Many-body wavefunction. quantum Monte

The quality of a variational quantum Monte Carlo calculation is determined by the choice of the many-body wavefunction. The many-body wavefunction we use is of the parameterized Slater-Jastrow type which has been shown to yield accurate results both for the homogeneous electron gas and for solid silicon (14) (In the case of silicon, for example, 85% of the fixed-node diffusion Monte Carlo correlation energy is recovered). At a given coupling A, 4>A is written as... 

There are numerous approaches to approximate solutions for (1), most of which involve finding the system s total ground state energy, E, including methods that treat the many-body wavefunction as an antisymmetric function of one-body orbitals (discussed in later sections), or methods that allow a direct representatiOTi of many-body effects in the wave function such as Quantum Monte Carlo (QMC), or hybrid methods such as coupled cluster (CC), which adds multi-electrOTi wave-function corrections to account for the many-body (electron) correlatirais. 

A different approach simulates the thermodynamic parameters of a finite spin system by using Monte Carlo statistics. Both classical spin and quantum spin systems of very large dimension can be simulated, and Monte Carlo many-body simulations are especially suited to fit a spin ensemble with defined interaction energies to match experimental data. In the case of classical spins, the simulations involve solving the equations of motion governing the orientations of the individual unit vectors, coupled to a heat reservoir, that take the form of coupled deterministic nonlinear differential equations.23 Quantum Monte Carlo involves the direct representation of many-body effects in a wavefunction. Note that quantum Monte Carlo simulations are inherently limited in that spin-frustrated systems can only be described at high temperatures.24... 

We apply a low density approximation to the Jastrow ansatz and find analytical results for the roton height and position. These low density results compare favorably to a Monte-Carlo quantum (MCQ) calculation of the wavefunction up to e = 0.1. Using the MCQ simulations we find a many-body enhancement of the roton at higher e, leading to a roton peak of almost 8% at e = 0.22. 

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