Quantum Monte Carlo methods
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- Work cat.: Richie-Halford, A. Quantum Monte Carlo studies of the BCS-BEC crossover, 2020:abstr. (quantum MonteCarlo techniques to determine the quasiparticle properties of infinite neutron matter, namely the effective mass, self-energy, and pairing gap) p. vii (QMC: quantum Monte Carlo) p. 18 (quantum Monte Carlo techniques required to accurately simulate Fermi gases near unitarity; quantum Monte Carlo methods) pp. 22-23 (Quantum Monte Carlo (QMC) methods encompass all approaches that use classical Monte Carlo methods to estimate multi-dimensional integrals that arise while solving many-body quantum mechanics problems; QMC methods)
- Pang, T. An introduction to quantum Monte Carlo methods, 2016:publ. website (Monte Carlo methods have been very prominent in computer simulation of various systems in physics, chemistry, biology, and materials science. This book focuses on the discussion and path-integral quantum Monte Carlo methods in many-body physics)
- Kent, P.R.C. Techniques and applications of quantum Monte Carlo, 1999, via WWW, Nov. 16, 2020:1.2 (Quantum Monte Carlo (QMC) methods treat electron-electron interactions almost without approximation and with a computational cost scaling cubically with system size. Their accuracy enables an unprecedented degree of confidence to be placed in the results obtained) 1.3 (QMC techniques) 2.1 (Quantum Monte Carlo techniques provide a direct and potentially efficient means for solving the many-body Schrödinger equation of quantum mechanics; Monte Carlo methods are statistical)
- Foulkes, W.M.C. Quantum Monte Carlo simulations of solids, in Reviews of modern physics, Jan. 2001, via WWW, Nov. 16, 2020:abstr. (this article describes the variational and fixed-node diffusion quantum Monte Carlo methods and how they may be used to calculate the properties of many-electron systems) p. 34 (quantum Monte Carlo (QMC) methods; the term "quantum Monte Carlo" covers several different techniques based on random sampling)
Wikipedia description:
Quantum Monte Carlo encompasses a large family of computational methods whose common aim is the study of complex quantum systems. One of the major goals of these approaches is to provide a reliable solution (or an accurate approximation) of the quantum many-body problem. The diverse flavors of quantum Monte Carlo approaches all share the common use of the Monte Carlo method to handle the multi-dimensional integrals that arise in the different formulations of the many-body problem. Quantum Monte Carlo methods allow for a direct treatment and description of complex many-body effects encoded in the wave function, going beyond mean-field theory. In particular, there exist numerically exact and polynomially-scaling algorithms to exactly study static properties of boson systems without geometrical frustration. For fermions, there exist very good approximations to their static properties and numerically exact exponentially scaling quantum Monte Carlo algorithms, but none that are both.
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