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.

scholarly journals Phase separation in the two-dimensional Hubbard model: A fixed-node quantum Monte Carlo study

1998 ◽  
Vol 58 (22) ◽  
pp. R14685-R14688 ◽  
Author(s):  
A. C. Cosentini ◽  
M. Capone ◽  
L. Guidoni ◽  
G. B. Bachelet
Keyword(s):  
Monte Carlo ◽  
Phase Separation ◽  
Hubbard Model ◽  
Quantum Monte Carlo ◽  
Monte Carlo Study ◽  
Two Dimensional ◽  
Fixed Node

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.

Phase diagram of cuprate high-temperature superconductors based on the optimization Monte Carlo method

2020 ◽  
Vol 34 (19n20) ◽  
pp. 2040046
Author(s):  
T. Yanagisawa ◽  
M. Miyazaki ◽  
K. Yamaji
Keyword(s):  
Phase Diagram ◽  
Monte Carlo ◽  
Wave Function ◽  
High Temperature ◽  
Hubbard Model ◽  
Ground State ◽  
State Energy ◽  
High Temperature Superconductivity ◽  
Two Dimensional ◽  
Text Model

It is important to understand the phase diagram of electronic states in the CuO2 plane to clarify the mechanism of high-temperature superconductivity. We investigate the ground state of electronic models with strong correlation by employing the optimization variational Monte Carlo method. We consider the two-dimensional Hubbard model as well as the three-band [Formula: see text]–[Formula: see text] model. We use the improved wave function that takes account of inter-site electron correlation to go beyond the Gutzwiller wave function. The ground state energy is lowered considerably, which now gives the best estimate of the ground state energy for the two-dimensional Hubbard model. The many-body effect plays an important role as an origin of spin correlation and superconductivity in correlated electron systems. We investigate the competition between the antiferromagnetic state and superconducting state by varying the Coulomb repulsion [Formula: see text], the band parameter [Formula: see text] and the electron density [Formula: see text] for the Hubbard model. We show phase diagrams that include superconducting and antiferromagnetic phases. We expect that high-temperature superconductivity occurs near the boundary between antiferromagnetic phase and superconducting one. Since the three-band [Formula: see text]–[Formula: see text] model contains many-band parameters, high-temperature superconductivity may be more likely to occur in the [Formula: see text]–[Formula: see text] model than in single-band models.

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").

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