Quantum Monte Carlo Studies of Small Clusters

Fung-kiu Chow

J. P. Hague, Mark Jarrell, T. C. Schulthess

This paper introduces an ansatz-based technique for solution of the Hubbard model over two length scales. Short-range correlations are treated exactly using a dynamical cluster approximation quantum Monte Carlo (QMC) simulation, while longer-length-scale physics requiring larger cluster sizes is incorporated through the introduction of the fluctuation-exchange approximation. The properties of the resulting hybrid scheme are examined and the description of local-moment formation is compared to exact results in one dimension (1D). The effects of electron-electron coupling and electron doping on the shape of the Fermi surface are demonstrated in 2D. Causality is examined in both 1D and 2D. We find that the scheme is successful if QMC clusters of ${N}_{C}>~4$ are used (with sufficiently high temperatures in 1D), however, very small QMC clusters of ${N}_{C}=1$ lead to acausal results.

Naoki Kawashima

James S. Spencer, Nick S. Blunt, Seonghoon Choi +15 more

Building on the success of Quantum Monte Carlo techniques such as diffusion Monte Carlo, alternative stochastic approaches to solve electronic structure problems have emerged over the past decade. The full configuration interaction quantum Monte Carlo (FCIQMC) method allows one to systematically approach the exact solution of such problems, for cases where very high accuracy is desired. The introduction of FCIQMC has subsequently led to the development of coupled cluster Monte Carlo (CCMC) and density matrix quantum Monte Carlo (DMQMC), allowing stochastic sampling of the coupled cluster wave function and the exact thermal density matrix, respectively. In this Article, we describe the HANDE-QMC code, an open-source implementation of FCIQMC, CCMC and DMQMC, including initiator and semistochastic adaptations. We describe our code and demonstrate its use on three example systems; a molecule (nitric oxide), a model solid (the uniform electron gas), and a real solid (diamond). An illustrative tutorial is also included.

Matthias Troyer, Philipp Werner, Adolfo Avella +1 more

Petar Stipanović, Leandra Vranješ Markić, Jordi Boronat +1 more

We report results for the ground-state energy and structural properties of small (4)He-T↓ clusters consisting of up to four T↓ and eight (4)He atoms. These results have been obtained using very well-known (4)He-(4)He and T↓- T↓ interaction potentials and several models for the (4)He- T↓ interatomic potential. All the calculations have been performed with variational and diffusion Monte Carlo methods. It takes at least three atoms to form a mixed bound state. In particular, for small clusters the binding energies are significantly affected by the precise form of the (4)He- T↓ interatomic potential but the stability limits remain unchanged. The only exception is the (4)He(2)T↓ trimer whose stability in the case of the weakest (4)He- T↓ interaction potential is uncertain while it seems stable for other potentials. The mixed trimer (4)He(T↓)(2), a candidate for the Borromean state, is not bound. All other studied clusters are stable. Some of the weakest bound clusters can be classified as quantum halo as a consequence of having high probability of being in a classically forbidden region.