate the usefulness of the cumulant method by applying it to examples from solid-state physics and quantum chemistry.

Wigner-Kirkwood expansion: Calculation of "almost classical" static properties of a Lennard-Jones many-body system.

We have applied the Wigner--distribution-function formalism for the determination of the quantum corrections, which appear in the \ensuremath{\Elzxh} series expansion of the various ``almost classical'' properties of a many-body system. We have calculated the various averages which appear in the quantum corrections by means of molecular-dynamics computer simulation, up to the order ${\ensuremath{\Elzxh}}^{6}$ for the case of Boltzmann particles interacting via a Lennard-Jones potential. Here we report the results of the calculation for the potential and kinetic energies, for the pressure, for the free energy, and for the radial distribution function g(r) at nine different thermodynamic points. The application to the case of He, Ne, Ar, ${\mathrm{H}}_{2}$, and ${\mathrm{D}}_{2}$ are given whenever the \ensuremath{\Elzxh} series expansion can be considered convergent. The advantages and disadvantages of our method are also discussed.

Renormalized Kinetic Theory of Dense Fluids

The purpose of this review, which belongs to the series on time-depen­ dent statistical mechanics (1-4), is to assess the current status of kinetic theory description of thermal fluctuations in a dense fluid. The quanti­ ties of interest are the space-time correlation functions through which one can study theoretically and experimentally the nonequilibrium properties of many-body systems. Besides the review articles in these volumes, there exist recent reviews (5, 6) and monographs (7-9) dealing with the methods for calculating time correlation functions and the study of dynamics of simple liquids. Reviews (10-12) and a monograph (13) on the kinetic theory approach have also appeared. In the present discussions we focus on fluctuations at finite wavelengths and frequen­ cies and emphasize the direct confrontation between theoretical predic­ tions and experimental data. The problem to be addressed is the derivation of a kinetic equation for fluids over a wide range of density and without restrictions on the range of space-time variations, and the demonstration of the validity of such an equation. For dilute fluids the appropriate kinetic equation is the well-known linearized Boltzmann equation or its generalization to arbitrary frequency and wavelength. These equations involve only un­ correlated binary collisions, and they are computationally tractable. For dense fluids an appropriate equation that treats the dynamics realisti­ cally and is yet tractable for practical calculations is still a subject of active investigation. The development and analysis of equations of this kind is therefore the central theme of our review. There exists a reasonable amount of experimental results to indicate what are the important effects to consider in developing a kinetic theory description of dense fluids. These effects are not unique to kinetic