Quantum Monte Carlo Algorithm Based on Two-Body Density Functional Theory for Fermionic Many-Body Systems: Application to 3He

Compact and accurate wave functions can be constructed by quantum Monte Carlo methods. Typically, these wave functions consist of a sum of a small number of Slater determinants multiplied by a Jastrow factor. In this paper we study the importance of including high-order, nucleus-three-electron correlations in the Jastrow factor. An efficient algorithm based on the theory of invariants is used to compute the high-body correlations. We observe significant improvements in the va...

It has become increasingly feasible to use quantum Monte Carlo (QMC) methods to study correlated fermion systems for realistic Hamiltonians. We give a summary of these techniques targeted at researchers in the field of correlated electrons, focusing on the fundamentals, capabilities, and current status of this technique. The QMC methods often offer the highest accuracy solutions available for systems in the continuum, and, since they address the many-body problem directly, th...

In a recent Letter we introduced Hellmann-Feynman operator sampling in diffusion Monte Carlo calculations. Here we derive, by evaluating the second derivative of the total energy, an efficient method for the calculation of the static density-response function of a many-electron system. Our analysis of the effect of the nodes suggests that correlation is described correctly and we find that the effect of the nodes can be dealt with.

The application of the diffusion Monte Carlo method to a strongly interacting Fermi system as normal liquid $^3$He is explored. We show that the fixed-node method together with the released-node technique and a systematic method to analytically improve the nodal surface constitute an efficient strategy to improve the calculation up to a desired accuracy. This methodology shows unambiguously that backflow correlations, when properly optimized, are enough to generate an equatio...

We demonstrate the existence of different density-density functionals designed to retain selected properties of the many-body ground state in a non-interacting solution starting from the standard density functional theory ground state. We focus on diffusion quantum Monte Carlo applications that require trial wave functions with optimal Fermion nodes. The theory is extensible and can be used to understand current practices in several electronic structure methods within a gener...

The quantum Monte Carlo (QMC) is one of the most promising many-body electronic structure approaches. It employs stochastic techniques for solving the stationary Schr\" odinger equation and for evaluation of expectation values. The key advantage of QMC is its capability to use the explicitly correlated wave functions, which allow the study of many-body effects beyond the reach of mean-field methods. The most important limit on QMC accuracy is the fixed-node approximation, whi...

Recent neutron scattering experiments on 3He films have observed a zero-sound mode, its dispersion relation and its merging with -and possibly emerging from- the particle-hole continuum. Here we address the study of the excitations in the system via quantum Monte Carlo methods: we suggest a practical scheme to calculate imaginary time correlation functions for moderate-size fermionic systems. Combined with an efficient method for analytic continuation, this scheme affords an ...

The description of the properties of liquid Helium is a challenge for any microscopic many-body theory. In this context, we study the ground state and the excitation spectrum of one $^3$He impurity in liquid $^4$He at T=0 with the aim of illustrating the power of the correlated basis function formalism in describing heavily correlated systems. The strong interatomic interaction and the large density require the theory to be pushed to a high degree of sophistication. A many-bo...

The recently developed density matrix quantum Monte Carlo (DMQMC) algorithm stochastically samples the N -body thermal density matrix and hence provides access to exact properties of many-particle quantum systems at arbitrary temperatures. We demonstrate that moving to the interaction picture provides substantial benefits when applying DMQMC to interacting fermions. In this first study, we focus on a system of much recent interest: the uniform electron gas in the warm dense r...

With our recently proposed effective Hamiltonian via Monte Carlo, we are able to compute low energy physics of quantum systems. The advantage is that we can obtain not only the spectrum of ground and excited states, but also wave functions. The previous work has shown the success of this method in (1+1)-dimensional quantum mechanical systems. In this work we apply it to higher dimensional systems.