Session C4 - Quantum Monte Carlo.
FOCUS session, Monday afternoon, June 25
Building 4, Room 231,

[C4.001] Simulation of quantum phase transitions

The accurate simulation of phase transitions in quantum systems has become possible with the development of cluster Monte Carlo algorithms for quantum systems. The first such algorithm, the loop algorithm [H.G. Evertz et al., Phys. Rev. Lett. 70, 875 (1993)], turned out to be as efficient as its classical counterpart, the Swendsen-Wang algorithm, but suffered from an exponential slow down in an external magnetic field. This problems was solved by the worm algorithm [N.V. Prokof'ev et al., Phys. Lett. A 238, 253 (1998)], which was recently combined with the stochastic series expansion (SSE) algorithm [A.W. Sandvik, Phys. Rev. B 59, R14157 (1999)]. I will review applications of these new algorithms to quantum magnets and bosonic systems and show that they allow high precision simulations of large quantum systems. Examples will include the low-temperature asymptotic scaling behavior of two-dimensional quantum Heisenberg antiferromagnets, the critical behavior at quantum phase transitions in these systems, and quantitatve modeling of antiferromagnetic materials. In bosonic systems I will address some long standing problems, such as the existence of supersolids, and the melting of stripe phases. These examples show that today we can simulate quantum statistical systems with the same accuracy as classical systems, which enables the investigation of new universal behavior that has never been observed in classical systems.

[C4.002] Path Integrals for the Projection of the Electronic Ground State

Diffusion Monte Carlo (DMC) has been used for the high-accuracy study of the ground state properties of large electronic systems for many years. Despite its many successes, DMC has major shortcomings (eg. mixed estimators, time step errors). We present an evaluation of an alternative ground state Monte Carlo method, based on path integrals, which addresses some of these shortcomings. In particular, we provide a brief description of the ground state path integral (GSPIMC) method and compare its scaling behavior, efficiencies, and deficiencies with those of DMC. We provide results from a number of test calculations on molecular systems. We attempt to provide insight into the circumstances under which it is preferable to utilize each algorithm.

[C4.003] Comparison of Quantum Monte Carlo and Density Functional Models of the Correlation Hole in Second Row Atoms

We study the system-averaged correlation hole at full coupling constant in the valence (3s^2 3p^N) shell of the second row atoms, using variational Quantum Monte Carlo methods and nonlocal pseudopotentials. A Boys and Handy correlation factor is used which obtains around 97% of the total correlation energy of the valence shell. The correlation hole is measured by means of correlated estimates, reducing statistical noise by a factor of ten. The scaling of the valence shell density over the row can be used to study trends in density functional models of the correlation hole as a function of density and relative density gradient. In particular we focus on the role of self interaction which is a large source of error in the generalized gradient approximation (GGA) in density functional theory, and test several approaches of removing it, including modern "meta-GGA" methods. We also study the errors in local and "semilocal" density functional approximation at large interparticle separation where the RPA predictions of the homogeneous electron gas tend to fail.

[C4.004] MeronCluster Algorithms for Strongly Correlated Fermion Systems

Numerical simulations of strongly correlated fermionic systems suffer from the notorious fermion sign problem. For example, this has prevented progress in understanding if systems like the Hubbard model display high-temperature superconductivity. Here we consider a large class of systems --- some of them in the Hubbard model family --- for which the fermion sign problem can be solved completely with a meron-cluster algorithm. Improved estimators are constructed for various observables of physical interest, and the inclusion of a chemical potential is also discussed. Recent numerical results have demonstrated that some of these systems show a Kosterlitz-Thouless type transition to a superconducting state.

[C4.005] Quantum Monte Carlo Study of the Ferromagnetic Properties of the Periodic Anderson Model.

Using the Constrained-Path Monte Carlo method, we performed a series of zero temperature quantum Monte Carlo simulations of the two-dimensional periodic Anderson model. We found three regimes of partially saturated ferromagnetic behavior and in each regime we able to identify the physical mechanism causing this behavior. In the mixed-valence regime, we also demonstrated that a spin-polarized Hartree-Fock approximation accurately reproduces the quantum Monte Carlo results. Extending this approximation to finite-temperature, we found it qualitatively predicts several of the unusual temperature dependent properties of various 4f and 5f heavy fermion mixed-valence materials.

[C4.006] QMC studies of the Antiferromagnetic phase Transition in the 3D Hubbard Model

We have used the Determinant Method (S. White et al. 1989) to investigate the magnetic phase transition of the anisotropic Hubbard Model in three dimensions. The transition temperature is found to decrease as the coupling between the 2D layers is decreased, in agreement with expectations. Preliminary results indicate a transition temperature below that previously found with this method. We also discuss several techniques for parallelizing this algorithm and compare their relative performance.

Part C of program listing