Quantum Monte Carlo Estimates Research Articles

Starting-point-independent quantum Monte Carlo calculations of iron oxide

Quantum Monte Carlo (QMC) methods are useful for studies of strongly correlated materials because they are many body in nature and use the physical Hamiltonian. Typical calculations assume as a starting point a wave function constructed from single-particle orbitals obtained from one-body methods, e.g., density functional theory. However, mean-field-derived wave functions can sometimes lead to systematic QMC biases if the mean-field result poorly describes the true ground state. Here, we study the accuracy and flexibility of QMC trial wave functions using variational and fixed-node diffusion QMC estimates of the total spin density and lattice distortion of antiferromagnetic iron oxide (FeO) in the ground state $B1$ crystal structure. We found that for relatively simple wave functions the predicted lattice distortion was controlled by the choice of single-particle orbitals used to construct the wave function, rather than by subsequent wave function optimization techniques within QMC. By optimizing the orbitals with QMC, we then demonstrate starting-point independence of the trial wave function with respect to the method by which the orbitals were constructed by demonstrating convergence of the energy, spin density, and predicted lattice distortion for two qualitatively different sets of orbitals. The results suggest that orbital optimization is a promising method for accurate many-body calculations of strongly correlated condensed phases.

A classical fluctuation theory of the superfluid, Mott, and normal phases of correlated bosons

We present a method that generalises the standard mean field theory of correlated lattice bosons to include amplitude and phase fluctuations of the U(1) field that induces onsite particle number mixing. We solve the resulting problem, initially, by using a classical approximation for the particle number mixing field and a Monte Carlo treatment of the resulting bosonic model. In two dimensions we obtain Tc scales that dramatically improve on mean field theory and are within about 20% of quantum Monte Carlo estimates at density n = 1. The ground state, however, is still mean field, with an overestimate of the critical interaction, Uc, for the superfluid to Mott transition. Further including gaussian quantum fluctuations strikingly improves the Uc and the overall thermal phase diagram. The approach has a computational cost that is linear in system size, readily generalises to multispecies bosons, disorder, and the presence of traps, and yields real frequency response functions.

Ground state properties of quantum Kagomé ice hardcore bosons

We study the quantum Kagomé ice hardcore bosons, which correspond to the XY limit of the quantum spin ice Hamiltonian. We estimate the values of their zero-temperature thermodynamic quantities using the large-S expansion. We show that our semiclassical analysis is consistent with the finite temperature quantum Monte Carlo estimates.

A real space auxiliary field approach to the BCS-BEC crossover

The BCS to BEC crossover in attractive Fermi systems is a prototype of weak to strong coupling evolution in many body physics. While extensive numerical results are available, and several approximate methods have been developed, most of these schemes are unsuccessful in the presence of spatial inhomogeneity. Such situations call for a real space approach that can handle large spatial scales and retain the crucial thermal fluctuations. With this in mind, we present comprehensive results of a real space auxiliary field approach to the BCS to BEC crossover in the attractive Hubbard model in two dimensions. The scheme reproduces the Hartree-Fock-Bogoliubov ground state, and leads to a $T_c$ scale that agrees with quantum Monte Carlo estimates to within a few percent. We provide results on the $T_c$, amplitude and phase fluctuations, density of states, and the momentum resolved spectral function over the entire interaction and temperature window. We suggest how the method generalises successfully to the presence of disorder, trapping, and population imbalance.

Spin-wave theory applied to the low-temperature properties of the spin-[formula omitted] ferromagnetic chain with the y-direction exchange anisotropy

In this paper, we apply the spin-wave theory within the simple self-consistent method, and provide a simple way to investigate the spin-1/2 ferromagnetic chain with the y-direction exchange anisotropy. It is found that the anisotropy has an influence on the ground-state and low-temperature properties of the system. Anisotropy dependences of both the susceptibility maximum and specific heat maximum fit well to the exponential laws. The linear decrease is shown for the position of the susceptibility maximum. The position of the specific heat maximum displays three kinds of the anisotropy dependence, i.e., the power law, constant law and exponential law. The specific heat coefficient is calculated to be a monotonically increasing function of the anisotropy in the zero-temperature limit. At some low temperature, the Heisenberg behavior is observed to cross over the XY behavior, which agrees with the experimental result of the quasi-one-dimensional compound (C6H11NH3)CuBr3. In the isotropic and anisotropic cases, our results are in good accord with the exact Bethe-ansatz results and quantum Monte Carlo estimates, and have some advantages over the findings of Green-function method and the renormalization group method at low temperatures.

Monte Carlo configuration interaction with perturbation corrections for dissociation energies of first row diatomic molecules: C2, N2, O2, CO, and NO

Dissociation energies for the diatomic molecules C2, N2, O2, CO, and NO are estimated using the Monte Carlo configuration interaction (MCCI) and augmented by a second order perturbation theory correction. The calculations are performed using the correlation consistent polarized valence "triple zeta" atomic orbital basis and resulting dissociation energies are compared to coupled cluster calculations including up to triple excitations (CCSDT) and Full Configuration Interaction Quantum Monte Carlo (FCIQMC) estimates. It is found that the MCCI method readily describes the correct behavior for dissociation for the diatomics even when capturing only a relatively small fraction (∼80%) of the correlation energy. At this level only a small number of configurations, typically O(10(3)) from a FCI space of dimension O(10(14)), are required to describe dissociation. Including the perturbation correction to the MCCI estimates, the difference in dissociation energies with respect to CCSDT ranges between 1.2 and 3.1 kcal/mol, and the difference when comparing to FCIQMC estimates narrows to between 0.5 and 1.9 kcal/mol. Discussions on MCCI's ability to recover static and dynamic correlations and on the form of correlations in the electronic configuration space are presented.

MODIFIED SPIN-WAVE THEORY FOR THE FRUSTRATED HEISENBERG ANTIFERROMAGNET ON A SQUARE LATTICE

The effects of quantum fluctuations due to frustration between nearest neighbors and next-nearest neighbors of the quantum spin-half Heisenberg antiferromagnet on a square lattice are investigated by using the modified spin-wave theory (MSW). We have extended Takahashi's MSW theory, and studied the ground-state and finite-temperature properties of this model. The results calculated within this formalism on the thermodynamics agree quite well with the quantum Monte Carlo estimates, and exact diagonalization results. We have also compared the present method with the conventional spin wave theory.

Zero-variance zero-bias quantum Monte Carlo estimators for the electron density at a nucleus

We derive new quantum Monte Carlo (QMC) estimators for the electronic density at the position of a point nucleus using the zero-variance and zero-bias principles. The resulting estimators are highly efficient, and are significantly simpler to implement and use than alternative methods, as they contain no adjustable parameters. In addition, they can be used in both variational and diffusion QMC calculations. Our best estimator is used to calculate the most accurate available estimates of the total electron density at the nucleus for the first-row atoms Li-Ne, the Ar atom, and the diatomic molecules B(2), N(2), and F(2).

Anisotropic intracule densities and electron correlation in H2: A quantum Monte Carlo study

We derive efficient quantum Monte Carlo estimators for the anisotropic intracule and extracule densities. These estimators are used in conjunction with an accurate explicitly correlated wave function to investigate the bond-length dependence of electron correlation effects in the ground-state H(2) molecule. It is shown that the localized increase in the magnitude of the correlation energy as the bond is stretched is accompanied by highly anisotropic correlation effects. In addition, we find a small long-range part of the Coulomb hole, which is present even at the equilibrium bond length.

Efficient and robust quantum Monte Carlo estimate of the total and spin electron densities at nuclei

The computational performance of two different variational quantum Monte Carlo estimators for both the electron and spin densities on top of nuclei are tested on a set of atomic systems containing also third-row species. Complications due to an unbounded variance present for both estimators are circumvented using appropriate sampling strategies. Our extension of a recently proposed estimator [Phys. Rev. A 69, 022701 (2004)] to deal with heavy fermionic systems appears to provide improved computational efficiency, at least an order of magnitude, with respect to alternative literature approaches for our test set. Given the importance of an adequate sampling of the core region in computing the electron density at a nucleus, a further reduction in the overall simulation cost is obtained by employing accelerated sampling algorithms.

Trial wave functions for high-pressure metallic hydrogen

Many body trial wave functions are the key ingredient for accurate Quantum Monte Carlo estimates of total electronic energies in many electron systems. In the Coupled Electron–Ion Monte Carlo method, the accuracy of the trial function must be conjugated with the efficiency of its evaluation. We report recent progress in trial wave functions for metallic hydrogen implemented in the Coupled Electron–Ion Monte Carlo method. We describe and characterize several types of trial functions of increasing complexity in the range of the coupling parameter 1.0 ⩽ r s ⩽ 1.55 . We report wave function comparisons for disordered protonic configurations and preliminary results for thermal averages.

Zero-variance zero-bias quantum Monte Carlo estimators of the spherically and system-averaged pair density

We construct improved quantum Monte Carlo estimators for the spherically and system-averaged electron pair density (i.e., the probability density of finding two electrons separated by a relative distance u), also known as the spherically averaged electron position intracule density I(u), using the general zero-variance zero-bias principle for observables, introduced by Assaraf and Caffarel. The calculation of I(u) is made vastly more efficient by replacing the average of the local delta-function operator by the average of a smooth nonlocal operator that has several orders of magnitude smaller variance. These new estimators also reduce the systematic error (or bias) of the intracule density due to the approximate trial wave function. Used in combination with the optimization of an increasing number of parameters in trial Jastrow-Slater wave functions, they allow one to obtain well converged correlated intracule densities for atoms and molecules. These ideas can be applied to calculating any pair-correlation function in classical or quantum Monte Carlo calculations.

Interdimensional degeneracies in van der Waals clusters and quantum Monte Carlo computation of rovibrational states

Quantum Monte Carlo estimates of the spectrum of rotationally invariant states of noble gas clusters suggest interdimensional degeneracy in N-1 and N+1 spatial dimensions. We derive this property by mapping the Schrodinger eigenvalue problem onto an eigenvalue equation in which D appears as a continuous variable. We discuss implications for quantum Monte Carlo and dimensional scaling methods.

Infinite-range quantum random Heisenberg magnet

We study with exact diagonalization techniques the Heisenberg model for a system of SU(2) spins with S=1/2 and random infinite-range exchange interactions. We calculate the critical temperature T_g for the spin-glass to paramagnetic transition. We obtain T_g ~ 0.13, in good agreement with previous quantum Monte Carlo and analytical estimates. We provide a detailed picture for the different kind of excitations which intervene in the dynamical response chi''(w,T) at T=0 and analyze their evolution as T increases. We also calculate the specific heat Cv(T). We find that it displays a smooth maximum at TM ~ 0.25, in good qualitative agreement with experiments. We argue that the fact that TM>Tg is due to a quantum disorder effect.

Improved finite-lattice estimates of the properties of two quantum spin models on the infinite square lattice

This paper describes an improvement in the method of exact diagonalization of Hamiltonians of quantum spin models on finite square lattices and the statistical analysis of the data so obtained to estimate the physical properties of the models on the infinite square lattices at zero temperature. The geometry and topology of finite square lattices are described. The models studied are the spin one-half XY and Heisenberg antiferromagnets using 28 finite square lattices with up to 32 vertices. Our estimates of the energy and magnetization on each model on the infinite lattice at zero temperature compare very well with recent estimates using quantum Monte Carlo, series expansion, and spin wave estimates. Estimates of spin wave velocity and transverse susceptibilities are more scattered.PACS No.: 75.10J

Normal state properties of the attractive Hubbard model: moment approach

We introduce a two-δ-peak ansatz for the spectral density of the attractive Hubbard model in the normal state and in d-dimensions. The resulting two excitation branches and their weights are fixed in terms of the exact first four frequency moments. This ansatz correctly reproduces the atomic limit, the free case and the strong coupling limit to first order in the hopping amplitude. For this reason it is expected to provide a reasonable interpolation scheme covering the intermediate and strong coupling regimes for properties that do not depend sensitively on the damping of the two excitation branches. In the strong coupling regime, the upper excitation branch describes the creation of a fermion in an empty state, whereas the lower band arises from pair formation due to the creation of a fermion in a state already occupied by a fermion of opposite spin. Consequently, anomalous normal state properties can be expected whenever the chemical potential is within the correlation gap. This turns out to be the case when half-filling is approached for intermediate coupling as well as for any finite band filling in the strong coupling regime. In these filling and coupling regimes, there is no Fermi surface, and the formation and dissociation of pairs occur in the normal state as revealed by the temperature dependence of the double occupancy. For this reason the normal state properties exhibit an anomalous temperature dependence. Comparison with t-matrix calculations in the dilute and intermediate coupling regimes and quantum Monte Carlo estimates covering intermediate band fillings as well as intermediate and strong coupling suggest that the predictions of the moment approach are essentially correct whenever the correlation gap is not smeared out by damping effects or overlapping bands. Exploring the three-dimensional case as well, we conclude that this scenario applies to the d-dimensional attractive Hubbard model.

The Phase Diagram of the Two-Dimensional t-J Model from High Temperature Expansions

The phase diagram of the 2D t-J model has been investigated using high temperature expansions. Series for the Helmholtz free energy, the inverse compressibility, the chemical potential and the uniform spin susceptibility through tenth order on a square lattice have been calculated using the finite cluster method.1 The series are analytically continued beyond their radius of convergence by Padé and integral approximants. The most accurate extrapolations can be made for the Helmholtz free energy where for J/t≈0.3 and n≈0.9 we can reach T~t/5. We can test the accuracy of the continuation methods by comparing with the 1D results for the boundary of phase separation of Ogata et al.2 In 2D a region of phase separation was found at T=0 for J/t lying above a line extending from J/t=3.8 at zero filling to J/t=1.2 at half filling. No phase separation was found at very small J/t contrary to the earlier suggestion of Emery et al3 which was based on results from exact diagonalisation on 4×4 clusters but in agreement with Quantum Monte Carlo (QMC) calculations on the Hubbard model.4 For very small J/t near half filling where the Nagaoka effect is possible, we find a region of divergent uniform magnetic susceptibility at T=0. However the divergence is very weak when compared with the exponential behaviour expected from a 2D ferromagnet. This might imply a substantially reduced moment which is consistent with the recent QMC estimates of Zhang et al.5