Quantum Monte Carlo Results Research Articles

Transcorrelated calculations of homogeneous electron gases

We have constructed the complete transcorrelated equation for homogeneous electron gases and investigated this equation on two- and three-dimensional systems. Correct asymptotic behaviours of the correlation factors can be easily obtained from the transcorrelated equation, both the long-range RPA type decay and the short-range spin dependent cusp conditions. The complete transcorrelated equation is solved numerically and the outcome correlation energies agree very well with variational quantum Monte Carlo results. Possible simplifications of the transcorrelated calculations are discussed, where we find that the RPA equation for the correlation factor can be considerably improved by adding one more term in the equation.

Nonperturbative effects on the ferromagnetic transition in repulsive Fermi gases

It is generally believed that a dilute spin-1/2 Fermi gas with repulsive interactions can undergo a ferromagnetic phase transition to a spin-polarized state at a critical gas parameter $(k_{\rm F}a)_c$. Previous theoretical predictions of the ferromagnetic phase transition have been based on the perturbation theory, which treats the gas parameter as a small number. On the other hand, Belitz, Kirkpatrick, and Vojta (BKV) have argued that the phase transition in clean itinerant ferromagnets is generically of first order at low temperatures, due to the correlation effects that lead to a nonanalytic term in the free energy. The second-order perturbation theory predicts a first-order phase transition at $(k_{\rm F}a)_c=1.054$, consistent with the BKV argument. However, since the critical gas parameter is expected to be of order O(1), perturbative predictions may be unreliable. In this paper we study the nonperturbative effects on the ferromagnetic phase transition by summing the particle-particle ladder diagrams to all orders in the gas parameter. We consider a universal repulsive Fermi gas where the effective range effects can be neglected, which can be realized in a two-component Fermi gas of $^6$Li atoms by using a nonadiabatic field switch to the upper branch of a Feshbach resonance with a positive s-wave scattering length. Our theory predicts a second-order phase transition, which indicates that ferromagnetic transition in dilute Fermi gases is possibly a counterexample to the BKV argument. The predicted critical gas parameter $(k_{\rm F}a)_c=0.858$ is in good agreement with the recent quantum Monte Carlo result $(k_{\rm F}a)_c=0.86$ for a nearly zero-range potential [S. Pilati, \emph{et al}., Phys. Rev. Lett. {\bf 105}, 030405 (2010)]. We also compare the spin susceptibility with the quantum Monte Carlo result and find good agreement.

Improving density functional theory for crystal polymorph energetics

We show that the quality of density functional theory (DFT) predictions for the relative stabilities of polymorphs of crystalline para-diiodobenzene (PDIB) is dramatically improved through a simple two-body correction using wavefunction-based electronic structure theory. PDIB has two stable polymorphs under ambient conditions, and like Hongo et al. [J. Phys. Chem. Lett., 1, 1789 (2010)] we find that DFT makes wildly variable predictions of the relative stabilities, depending on the approximate functional used. The two-body corrected scheme, using Grimme's spin-scaled variant of second-order Møller-Plesset perturbation theory and any of the tested density functionals, predicts the α-polymorph to be more stable, consistent with experiment, and produces a relative stability that agrees with the benchmark quantum Monte-Carlo results of Hongo et al. within statistical uncertainty.

SUPERCONDUCTIVITY IN THE 2D ATTRACTIVE HUBBARD MODEL WITHIN A FUNCTIONAL FIELD-THEORETICAL RG

We apply the functional field-theoretical renormalization group methodology up to two-loop order to the 2D attractive Hubbard model for weak bare interaction. Since the momentum-resolved quasiparticle weight ZΛ(p) is always close to unity in the RG flow, higher-order quantum fluctuations do not affect crucially the low-energy dynamics in this case. As a result, we observe a s-wave singlet superconducting quasi-long-range order phase as a function of doping in good agreement with other numerical methods. To assess the role played by the fluctuations we compare the critical temperature Tc in which the quasi-long-range superconducting order phase takes place within our approach with mean-field theory and quantum Monte Carlo results.

Coupled-cluster calculations for the ground and excited states of the spin-half XXZ model

The coupled-cluster method is applied to the spin-1/2 antiferromagnetic XXZ model on a square lattice by employing an approximation which contains two-body long-range correlations and high-order four-body local correlations. Improvement is found for the ground-state energy, the sublattice magnetization and the critical anisotropy when comparing with the approximation including the two-body correlations alone. We also obtain the full excitation spectrum which is in good agreement with the quantum Monte Carlo results and the high-order spin-wave theory.

Nonperturbative renormalization group approach to the Bose-Hubbard model

We present a nonperturbative renormalization group (RG) approach to the Bose-Hubbard model. By taking as initial condition of the RG flow the (local) limit of decoupled sites, we take into account both local and long-distance fluctuations in a nontrivial way. This approach yields a phase diagram in very good quantitative agreement with the quantum Monte Carlo results and reproduces the two universality classes of the superfluid--Mott-insulator transition with a good estimate of the critical exponents. Furthermore, it reveals the crucial role of the ``Ginzburg length'' as a crossover length between a weakly and a strongly correlated superfluid phase.

Water as a solute: competitive shell formation in (He,Ne) mixed microdroplets

Quantum Monte Carlo (QMC) stochastic calculations are carried out for a series of mixed rare gas clusters containing He and Ne which further include one H(2)O molecule as a single dopant. The ab initio potentials employed in the calculations, and the structural details provided by the QMC results, clearly reveal that the differences in the interaction forces which exist between the two solvent adatoms and the molecular solute are causing strongly competing environments that generate preferential shell structuring when surrounding the water molecule. The different behaviour of the two solvents, and the energetics of mixing, are analyzed in detail for small aggregates and for larger mixtures, revealing structural effects which originate from the different networking between solvent adatoms.

Bulk and surface energetics of crystalline lithium hydride: Benchmarks from quantum Monte Carlo and quantum chemistry

We show how accurate benchmark values of the surface formation energy of crystalline lithium hydride can be computed by the complementary techniques of quantum Monte Carlo (QMC) and wavefunction-based molecular quantum chemistry. To demonstrate the high accuracy of the QMC techniques, we present a detailed study of the energetics of the bulk LiH crystal, using both pseudopotential and all-electron approaches. We show that the equilibrium lattice parameter agrees with experiment to within 0.03 %, which is around the experimental uncertainty, and the cohesive energy agrees to within around 10 meV per formula unit. QMC in periodic slab geometry is used to compute the formation energy of the LiH (001) surface, and we show that the value can be accurately converged with respect to slab thickness and other technical parameters. The quantum chemistry calculations build on the recently developed hierarchical scheme for computing the correlation energy of a crystal to high precision. We show that the hierarchical scheme allows the accurate calculation of the surface formation energy, and we present results that are well converged with respect to basis set and with respect to the level of correlation treatment. The QMC and hierarchical results for the surface formation energy agree to within about 1 %.

Comment on “Quantum phase transition in the four-spin exchange antiferromagnet”

In a recent paper [Phys. Rev. B 80, 174403 (2009)] Kotov et al. studied the paramagnetic-to-antiferromagnetic transition in the $J\text{\ensuremath{-}}Q$ model. Their findings were claimed to be in ``fairly good agreement'' with previous quantum Monte Carlo (QMC) results. In this Comment we show that the above claim is misleading and in reality their phase transition point is not only far from the corresponding QMC value but also lies in a region of parameter space not yet explored in the literature. We also show that their reference dimer state is unstable against formation of a plaquette condensate, which could in part explain the large fluctuations they found.

Quantum Monte Carlo calculations of dihydrogen binding energetics on Ca cations: An assessment of errors in density functionals for weakly bonded systems

We investigate the binding of single and quadruple hydrogen molecules on a positively charged Ca ion. By comparing with benchmark quantum Monte Carlo (QMC) calculations we demonstrate wide variability in other more approximate electronic structure methods including common density functionals. Single determinant QMC calculations find no binding at short range by approximately 0.1 eV for the quadruple hydrogen molecule case, for a fixed hydrogen bond length of 0.77 Angstrom. Density functional calculations using common functionals such a LDA and B3LYP differ substantially from the QMC binding curve. We show that use of full Hartree-Fock exchange and PBE correlation(HFX+PBEC) obtains close agreement with the QMC results, both qualitatively and quantitatively. These results both motivate the use and development of improved functionals and indicate that caution is required applying electronic structure methods to weakly bound systems such as hydrogen storage materials based on metal ion decorated nanostructures.

Toward accurate reaction energetics for molecular line growth at surface: Quantum Monte Carlo and density functional theory calculations

We revisit the molecular line growth mechanism of styrene on the hydrogenated Si(001)2x1 surface. In particular, we investigate the energetics of the radical chain reaction mechanism by means of diffusion quantum Monte Carlo (QMC) and density functional theory (DFT) calculations. For the exchange correlation (XC) functional we use the nonempirical generalized-gradient approximation (GGA) and meta-GGA. We find that the QMC result also predicts the intra-dimer-row growth of the molecular line over the inter-dimer-row growth, supporting the conclusion based on DFT results. However, the absolute magnitudes of the adsorption/reaction energies and the heights of the energy barriers differ considerably between the QMC and DFT with the GGA/meta-GGA XC functionals.

Quantum Monte Carlo Simulation of Nanoscale MgH2 Cluster Thermodynamics

We calculated the desorption energy of MgH(2) clusters using the highly accurate quantum Monte Carlo (QMC) approach, which can provide desorption energies with chemical accuracy (within approximately 1 kcal/mol) and therefore provides a valuable benchmark for such hydrogen-storage simulations. Compared with these QMC results, the most widely used density functional theory (DFT) computations (including a wide range of exchange-correlation functionals) cannot reach a consistent and suitable level of accuracy across the thermodynamically tunable range for MgH(2) clusters. Furthermore, our QMC calculations show that the DFT error depends substantially on cluster size. These results suggest that in simulating metal-hydride systems it is very important to apply accurate methods that go beyond traditional mean-field approaches as a benchmark of their performance for a given material, and QMC is an appealing method to provide such a benchmark due to its high level of accuracy and favorable scaling (N(3)) with the number of electrons.

Induced Interactions for Ultracold Fermi Gases in Optical Lattices

We investigate the effect of optical lattices on the BCS superfluidity by using the Gorkov-Melik-Barkhudarov (GMB) correction for a two-component Fermi gas. We find that the suppression of the order parameter is strongly enhanced by the lattice effects. The predictions made by the GMB corrections are in qualitative and, for the cases studied, quantitative agreement with previous quantum Monte Carlo results. We discuss how the GMB correction extends the validity of the mean-field theory to a wider range of tunable optical lattice systems in different dimensions.

The ground-state energy of an attractive Fermi gas along the Bardeen–Cooper–Schrieffer-unitarity crossover

The ratio f(x) of the ground-state energy of an attractive Fermi gas to that of the noninteracting Fermi gas is a smooth and continuous function of x = kFa in the Bardeen–Cooper–Schrieffer (BCS)-unitarity crossover regime −∞ < x ⩽ 0. Here kFℏ is the Fermi momentum, ℏ is the Planck constant and a is the s-wave scattering length. The respective coefficients of the perturbation expansions of f(x) in the BCS regime and in the unitary regime are expected to be related to each other. Unitary Fermi gases are expected to exhibit universal behaviors. So f(−∞) is universal and is only a function of the universal coefficients of the perturbation expansion of f(x) in the BCS regime. Using these facts, we extend the perturbation expansion of f(x) in the BCS regime to the BCS-unitarity crossover regime. f(−∞) is predicted to be 0.400 98(0.422 94) for the Bose (Fermi) function, which are in good agreement with the quantum Monte Carlo results and the experimental results.

Charge transfer dynamics in driven molecular ratchets: quantum Monte Carlo results and rate models

Charge transfer dynamics is studied in a ratchet-type molecular wire subject to finite frequency driving. Numerically exact data are obtained within the path integral Monte Carlo approach over the full transient time regime until a stationary net population imbalance has been established. This allows for a quantitative comparison with the master equation approaches and, in particular, underlines the usefulness of these rate models.

Opto-electronic properties of adamantane and hydrogen-terminated sila- and germa-adamantane: A comparative study

We present the opto-electronic properties of adamantane (C 10H 16) compared to hydrogen-terminated sila- and germa-adamantane (Si 10H 16 and Ge 10H 16) as calculated by the density functional theory. We have shown that the electronic properties of adamantane in comparison to sila- and germa-adamantane are more affected by hydrogen atoms. Our calculations show that the electron affinity of C 10H 16 is negative, while those of Si 10H 16 and Ge 10H 16 are positive. Electronic properties and optical gaps resulting from hybrid functionals are in close agreement with quantum Monte Carlo results.

Perturbative quantum Monte Carlo study ofLiHoF4in a transverse magnetic field

Results from a recent quantum Monte Carlo (QMC) study [P. B. Chakraborty et al., Phys. Rev. B 70, 144411 (2004)] of a model of the ${\text{LiHoF}}_{4}$ Ising magnetic material in an external transverse magnetic field, ${B}_{x}$, show a discrepancy with experimental results, even for small ${B}_{x}$ where quantum fluctuations are small. This discrepancy persists asymptotically close to the classical ferromagnet to paramagnet phase transition. In this paper, we numerically reinvestigate the temperature $T$ versus transverse-field phase diagram of ${\text{LiHoF}}_{4}$ in the regime of weak ${B}_{x}$. In this regime, starting from an effective low-energy spin-1/2 description of ${\text{LiHoF}}_{4}$, we apply a cumulant expansion to derive an effective temperature-dependent classical Hamiltonian that incorporates perturbatively the small quantum fluctuations in the vicinity of the classical phase transition at ${B}_{x}=0$. Via this effective classical Hamiltonian, we study the ${B}_{x}\text{\ensuremath{-}}T$ phase diagram via classical Monte Carlo simulations. In particular, we investigate the influence on the phase diagram of various effects that may be at the source of the discrepancy between the previous QMC results and the experimental ones. In particular, we consider two different ways of handling the long-range dipole-dipole interactions and explore how the ${B}_{x}\text{\ensuremath{-}}T$ phase diagram is modified when using different microscopic crystal-field Hamiltonians. The main conclusion of our work is that we fully reproduce the previous QMC results at small ${B}_{x}$. Unfortunately, none of the modifications to the microscopic Hamiltonian that we explore are able to provide a ${B}_{x}\text{\ensuremath{-}}T$ phase diagram compatible with the experiments in the quasiclassical small ${B}_{x}$ regime.

Spin-spin correlations of the spin-ladder compound(C5H12N)2CuBr4measured by magnetostriction and comparison to quantum Monte Carlo results

Magnetostriction and thermal expansion of the spin-ladder compound piperidinium copper bromide ${({\text{C}}_{5}{\text{H}}_{12}\text{N})}_{2}{\text{CuBr}}_{4}$ are analyzed in detail. We find perfect agreement between experiments and the theory of a two-leg spin-ladder Hamiltonian for more than a decade in temperature and in a wide range of magnetic fields. Relating the magnetostriction along different crystallographic directions to two static spin-spin correlation functions, which we compute with quantum Monte Carlo, allows us to reconstruct the magnetoelastic couplings of ${({\text{C}}_{5}{\text{H}}_{12}\text{N})}_{2}{\text{CuBr}}_{4}$. We especially focus on the quantum critical behavior near the two critical magnetic fields ${H}_{c1}$ and ${H}_{c2}$, which is characterized by strong singularities rooted in the low dimensionality of the critical spin system. Extending our discussion in Lorenz [ et al. Phys. Rev. Lett. 100, 067208 (2008)], we show explicitly that the thermal expansion near the upper critical field ${H}_{c2}$ is quantitatively described by a parameter-free theory of one-dimensional, nonrelativistic fermions. We also point out that there exists a singular quantum critical correction to the elastic moduli. This correction is proportional to the magnetic susceptibility $\ensuremath{\chi}$, which diverges as $\ensuremath{\chi}\ensuremath{\sim}1/\sqrt{T}$ at the critical fields and thus leads to a strong softening of the crystal.

Exchange-correlation orbital functionals in current-density functional theory: Application to a quantum dot in magnetic fields

The description of interacting many-electron systems in external magnetic fields is considered in the framework of the optimized effective potential method extended to current-spin-density functional theory. As a case study, a two-dimensional quantum dot in external magnetic fields is investigated. Excellent agreement with the quantum Monte Carlo results is obtained when self-interaction corrected correlation energies from the standard local spin-density approximation are added to exact-exchange results. Full self-consistency within the complete current-spin-density-functional framework is found to be of minor importance.

Quantum fluctuations in the superfluid state of the BCS-BEC crossover

We determine the effects of quantum fluctuations about the $T=0$ mean-field solution of the BCS-BEC crossover in a dilute Fermi gas using the functional integral method. These fluctuations are described in terms of the zero-point motion of collective modes and the virtual scattering of gapped quasiparticles. We calculate their effects on various measurable properties, including chemical potential, ground-state energy, the gap, the speed of sound and the Landau critical velocity. At unitarity, we find excellent agreement with quantum Monte Carlo and experimental results. In the BCS limit, we show analytically that we obtain Fermi liquid interaction corrections to thermodynamics including the Hartree shift. In the Bose-Einstein condensation (BEC) limit, we show that the theory leads to an approximate description of the reduction of the scattering length for bosonic molecules and also obtain quantum depletion of the Lee-Yang form. At the end of the paper, we describe a method to include feedback of quantum fluctuations into the gap equation, and discuss the problems of self-consistent calculations in satisfying Goldstone's theorem and obtaining ultraviolet finite results at unitarity.