Quantum Monte Carlo Research Articles

Multicomponent synthesis and designing of tetrasubstituted imidazole compounds catalyzed via ionic-liquid for acid steel corrosion protection: Experimental exploration and theoretical calculations

Five new tetrasubstituted imidazoles were designed with outstanding yields (83%−92%) in the occurrence of ionic liquid-based-pyridinium as a catalyst. The constructions of all synthesized derivatives were established by spectral tools and their purities were verified using thin-layer chromatography (TLC), displaying single-spot. The performance of corrosion protection of the prepared imidazole derivatives was examined theoretically and practically for acid steel corrosion. The experimental study was conducted by electrochemical (electrochemical impedance spectroscopy (EIS) and Tafel polarization (PPS)) tools. The findings from the used approaches concluded that the synthesized compounds were well-organized inhibitors with an efficiency of 90.7%−98.5% at 50 °C and 0.7 mmol·L−1. The Tafel polarization results indicate the protective action of the additives was under mixed-monitoring. The additive adsorption on the electrode interface performed as a distinguished aspect for protection. The surface exploration on the blank and protected metal was completed by field emission scanning electron microscopy (FE-SEM). Computational studies by Monte Carlo (MC) simulation and quantum chemical calculation (DFT) were related to practical findings. The corrosion protection adsorption mechanism was reinforced by the preferable fitted Langmuir isotherm model. All findings from the applied-inspected approaches alternately confirm each other.

Perturbative Quantum MonteCarlo Method for Nuclear Physics.

While first order perturbation theory is routinely used in quantum MonteCarlo (QMC) calculations, higher-order terms present significant numerical challenges. We present a new approach for computing perturbative corrections in projection QMC calculations. We demonstrate the method by computing nuclear ground state energies up to second order for a realistic chiral interaction. We calculate the binding energies of several light nuclei up to ^{16}O by expanding the Hamiltonian around the Wigner SU(4) limit and find good agreement with data. In contrast to the natural ordering of the perturbative series, we find remarkably large second-order energy corrections. This occurs because the perturbing interactions break the symmetries of the unperturbed Hamiltonian. Our method is free from the sign problem and can be applied to QMC calculations for many-body systems in nuclear physics, condensed matter physics, ultracold atoms, and quantum chemistry.

Ab initio diffusion quantum Monte Carlo study of the structural and electronic properties of small Lithium-Chloride LinCl (0,1+) (n = 1–7) clusters

Superalkali metal clusters as the potential building blocks of nanostructured materials have excellent nonlinear optical properties. In the present study, the structural and electronic properties of small LinCl (0,1+) (n = 1–7) clusters are investigated by the diffusion Monte Carlo method for the first time. We calculate the total ground state energy, ionization potential, binding energy, dissociation energy, and second difference in energy. We also analyze the contribution of electron correlation effects to the electron properties of the clusters. The DMC results of ionization potentials are more consistent with the experimental values. In addition, there is an odd–even alternation phenomenon that Li3Cl, Li5Cl, and Li7Cl are more stable, while Li2Cl+, Li4Cl+, and Li6Cl+ are more stable. The successful application of the quantum Monte Carlo (QMC) method on the small LinCl (0,1+) (n = 1–7) clusters implies that QMC may serve as a feasible tool to investigate the electronic properties of other superalkli metal clusters.

Family of Nanoclusters, Ln33 (Ln = Sm/Eu) and Gd32, Exhibiting Magnetocaloric Effects and Fluorescence Sensing for MnO4.

A family of nanoclusters, [Ln33(EDTA)12(OAc)2(CO3)4(μ3-OH)36(μ5-OH)4(H2O)38]·OAc·xH2O (x ≈ 50, Ln = Sm for 1; x ≈ 70, Ln = Eu for 2) and [Gd32(EDTA)12(OAc)2(C2O4)(CO3)2(μ3-OH)36(μ5-OH)4(H2O)36]·x(H2O) (x ≈ 70 for 3; H4EDTA = ethylene diamine tetraacetic acid), was prepared through the assembly of repeating subunits under the action of an anion template. The analysis of the structures showed that compounds 1 and 2 containing 33 Ln3+ ions were isostructural, which were constructed by three kinds of subunits in the presence of CO32- as an anion template, while compound 3 had a slightly different structure. Compound 3 containing 32 Gd3+ ions was formed by three types of subunits in the presence of CO32- and C2O42- as a mixed anion template. The CO32- anions came from the slow fixation of CO2 in the air. Meanwhile, one kind of high-nuclearity lanthanide clusters showed high chemical stability. The quantum Monte Carlo (QMC) calculation suggested that weak antiferromagnetic interactions were dominant between Gd3+ ions in 3. Magnetocaloric studies showed that compound 3 had a large entropy change of 43.0 J kg-1 K-1 at 2 K and 7 T. Surprisingly, compound 2 showed excellent recognition and detection effects for permanganate in aqueous solvents based on the fluorescence quenching phenomenon.

Superconductivity in graphene-related systems: A study of quantum MonteCarlo methods

We review a quantum Monte Carlo approach to study superconductivity in graphene-related systems.The emergence of superconductivity in doped graphene-based materials hasbeen theoretically predicted for over a decade.For single-layer graphene, antiferromagnetic fluctuations favor thespin-singlet superconductivity when packed near the Dirac point.However, quantum Monte Carlo studies have found electronic correlations tobe insufficient to drive superconductivity because of the single-layergraphene's extremely low electronic density of states.Unconventional superconductivity with $p+{\rm~i}p$ superconducting pairingsymmetry is possible if the system is doped to a van Hove singularity,where the density of states diverges.However, despite extensive experimental work, superconductivity has yet tobe found in single-layer graphene.Recently, unconventional superconductivity was discovered in experimentson twisted bilayer graphene, followed by the experimental discovery ofsuperconductivity in ABC-stacked trilayer graphene and multilayer graphenesystems.These findings have attracted the attention of many physicists.In this study, we review the unique properties of superconducting statesin graphene, experimentalcontrol of superconductivity in the twisted bilayer and trilayer graphene,and associated gate-tunable insulator.In addition, a brief overview of recent research progress in condensedmatter physics in term of electronically correlated states in twistedmultilayer graphene is presented.

Quantum Coulomb glass on the Bethe lattice

We study the Coulomb glass emerging from the interplay of strong interactions and disorder in a model of spinless fermions on the Bethe lattice. In the infinite coordination number limit, strong interactions induce a metallic Coulomb glass phase with a pseudogap structure at the Fermi energy. Quantum and thermal fluctuations both melt this glass and induce a disordered quantum liquid phase. We combine self-consistent diagrammatic perturbation theory with continuous time quantum Monte-Carlo simulations to obtain the complete phase diagram of the electron glass and to characterize its dynamical properties in the quantum liquid, as well as in the replica symmetry broken glassy phase. Tunneling spectra display an Efros-Shklovskii pseudogap upon decreasing temperatures, but the density of states remains finite at the Fermi energy due to residual quantum fluctuations. Our results bear relevance to the metallic glass phase observed in Si inversion layers.

Making the most of data: Quantum Monte Carlo postanalysis revisited.

In quantum Monte Carlo (QMC) methods, energy estimators are calculated as (functions of) statistical averages of quantities sampled during a calculation. Associated statistical errors of these averages are often estimated. This error estimation is not straightforward and there are several choices of the error estimation methods. We evaluate the performance of three methods (the Straatsma method, an autoregressive model, and a blocking analysis based on von Neumann's ratio test for randomness) for the energy time series given by three QMC methods [diffusion Monte Carlo, full configuration interaction Quantum Monte Carlo (FCIQMC), and coupled cluster Monte Carlo (CCMC)]. From these analyses, we describe a hybrid analysis method which provides reliable error estimates for a series of various lengths of FCIQMC and CCMC's time series. Equally important is the estimation of the appropriate start point of the equilibrated phase. We establish that a simple mean squared error rule method as described by White [K. P. White, Jr., Simulation 69(6), 323 (1997)10.1177/003754979706900601] can provide reasonable estimations.

Electron correlation and confinement effects in quasi-one-dimensional quantum wires at high density

We study the ground-state properties of ferromagnetic quasi-one-dimensional quantum wires using the quantum Monte Carlo (QMC) method for various wire widths $b$ and density parameters $r_\text{s}$. The correlation energy, pair-correlation function, static structure factor, and momentum density are calculated at high density, $r_\text{s}=0.5$. It is observed that the peak in the static structure factor at $k=2k_\text{F}$ grows as the wire width decreases. We obtain the Tomonaga-Luttinger liquid parameter $K_\rho$ from the momentum density. It is found that $K_\rho$ increases by about $10$\% between wire widths $b=0.01$ and $b=0.5$. We also obtain ground-state properties of finite thickness wires theoretically using the first-order random phase approximation (RPA) with exchange and self-energy contributions, which is exact in the high-density limit. Analytical expressions for the static structure factor and correlation energy are derived for $b \ll r_\text{s}<1$. It is found that the correlation energy varies as $b^2$ for $b \ll r_\text{s}$ from its value for an infinitely thin wire. It is observed that the correlation energy depends significantly on the wire model used (harmonic versus cylindrical confinement). The first-order RPA expressions for the structure factor, pair-correlation function, and correlation energy are numerically evaluated for several values of $b$ and $r_\text{s} \leq 1$. These are compared with the QMC results in the range of applicability of the theory.

Unbiasing fermionic quantum Monte Carlo with a quantum computer

Interacting many-electron problems pose some of the greatest computational challenges in science, with essential applications across many fields. The solutions to these problems will offer accurate predictions of chemical reactivity and kinetics, and other properties of quantum systems1–4. Fermionic quantum Monte Carlo (QMC) methods5,6, which use a statistical sampling of the ground state, are among the most powerful approaches to these problems. Controlling the fermionic sign problem with constraints ensures the efficiency of QMC at the expense of potentially significant biases owing to the limited flexibility of classical computation. Here we propose an approach that combines constrained QMC with quantum computation to reduce such biases. We implement our scheme experimentally using up to 16 qubits to unbias constrained QMC calculations performed on chemical systems with as many as 120 orbitals. These experiments represent the largest chemistry simulations performed with the help of quantum computers, while achieving accuracy that is competitive with state-of-the-art classical methods without burdensome error mitigation. Compared with the popular variational quantum eigensolver7,8, our hybrid quantum-classical computational model offers an alternative path towards achieving a practical quantum advantage for the electronic structure problem without demanding exceedingly accurate preparation and measurement of the ground-state wavefunction.

Quantum Criticality of Antiferromagnetism and Superconductivity with Relativity.

We study a quantum phase transition from a massless to massive Dirac fermion phase in a new two-dimensional bipartite lattice model of electrons that is amenable to sign-free quantum MonteCarlo simulations. Importantly, interactions in our model are not only invariant under SU(2) symmetries of spin and charge like the Hubbard model, but they also preserve an Ising-like electron spin-charge flip symmetry. From unbiased fermion bag MonteCarlo simulations with up to 2304 sites, we show that the massive fermion phase spontaneously breaks this Ising symmetry, picking either antiferromagnetism or superconductivity, and that the transition at which both orders are simultaneously quantum critical belongs to a new "chiral spin-charge symmetric" universality class. We explain our observations using effective potential and renormalization group calculations within the framework of a continuum field theory.

Nonlocal Correlation and Entanglement of Ultracold Bosons in the 2D Bose–Hubbard Lattice at Finite Temperature

AbstractThe temperature‐dependent behavior emerging in the vicinity of the superfluid (SF) to Mott‐insulator (MI) transition of interacting bosons in a 2D optical lattice, described by the Bose–Hubbard model is investigated. The equilibrium phase diagram at finite‐temperature is computed using the cluster mean‐field (CMF) theory including a finite‐cluster‐size‐scaling. The SF, MI, and normal fluid (NF) phases are characterized as well as the transition or crossover temperatures between them are estimated by computing physical quantities such as the superfluid fraction, compressibility and sound velocity using the CMF method. It is found that the nonlocal correlations included in a finite cluster, when extrapolated to infinite size, leads to quantitative agreement of the phase boundaries with quantum Monte Carlo (QMC) results as well as with experiments. Moreover, it is shown that the von Neumann entanglement entropy within a cluster corresponds to the system's entropy density and that it is enhanced near the SF–MI quantum critical point (QCP) and at the SF–NF boundary. The behavior of the transition lines near this QCP, at and away from the particle‐hole (p–h) symmetric point located at the Mott‐tip, is also discussed. The results obtained by using the CMF theory can be tested experimentally using the quantum gas microscopy method.

Ultra-Dilute Gas of Polarons in a Bose–Einstein Condensate

We investigate the properties of a dilute gas of impurities embedded in an ultracold gas of bosons that forms a Bose–Einstein condensate (BEC). This work focuses mainly on the equation of state (EoS) of the impurity gas at zero temperature and the induced interaction between impurities mediated by the host bath. We use perturbative field-theory approaches, such as Hugenholtz–Pines formalism, in the weakly interacting regime. In turn, for strong interactions, we aim at non-perturbative techniques such as quantum–Monte Carlo (QMC) methods. Our findings agree with experimental observations for an ultra dilute gas of impurities, modeled in the framework of the single impurity problem; however, as the density of impurities increases, systematic deviations are displayed with respect to the one-body Bose polaron problem.

Quantum Monte Carlo simulations of highly frustrated magnets in a cluster basis: The two-dimensional Shastry-Sutherland model

Quantum Monte Carlo (QMC) simulations constitute nowadays one of the most powerful methods to study strongly correlated quantum systems, provided that no “sign problem” arises. However, many systems of interest, including highly frustrated magnets, suffer from an average sign that is close to zero in standard QMC simulations. Nevertheless, a possible sign problem depends on the simulation basis, and here we demonstrate how a suitable choice of cluster basis can be used to eliminate or at least reduce the sign problem in highly frustrated magnets that were so far inaccessible to efficient QMC simulations. We focus in particular on the application of a two-spin (dimer)-based QMC method to the thermodynamics of the spin-1/2 Shastry-Sutherland model for SrCu2(BO3)2.

Ground-state properties of the narrowest zigzag graphene nanoribbon from quantum Monte Carlo and comparison with density functional theory.

By means of quantum Monte Carlo (QMC) calculations from first-principles, we study the ground-state properties of the narrowest zigzag graphene nanoribbon with an infinite linear acene structure. We show that this quasi-one-dimensional system is correlated and its ground state is made of localized π electrons whose spins are antiferromagnetically ordered. The antiferromagnetic (AFM) stabilization energy [36(3) meV per carbon atom] and the absolute magnetization [1.13(0.11) μB per unit cell] predicted by QMC are sizable, and they suggest the survival of antiferromagnetic correlations above room temperature. These values can be reproduced to some extent by density functional theory (DFT) within the DFT+U framework or by using hybrid functionals. Based on our QMC results, we then provide the strength of Hubbard repulsion in DFT+U suitable for this class of systems.

Metallic and Deconfined Quantum Criticality in Dirac Systems

Motivated by the physics of spin-orbital liquids, we study a model of interacting Dirac fermions on a bilayer honeycomb lattice at half filling, featuring an explicit global SO(3)×U(1) symmetry. Using large-scale auxiliary-field quantum MonteCarlo (QMC) simulations, we locate two zero-temperature phase transitions as function of increasing interaction strength. First, we observe a continuous transition from the weakly interacting semimetal to a different semimetallic phase in which the SO(3) symmetry is spontaneously broken and where two out of three Dirac cones acquire a mass gap. The associated quantum critical point can be understood in terms of a Gross-Neveu-SO(3) theory. Second, we subsequently observe a transition toward an insulating phase in which the SO(3) symmetry is restored and the U(1) symmetry is spontaneously broken. While strongly first order at the mean-field level, the QMC data are consistent with a direct and continuous transition. It is thus a candidate for a new type of deconfined quantum critical point that features gapless fermionic degrees of freedom.

Perils of embedding for quantum sampling

Given quantum hardware that enables sampling from a family of natively implemented Hamiltonians, how well can one use that hardware to sample from a Hamiltonian outside that family? A common approach is to minor embed the desired Hamiltonian in a native Hamiltonian. In Phys. Rev. Research 2, 023020 (2020) it was shown that minor embedding can be detrimental for classical thermal sampling. Here, we generalize these results by considering quantum thermal sampling in the transverse-field Ising model, i.e. sampling a Hamiltonian with non-zero off diagonal terms. To study these systems numerically we introduce a modification to standard cluster update quantum Monte-Carlo (QMC) techniques, which allows us to much more efficiently obtain thermal samples of an embedded Hamiltonian, enabling us to simulate systems of much larger sizes and larger transverse-field strengths than would otherwise be possible. Our numerics focus on models that can be implemented on current quantum devices using planar two-dimensional lattices, which exhibit finite-temperature quantum phase transitions. Our results include: i) An estimate on the probability to sample the logical subspace directly as a function of transverse-field, temperature, and total system size, which agrees with QMC simulations. ii) We show that typically measured observables (diagonal energy and magnetization) are biased by the embedding process, in the regime of intermediate transverse field strength, meaning that the extracted values are not the same as in the native model. iii) By considering individual embedding realizations akin to 'realizations of disorder', we provide numerical evidence suggesting that as the embedding size is increased, the critical point shifts to increasingly large values of the transverse-field.

Spectral and thermodynamic properties of the Holstein polaron: Hierarchical equations of motion approach

We develop a hierarchical equations of motion (HEOM) approach to compute real-time single-particle correlation functions and thermodynamic properties of the Holstein model at finite temperature. We exploit the conservation of the total momentum of the system to formulate the momentum-space HEOM whose dynamical variables explicitly keep track of momentum exchanges between the electron and phonons. Our symmetry-adapted HEOM enable us to overcome the numerical instabilities inherent to the commonly used real-space HEOM. The HEOM method is then used to study the spectral function and thermodynamic quantities of chains containing up to ten sites. The HEOM results compare favorably to existing literature. To provide an independent assessment of the HEOM approach and to gain insight into the importance of finite-size effects, we devise a quantum Monte Carlo (QMC) procedure to evaluate finite-temperature single-particle correlation functions in imaginary time and apply it to chains containing up to twenty sites. QMC results reveal that finite-size effects are quite weak, so that the results on 5 to 10-site chains, depending on the parameter regime, are representative of larger systems. A detailed comparison between the HEOM and QMC data place our HEOM method among reliable methods to compute real-time finite-temperature correlation functions in parameter regimes ranging from low- to high-temperature, and weak- to strong-coupling regime.

Matrix-Model Simulations Using Quantum Computing, Deep Learning, and Lattice Monte Carlo

Matrix quantum mechanics plays various important roles in theoretical physics, such as a holographic description of quantum black holes, and it underpins the only practical numerical approach to the study of complex high-dimensional supergravity theories. Understanding quantum black holes and the role of entanglement in a holographic setup is of paramount importance for the realization of a quantum theory of gravity. Moreover, a complete numerical understanding of the holographic duality and the emergence of geometric space-time features from microscopic degrees of freedom could pave the way for new discoveries in quantum information science. Euclidean lattice Monte Carlo simulations are the de facto numerical tool for understanding the spectrum of large matrix models and have been used to test the holographic duality. However, they are not tailored to extract dynamical properties or even the quantum wave function of the ground state of matrix models. Quantum computing and deep learning provide potentially useful approaches to study the dynamics of matrix quantum mechanics. If successful in the context of matrix models, these rapidly improving numerical techniques could become the new Swiss army knife of quantum gravity practitioners. In this paper, we perform the first systematic survey for quantum computing and deep-learning approaches to matrix quantum mechanics, comparing them to lattice Monte Carlo simulations. These provide baseline benchmarks before addressing more complicated problems. In particular, we test the performance of each method by calculating the low-energy spectrum.22 MoreReceived 23 August 2021Accepted 20 December 2021DOI:https://doi.org/10.1103/PRXQuantum.3.010324Published 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 AreasLattice gauge theoryMachine learningQuantum algorithmsSupersymmetric field theoriesTechniquesHybrid Monte Carlo algorithmPath-integral Monte CarloQuantum InformationParticles & Fields

Ultradilute Quantum Liquid of Dipolar Atoms in a Bilayer.

We show that ultradilute quantum liquids can be formed with ultracold bosonic dipolar atoms in a bilayer geometry. Contrary to previous realizations of ultradilute liquids, there is no need for stabilizing the system with an additional repulsive short-range potential. The advantage of the proposed system is that dipolar interactions on their own are sufficient for creation of a self-bound state and no additional short-range potential is needed for the stabilization. We perform quantum MonteCarlo simulations and find a rich ground-state phase diagram that contains quantum phase transitions between liquid, solid, atomic gas, and molecular gas phases. The stabilization mechanism of the liquid phase is consistent with the microscopic scenario in which the effective dimer-dimer attraction is balanced by an effective three-dimer repulsion. The equilibrium density of the liquid, which is extremely small, can be controlled by the interlayer distance. From the equation of state, we extract the spinodal density, below which the homogeneous system breaks into droplets. Our results offer a new example of a two-dimensional interacting dipolar liquid in a clean and highly controllable setup.

Quasi-one-dimensional He4 in nanopores

Low temperature structural and superfluid properties of $^{4}\mathrm{He}$ confined in cylindrical nanopores are theoretically investigated by means of first-principle quantum Monte Carlo (QMC) simulations. We vary the density of $^{4}\mathrm{He}$ inside the pore, as well as the pore diameter and the potential describing the interaction of each $^{4}\mathrm{He}$ atom with the pore surface. Accordingly, the $^{4}\mathrm{He}$ fluid inside the pore forms either a single channel along the axis, or a series of concentric cylindrical shells, with varying degrees of shell overlap. In the limit of pore length greatly exceeding its radius, the $^{4}\mathrm{He}$ fluid always displays markedly one-dimensional behavior, with no ``dimensional crossover'' above some specific pore radius and/or as multiple concentric shells form, in contrast to what was recently claimed by other authors [Phys. Rev. B 101, 104505 (2020)]. Indeed, the predicted robustness of one-dimensional physics suggests that this system may offer a broadly viable pathway to the experimental observation of exotic behavior of, e.g., junctions of interacting Tomonaga-Luttinger liquids, in an appropriately designed network of nanopores.