Quantum Monte Carlo with ground-state input to investigate platinum-doped aluminum catalyst: H2 production from adsorbed CO

2021 ◽  
pp. 155-170
Author(s):  
Philip E. Hoggan
Keyword(s):  
Monte Carlo ◽  
Ground State ◽  
Quantum Monte Carlo ◽  
H2 Production ◽  
Adsorbed Co

A survey on pure sampling in quantum Monte Carlo methods

2013 ◽  
Vol 91 (7) ◽  
pp. 505-510 ◽  
Author(s):  
Stuart M. Rothstein
Keyword(s):  
Monte Carlo ◽  
Ground State ◽  
Quantum Monte Carlo ◽  
Sampling Methods ◽  
Electrical Response ◽  
Distribution Functions ◽  
Monte Carlo Algorithm ◽  
Position Operator ◽  
Trial Solution ◽  
Mixed Distribution

The most commonly employed diffusion Monte Carlo algorithm and some of its variants afford a way to sample configuration space from a so-called “mixed distribution”, the product of an input trial solution to the Schrödinger equation for the ground state and its unknown exact solution. This mixed distribution is sufficient to compute the ground state energy and other properties represented by operators that commute with the Hamiltonian. These energy-related properties are exact, save for a small bias introduced by the input trial function’s incorrect exchange nodes, the so-called “fixed-node error”. However, properties represented by operators that commute with the position operator are also of interest. When calculated by sampling from the mixed distribution, these properties are much more strongly biased by the input trial function. Our objective is to review methods that allow sampling from the desired “pure” distribution, one that is unbiased except for the exchange node error. Thereby, one accurately calculates physical properties such as the dipole and other electrical moments, electrical response properties of molecules, and particle distribution functions for clusters. We survey the results of calculations that employ pure-sampling methods through what has been published in year 2012. Our review also touches on truly exact sampling methods.

scholarly journals Unconventional phase transitions in strongly anisotropic 2D (pseudo)spin systems

2018 ◽  
Vol 185 ◽  
pp. 08006
Author(s):  
Vitaly Konev ◽  
Evgeny Vasinovich ◽  
Vasily Ulitko ◽  
Yury Panov ◽  
Alexander Moskvin
Keyword(s):  
Magnetic Field ◽  
Monte Carlo ◽  
Phase Transitions ◽  
Ground State ◽  
Quantum Monte Carlo ◽  
Mean Field ◽  
Spin Systems ◽  
Field Approach ◽  
Generalized Mean

We have applied a generalized mean-field approach and quantum Monte-Carlo technique for the model 2D S = 1 (pseudo)spin system to find the ground state phase with its evolution under application of the (pseudo)magnetic field. The comparison of the two methods allows us to clearly demonstrate the role of quantum effects. Special attention is given to the role played by an effective single-ion anisotropy ("on-site correlation").

A SINGLE HOLE IN THE TWO-DIMENSIONAL INFINITE-U HUBBARD MODEL IN AN ORBITAL MAGNETIC FIELD

1994 ◽  
Vol 08 (06) ◽  
pp. 707-725
Author(s):  
S. V. MESHKOV ◽  
J. C. ANGLÈS D'AURIAC
Keyword(s):  
Magnetic Field ◽  
Monte Carlo ◽  
Hubbard Model ◽  
Ground State ◽  
Quantum Monte Carlo ◽  
Applied Field ◽  
Monte Carlo Algorithm ◽  
Two Dimensional ◽  
Thermodynamical Properties ◽  
Single Hole

Using an original Quantum Monte Carlo algorithm, we study the thermodynamical properties of a single hole in the two-dimensional infinite-U Hubbard model at finite temperature. We investigate the energy and the spin correlators as a function of an external orbital magnetic field. This field is found to destroy the Nagaoka ferromagnetism and to induce chirality in the spin background. The applied field is partially screened by a fictitious magnetic field coming from the chirality. Our algorithm allows us to reach a temperature low enough to discuss the ground state properties of the model.

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