Cluster Expansion Technique Research Articles

Classical Simulation of Short-Time Quantum Dynamics

Recent progress in the development of quantum technologies has enabled the direct investigation of the dynamics of increasingly complex quantum many-body systems. This motivates the study of the complexity of classical algorithms for this problem in order to benchmark quantum simulators and to delineate the regime of quantum advantage. Here, we present classical algorithms for approximating the dynamics of local observables and nonlocal quantities such as the Loschmidt echo, where the evolution is governed by a local Hamiltonian. For short times, their computational cost scales polynomially with the system size and the inverse of the approximation error. In the case of local observables, the proposed algorithm has a better dependence on the approximation error than algorithms based on the Lieb-Robinson bound. Our results use cluster-expansion techniques adapted to the dynamical setting, for which we give a novel proof of their convergence. This has important physical consequences besides our efficient algorithms. In particular, we establish a novel quantum speed limit, a bound on dynamical phase transitions, and a concentration bound for product states evolved for short times.Received 2 November 2022Accepted 25 April 2023DOI:https://doi.org/10.1103/PRXQuantum.4.020340Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Research AreasQuantum information theoryQuantum statistical mechanicsPhysical SystemsLattice models in statistical physicsQuantum spin modelsTechniquesApproximation methods for many-body systemsComputational complexitySeries expansions & exact enumerationQuantum InformationStatistical Physics

Energy spectrum and magnetic properties of the decorated spin ladder models of nanomagnets on the base of polymeric transition metal compounds

The work is devoted to the theoretical study of the energy spectrum and low-temperature magnetic properties of the decorated spin-ladder model with the polyacene topology and the three types of the site spins. On the base of cluster expansion technique an approximate analytical treatment of lowest part of the energy spectra of two isomeric ladder structures was given. It is shown that the ladder model with singlet ground state is more stable than its isomeric analog with the macroscopic ground state spin. In addition, the numerical study of field dependence of low-temperature magnetization of 8- spin clusters of both ladder models was performed by means of exact diagonalization method. On the base of these results, it was shown the presence of an intermediate plateau in low-temperature magnetization profile of the above spin ladder models.

Equilibrium states for the massive Sine-Gordon theory in the Lorentzian signature

In this paper we investigate the massive Sine-Gordon model in the ultraviolet finite regime in thermal states over the two-dimensional Minkowski spacetime. We combine recently developed methods of perturbative algebraic quantum field theory with techniques developed in the realm of constructive quantum field theory over Euclidean spacetimes to construct the correlation functions of the equilibrium state of the Sine-Gordon theory in the adiabatic limit. First of all, the observables of the Sine-Gordon theory are seen as functionals over the free configurations and are obtained as a suitable combination of the S−matrices of the interaction Lagrangian restricted to compact spacetime regions over the free massive theory. These S−matrices are given as power series in the coupling constant with values in the algebra of fields over the free massive theory. Adapting techniques like conditioning and inverse conditioning to spacetimes with Lorentzian signature, we prove that these power series converge when evaluated on a generic field configuration. The latter observation implies convergence in the strong operator topology in the GNS representations of the considered states. In the second part of the paper, adapting the cluster expansion technique to the Lorentzian case, we prove that the correlation functions of the interacting equilibrium state at finite temperature (KMS state) can be constructed also in the adiabatic limit, where the interaction Lagrangian is supported everywhere in space.

The effect of Ni-doping on the stability of Li2MnO3 cathode material: a DFT study

The density functional theory with Hubbard parameter (DFT+U) incorporated within the Vienna Ab Initio Simulation Package was utilized to investigate the structural, electronic, elastic, and dynamical properties of pristine and Ni-doped Li2MnO3. The cluster expansion technique was used to generate the doped phases of Li2MnO3. The binary phase diagram predicted Li2Mn0.83Ni0.17O3 as the most stable phase with the lowest heat of formation. The study shows that Li2Mn0.83Ni0.17O3 is more thermodynamically stable than Li2MnO3 with a lower heat of formation. Additionally, the density of states showed that Li2Mn0.83Ni0.17O3 has a narrower band gap of 1.54 eV compared to the undoped structure with a band gap of 1.89 eV which leads to a higher electrical conductivity of the material. The elastic constants show that both structures are mechanically stable and lastly the phonon dispersions showed that these structures are vibrationally stable with no presence of imaginary vibrations. Finally, based on the results, Li2Mn0.83Ni0.17O3 can be proposed as potential cathode materials for use in lithium-ion batteries.

Effect of alloying on β2-ordered FeAl with Pd and Ir for high-temperature application and ductility enhancement

Β2-ordered FeAl and Fe3Al composition amongst other various compounds of transition metals and aluminium compositions have been of significance to researchers for application in industries for steel-IT coating purposes due to their well-adherent protective oxide layer that forms on the surface of such alloys at the metal/gas interface. We employed Cluster expansion (CE) technique to predict meta-stable and stable compositions of Fe1-XPd/IrXAl ternary. A Cluster Expansion phase diagram was predicted, with five stable Fe1-XPdXAl structures and three stable Fe1-XIrXAl structures having the lowest formation energies, respectively. Employed a first-principles approach to predict the mechanical properties, with four and two Pd and Ir ternary doped ductile structures and DMol3 technique to determine temperature dependence dynamical properties, that is, the binding energy of Fe50Al50, FePdAl2 and FeIrAl2 at various temperatures. Our findings showed that doping on FeAl with Pd and Ir significantly enhanced the binding energy that more energy would be required to disassemble the particles of the Ir system into individual parts; the hardness and ductility of the material for high-temperature application component coating for steel-IT superior protection.

Modeling Neutron Star Matter in the Age of Multimessenger Astrophysics

The interpretation of available and forthcoming data obtained from multimessenger astrophysical observations—potentially providing unprecedented access to neutron star properties—will require the development of novel, accurate theoretical models of dense matter. Of great importance, in this context, will be the capability for devising a description of thermal effects applicable to the study of quantities other than the equation of state, such as the transport coefficients and the neutrino mean free path in the nuclear medium. A formalism based on correlated basis states and the cluster expansion technique has been previously employed to derive a well-behaved effective interaction—suitable for use in standard perturbation theory—from a state-of-the-art nuclear Hamiltonian, including phenomenological two- and three-nucleon potentials. Here, we provide a comprehensive and self-contained account of the extension of this approach to the treatment of finite-temperature effects, and report the results of numerical calculations of a number of properties of nuclear matter with arbitrary neutron excess and temperature up to 50 MeV.

Ab initio prediction of vacancy energetics in HCP Al-Hf-Sc-Ti-Zr high entropy alloys and the subsystems

We perform ab initio density-functional-theory (DFT) calculations to investigate the vacancy formation and migration energies in HCP Al-Hf-Sc-Ti-Zr high entropy alloys (HEAs) and their subsystems from binaries to quinaries. For the vacancy formation properties, we utilize the special quasi-random structure approach in conjunction with a statistical analysis, from which temperature-dependent formation Gibbs energies as well as averaged atomic environments can be extracted. We show that the temperature-dependent vacancy formation Gibbs energy due to configurational excitations has a negative configurational entropy contribution. For the vacancy migration barriers, obtained from the nudged elastic band method, we apply the local cluster expansion technique to the kinetically resolved activation barriers to explore extended vacancy migration phase spaces. The local chemical environment effect and general trends in terms of the “high entropy” effect are analyzed.

Long range order in atomistic models for solids

The emergence of long range order at low temperatures in atomistic systems with continuous symmetry is a fundamental, yet poorly understood phenomenon in physics. To address this challenge we study a discrete microscopic model for an elastic crystal with dislocations in three dimensions, previously introduced by Ariza and Ortiz. The model is rich enough to support some realistic features of three-dimensional dislocation theory, most notably grains and the Read– Shockley law for grain boundaries, which we rigorously derive in a simple, explicit geometry. We analyze the model at positive temperatures, in terms of a Gibbs distribution with energy function given by the Ariza–Ortiz Hamiltonian plus a contribution from the dislocation cores. Our main result is that the model exhibits long range positional order at low temperatures. The proof is based on the tools of discrete exterior calculus, together with cluster expansion techniques.

Modeling excitonic Mott transitions in two-dimensional semiconductors

We analyze the many-particle correlations that affect the optical properties of two-dimensional semiconductors. These correlations manifest themselves through the specific optical resonances such as excitons, trions, etc. Starting from the generic electron-hole Hamiltonian and employing the microscopic Heisenberg equation of motion the infinite hierarchy of differential equations can be obtained. In order to decouple the system we address the cluster expansion technique which provides a regular procedure of consistent accounting of many-particle correlation contributions into the interband polarization dynamics. In particular, the partially taken into account three-particle correlations modify the behavior of absorption spectra with the emergence of a trion-like peak additional to excitonic ones. In contrast to many other approaches, the proposed one allows us to model the optical response of 2d semiconductors in the regime when the Fermi energies are of the order of the exciton and trion binding energies, thus allowing us to rigorously model the onset of the excitonic Mott transition, the regime being recently studied in various 2d semiconductors, such as transition metal dichalcogenides.

Probing the Coherence of Solid-State Qubits at Avoided Crossings

Optically addressable paramagnetic defects in wide-band-gap semiconductors are promising platforms for quantum communications and sensing. The presence of avoided crossings between the electronic levels of these defects can substantially alter their quantum dynamics and be both detrimental and beneficial for quantum information applications. Avoided crossings give rise to clock transitions, which can significantly improve protection from magnetic noise and favorably increase coherence time. However, the reduced coupling between electronic and nuclear spins at an avoided crossing may be detrimental to applications where nuclear spins act as quantum memories. Here we present a combined theoretical and experimental study of the quantum dynamics of paramagnetic defects interacting with a nuclear spin bath at avoided crossings. We develop a computational approach based on a generalization of the cluster expansion technique, which can account for processes beyond pure dephasing and describe the dynamics of any solid-state spin-qubits near avoided crossings. Using this approach and experimental validation, we determine the change in nature and source of noise at avoided crossings for divacancies in SiC. We find that we can condition the clock transition of the divacancies in SiC on multiple adjacent nuclear spins states. In our experiments, we demonstrate that one can suppress the effects of fluctuating charge impurities with depletion techniques, leading to an increased coherence time at clock transition, limited purely by magnetic noise. Combined with ab-initio predictions of spin Hamiltonian parameters, the proposed theoretical approach paves the way to designing the coherence properties of spin qubits from first principles.

Formation of Lightweight Ternary Polyhydrides and Their Hydrogen Storage Mechanism

We have studied Na-Li-H compositions by mixing cations of Na and Li under high pressure using ab initio random structure searching and cluster expansion techniques. We have found that high pressure...

Effects of Mg substitution on electronic properties of CaF2

We investigated the phase transitions of CaF2, using the state-of-the-art density functional theory. The calculations show that the fluorite structure, with the space group , transforms into the cotunnite structure, with the space group Pnma, at 8 GPa. The electronic band structure of the Pnma-CaF2 structure can be classified as an insulating phase with a wide bandgap, and the bandgap decreases under pressure above 70 GPa. Also, we proposed the Ca/Mg-substituted fluorides MgxCa1-xF2, using the cluster expansion technique which is commonly used to study alloys. We found that the Mg0.25Ca0.75F2 compound with a Pm structure is stable at 70 GPa. The results of the electronic band structure reveal that the substitution of Mg enhances the bandgaps of the Mg0.25Ca0.75F2 compounds under pressure above 70 GPa, compared with those of CaF2.

Thermodynamics of Spinel-like Cation Partial Ordering in Ultrahigh Power and Energy Density Li-Ion Batteries for Fast-Charging Electric Vehicles

Recently, a class of new materials exhibiting partial spinel-like cation order, but with excess Li and excess cation content was found to combine very high rate performance with high energy density [1]. Such spinels with a cation to anion ratio higher than 3 are unusual as it requires the face sharing of some tetrahedral and octahedral cations. In this presentation we will report on the ab-initio modeling of the metastable cation arrangements in these lithium manganese oxyfluorides that are responsible for the high-rate performance. The high dimensional configurational space of the materials is described by the cluster-expansion technique and parameterized with multiple hundreds of DFT calculations.Local, atomic-scale features, such as Li-Mn dumbbell formation, antisite defects, and interstitial defects giving rise to face-sharing cations which are challenging to resolve with state-of-the-art diffraction techniques are possible to directly evaluate in our computational approach. We present a computational analysis on how cation excess in spinel-like materials is accommodated and how local cation perturbations ultimately influence short-range order and bulk Li transport. Our understanding of how features in cation-excess spinel-like Li-Mn-O-F materials influence their high rate capabilities may motivate and accelerate design of other high-performance, fast-charging battery materials.[1] Ji, H., Wu, J., Cai, Z. et al. Ultrahigh power and energy density in partially ordered lithium-ion cathode materials. Nat Energy 5, 213–221 (2020).

Surface energetics of [formula omitted] alloys

The (100), (110) and (111) surface energies of random AlxTi1-xN alloys with homogeneous concentration profile are determined in first-principles calculations. The (100) surface has the lowest energy of 1.25 J/m2 in the case of TiN and 1.32 J/m2 for cubic AlN and exhibit very little concentration dependence. The (110) and (111) surfaces have much higher energy for all the compositions. The segregation energies of Ti and Al were obtained for the (100) surface of pure TiN and cubic AlN as well as Al0.5Ti0.5N and Al0.9Ti0.1N random alloys. In the latter case, we have used two different methods: direct averaging of the substitution energies with respect to the local environment of the substitution site and the cluster expansion technique (CLE). We find that the segregation of Ti is favorable in the whole concentration range of random AlxTi1-xN alloys. However, it is weak in almost the whole concentration range except in the Al-rich alloys: Al0.9Ti0.1N and cubic AlN. The strengthening of the surface segregation of Ti in the latter case is related to the sharp increase in phase separation tendency in AlxTi1-xN alloys at compositions close to pure AlN. The increased tendency for Ti segregation close to pure AlN helps explain the formation of a lamella structure in industrially important AlxTi1-xN coatings. As for nitrogen vacancies, their segregation energies are relatively small in the whole concentration range, but for pure AlN where they exhibit strong preference for the surface. The latter is obviously connected with the fact that cubic AlN has a high degree of ionic bonding and a vacancy creation on the nitrogen sublattice is highly energetically unfavorable, especially in the bulk due to a larger number of Al-N ionic bonds.

High-field expansion approach to kagome antiferromagnets with Dzyaloshinskii-Moriya interactions

We apply linked cluster expansion techniques to study the polarized high-field phase of a spin-half antiferromagnet on the Kagome lattice with Heisenberg and Dzyaloshinskii-Moriya interactions (DMI). We find that the Dirac points of the single-magnon spectrum without DMI are robust against arbitrary DMI when the magnetic field lies in the Kagome plane. Unlike the typical case where DMI gaps the spectrum, here we find that varying the DMI merely shifts the location of the Dirac points. In contrast, a magnetic field with a component out of the Kagome plane gaps the spectrum, leading to topological magnon bands. We map out a topological phase diagram as the couplings are varied by computing the band Chern numbers. A pair of phase transitions are observed and we find an enhanced thermal Hall conductivity near the phase boundary.

Optically controlled entangling gates in randomly doped silicon

Randomly-doped silicon has many competitive advantages for quantum computation; not only is it fast to fabricate but it could naturally contain high numbers of qubits and logic gates as a function of doping densities. We determine the densities of entangling gates in randomly doped silicon comprising two different dopant species. First, we define conditions and plot maps of the relative locations of the dopants necessary for them to form exchange interaction mediated entangling gates. Second, using nearest neighbour Poisson point process theory, we calculate the doping densities necessary for maximal densities of single and dual-species gates. We find agreement of our results with a Monte Carlo simulation, for which we present the algorithms, which handles multiple donor structures and scales optimally with the number of dopants and use it to extract donor structures not captured by our Poisson point process theory. Third, using the moving average cluster expansion technique, we make predictions for a proof of principle experiment demonstrating the control of one species by the orbital excitation of another. These combined approaches to density optimization in random distributions may be useful for other condensed matter systems as well as applications outside physics.

Thermodynamics and superconductivity of SxSe1−xH3

The compression of SH$_2$ and its subsequent decomposition to SH$_3$, presumably in a cubic Im$\overline{3}$m structure, has lead to the discovery of conventional superconductivity with the highest measured and confirmed $T_c$ to date, 203 K at 160 GPa. Recent theoretical studies suggest that a mixture of S with other elements of the chalcogen group could improve the superconducting temperature. Here, we present a detailed analysis of the thermodynamic properties of S and Se mixtures in the bcc lattice with Im$\overline{3}$m symmetry using a cluster expansion technique to explore the phase diagram of S$_x$Se$_{1-x}$H$_{3}$. In contrast to earlier reports, we find that S$_{0.5}$Se$_{0.5}$H$_3$ is not stable in the pressure range between 150-200 GPa. However, phases at compositions S$_{0.2}$Se$_{0.8}$H$_3$, S$_{0.\overline{3}}$Se$_{0.\overline{6}}$H$_3$, and S$_{0.6}$Se$_{0.4}$H$_3$ are stable at 200 GPa, while additional phases at S$_{0.25}$Se$_{0.75}$H$_3$ and S$_{0.75}$Se$_{0.25}$H$_3$ are accessible at lower pressures. Electron-phonon calculations show that the values of $T_c$ are consistently lower for all ternary phases, indicating that mixtures of S and Se with H might not be a viable route towards compounds with improved superconducting properties.

Cluster expansion based configurational averaging approach to bandgaps of semiconductor alloys.

Configurationally disordered semiconducting materials including semiconductor alloys [e.g., (GaN)1-x(ZnO)x] and stoichiometric materials with fractional occupation (e.g., LaTiO2N) have attracted a lot of interest recently in search for efficient visible light photo-catalysts. First-principles modeling of such materials poses great challenges due to the difficulty in treating the configurational disorder efficiently. In this work, a configurational averaging approach based on the cluster expansion technique has been exploited to describe bandgaps of ordered, partially disordered (with short-range order), and fully disordered phases of semiconductor alloys on the same footing. We take three semiconductor alloys [Cd1-xZnxS, ZnO1-xSx, and (GaN)1-x(ZnO)x] as model systems and clearly demonstrate that semiconductor alloys can have a system-dependent short-range order that has significant effects on their electronic properties.

Disagreement percolation for the hard-sphere model

Disagreement percolation connects a Gibbs lattice gas and i.i.d. site percolation on the same lattice such that non-percolation implies uniqueness of the Gibbs measure. This work generalises disagreement percolation to the hard-sphere model and the Boolean model. Non-percolation of the Boolean model implies the uniqueness of the Gibbs measure and exponential decay of pair correlations and finite volume errors. Hence, lower bounds on the critical intensity for percolation of the Boolean model imply lower bounds on the critical activity for a (potential) phase transition. These lower bounds improve upon known bounds obtained by cluster expansion techniques. The proof uses a novel dependent thinning from a Poisson point process to the hard-sphere model, with the thinning probability related to a derivative of the free energy.

Quantum–Continuum Modeling of Pd-Au(111) Surface Alloys Under Electrochemical Conditions

Bimetallic surface alloys often exhibit enhanced electrocatalytic performance due to ligand, ensemble, and bifunctional effects that arise from the presence of different transition metals along the catalyst surface. Segregation, dealloying, and poisoning events are common modes of catalyst deactivation that are difficult to suppress, limiting the durability of bimetallic catalysts in harsh environments. Efforts to estimate the stability of these novel catalyst formulations under operational conditions via first principles techniques is challenging due to the critical influence of solvation, surface electrification, and finite temperature effects. In this talk, we present a quantum-continuum model of the electrode-solution interface [Weitzner & Dabo, npj Comp. Mater. 3, 1 (2017)] that directly accounts for the influence of the electrochemical environment and pair this model with a recently developed voltage-sensitive cluster expansion technique to perform semi-grand canonical Monte Carlo simulations of the interface [Weitzner & Dabo, Phys. Rev. B (in press)]. We apply this method to study the voltage-dependent stability of Pd-Au(111) surface alloys under realistic electrochemical conditions and discuss the role of environmental effects on the durability of the catalyst.