A Zero-Temperature Quantum Monte Carlo Algorithm and Quantum Spin Glasses

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.

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Efficient calculation of imaginary-time-displaced correlation functions in the projector auxiliary-field quantum Monte Carlo algorithm

Physical Review B ◽

10.1103/physrevb.63.073105 ◽

2001 ◽

Vol 63 (7) ◽

Cited By ~ 29

Author(s):

M. Feldbacher ◽

F. F. Assaad

Keyword(s):

Monte Carlo ◽

Correlation Functions ◽

Quantum Monte Carlo ◽

Monte Carlo Algorithm ◽

Auxiliary Field ◽

Imaginary Time ◽

Efficient Calculation

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

International Journal of Modern Physics B ◽

10.1142/s0217979294000270 ◽

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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