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Register a new userLinear-scaling quantum Monte Carlo with non-orthogonal localized orbitals
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We have reformulated the quantum Monte Carlo (QMC) technique so that a large part of the calculation scales linearly with the number of atoms. The reformulation is related to a recent alternative proposal for achieving linear-scaling QMC, based on maximally localized Wannier orbitals (MLWO), but has the advantage of greater simplicity. The technique we propose draws on methods recently developed for linear-scaling density functional theory. We report tests of the new technique on the insulator MgO, and show that its linear-scaling performance is somewhat better than that achieved by the MLWO approach. Implications for the application of QMC to large complex systems are pointed out.
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We derive an automatic procedure for generating a set of highly localized, non-orthogonal orbitals for linear scaling quantum Monte Carlo calculations. We demonstrate the advantage of these orbitals in calculations of the total energy of both semiconducting and metallic systems by studying bulk silicon and the homogeneous electron gas. For silicon, the improved localization of these orbitals reduces the computational time by a factor five and the memory by a factor of six compared to localized, orthogonal orbitals. For jellium, we demonstrate that the total energy is converged for orbitals truncated within spheres with radii 7-8 $r_s$, opening the possibility of linear scaling QMC calculations for realistic metallic systems.
We study, using quantum Monte Carlo (QMC) simulations, the ground state properties of a one dimensional Rabi-Hubbard model. The model consists of a lattice of Rabi systems coupled by a photon hopping term between near neighbor sites. For large enough coupling between photons and atoms, the phase diagram generally consists of only two phases: a coherent phase and a compressible incoherent one separated by a quantum phase transition (QPT). We show that, as one goes deeper in the coherent phase, the system becomes unstable exhibiting a divergence of the number of photons. The Mott phases which are present in the Jaynes-Cummings-Hubbard model are not observed in these cases due to the presence of non-negligible counter-rotating terms. We show that these two models become equivalent only when the detuning is negative and large enough, or if the counter-rotating terms are small enough.
This work expands recent investigations in the field of spin-polarized tritium (T$downarrow$) clusters . We report the results for the ground state energy and structural properties of large T$downarrow$ cl usters consisting of up to 320 atoms. All calculations have been performed with variational and diffusi on Monte Carlo methods, using an accurate {it ab initio} interatomic potential. Our results for $N le q 40$ are in good agreement with results obtained by other groups. Using a liquid-drop expression for t he energy per particle, we estimate the liquid equilibrium density, which is in good agreement with our recently obtained results for bulk T$downarrow$. In addition, the calculations of the energy for larg e clusters have allowed for an estimation of the surface tension. From the mean-square radius of the dr op, determined using unbiased estimators, we determine the dependence of the radii on the size of the c luster and extract the unit radius of the T$downarrow$ liquid.
Extended solids are frequently simulated as finite systems with periodic boundary conditions, which due to the long-range nature of the Coulomb interaction may lead to slowly decaying finite- size errors. In the case of Quantum-Monte-Carlo simulations, which are based on real space, both real-space and momentum-space solutions to this problem exist. Here, we describe a hybrid method which using real-space data models the spherically averaged structure factor in momentum space. We show that (i) by integration our hybrid method exactly maps onto the real-space model periodic Coulomb-interaction (MPC) method and (ii) therefore our method combines the best of both worlds (real-space and momentum-space). One can use known momentum-resolved behavior to improve convergence where MPC fails (e.g., at surface-like systems). In contrast to pure momentum-space methods, our method only deals with a simple single-valued function and, hence, better lends itself to interpolation with exact small-momentum data as no directional information is needed. By virtue of integration, the resulting finite-size corrections can be written as an addition to MPC.
We calculate the linear and non-linear susceptibilities of periodic longitudinal chains of hydrogen dimers with different bond-length alternations using a diffusion quantum Monte Carlo approach. These quantities are derived from the changes in electronic polarization as a function of applied finite electric field - an approach we recently introduced and made possible by the use of a Berry-phase, many-body electric-enthalpy functional. Calculated susceptibilities and hyper-susceptibilities are found to be in excellent agreement with the best estimates available from quantum chemistry - usually extrapolations to the infinite-chain limit of calculations for chains of finite length. It is found that while exchange effects dominate the proper description of the susceptibilities, second hyper-susceptibilities are greatly affected by electronic correlations. We also assess how different approximations to the nodal surface of the many-body wavefunction affect the accuracy of the calculated susceptibilities.
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