Quantum Monte Carlo Approaches

If one is only interested in the universal critical behavior of a quantum phase transition, then the quantum-to-classical mapping method discussed in the last section (if available) is usually the most efficient approach. If one is also interested in nonuniversal quantities such as critical coupling constants or numerical values of observables, however, the quantum system has to be simulated directly. This can be done, for example, by quantum Monte Carlo methods that are the topic of this section. 

One branch of quantum Monte Carlo research aims at providing a quantitative first-principle description of atoms, molecules, and solids beyond the accuracy of density functional theory. If the basic physics and chemistry of the material in question is well understood at least qualitatively, as is the case for many bulk semiconductors, for example, good trial wave functions such as the Jastrow-Slater type can be constructed. These functions can 

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R.M. Grimes et al., Quantum Monte Carlo approach to electronically excited molecules. J. Chem. Phys. 85, 4749-4750 (1986)... 

A Quantum Monte Carlo Approach to the Adiabatic Connection Method... 

The Diffusion Quantum Monte Carlo (DQMC) algorithm and related methods such as the Vibrational Quantum Monte Carlo approach have the important property of scahng well with system size (number of degrees of freedom). At the same time the method can be pursued in principle to yield a numerically exact energy. DQMC was introduced... 

In addition, there is the CASINO program based upon the quantum Monte Carlo approach by the Needs and Towler groups from the Cavendish Laboratory (UK), and the code is available from the authors. 

So far, we have discussed quantum Monte Carlo approaches to quantum phase transitions in boson and spin systems. In these systems, the statistical weight in the Monte Carlo procedure is generally positive definite, so there is no sign problem. Note that for spin systems, this is only true if there is no frustration. Frustrated spin systems in general do have a sign problem. 

S. Tanaka,/. Phys. Soc. Japan, 62,2112 (1993). CohesiveEnergy of NiO A Quantum Monte Carlo Approach. 

RQMC-MI and RQMC-MH were employed along with a variety of quantum Monte Carlo approaches to sample the pure density for ground-state dihydrogen [21]. RQMC-MI exhibited the smallest integrated absolute... 

An interesting approach analyzing the pairing of electrons was presented in 2(X)4 by Scemama et al. [69]. There, the basic ingredients are the average distances d (r) and daa r) between an electron located at (r) and the closest same-spin and opposite-spin electron, respectively (computed from quantum Monte Carlo approach). The electron pair localization function (EPLF) is defined as follows ... 

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