The numerical simulation of many electron systems in condensed matter physics is described. Numerical algorithms are discussed in detail, and results are presented from simulations of the Hubbard model in two and three dimensions.
The nature of the pairing mechanism responsible for high-temperature superconductivity remains a central theoretical puzzle in condensed matter physics. Here we discuss the properties of the two-dimensional CuO 2 layers common to these materials in terms of a three- band Hubbard model. We describe how recently devel oped quantum Monte Carlo simulation techniques al low one to calculate the physical properties of strongly interacting many-electron systems and discuss the re sources required for such simulations. Then we review what we have learned from these simulations about the antiferromagnetic, charge-transfer, and supercon ducting correlations in the three-band Hubbard model. We conclude with a discussion of future goals.
The nature of the pairing mechanism responsible for high-temperature superconductivity remains a central theoretical puzzle in condensed matter physics. In this paper the authors discuss the properties of the two-dimensional CuO{sub 2} layers common to these materials in terms of a three-bank Hubbard model. The authors describe how recently developed quantum Monte Carlo simulation techniques allow one to calculate the physical properties of strongly interacting many-electron systems and discuss the resources required for such simulations. Then the authors review what we have learned from these simulations about the antiferromagnetic, charge-transfer, and superconducting correlations in the three-band Hubbard model. The authors conclude with a discussion of future goals.
After reviewing the fermi-linearization approach to interacting electron systems, we propose here a refinement of the method based on the extension to itinerant ferminon systems of the philosophy of the Bethe-Peierls treatment of classical systems. We focus our attention on a Hubbard-like model, deriving a general self-consistent scheme which we solve explicitly in the simplest case. We obtain a rich phase-space, exhibiting in particular two phase transitions depending on the band filling. Among the results, we discuss in detail the local magnetic moment, by comparing the outcome of our scheme to some known numerical results in one and two dimensions respectively.