| Summary: | 博士 === 國立清華大學 === 物理學系 === 85 === To understand the physical properties and mechanism of the
hightemperature superconductors, a strongly correlated
electronicsystem, the two-dimensional $t-J$ model, is studied
numerically.A new trial wave function with both
antiferromagnetic andsuperconducting long-range order is derived
from the mean-field theory.We develop a powerful numerical
method, the power-Lanczos method,for studing the strongly
correlated electron systems.We found that the dispersion
relation of one hole in antiferromagnetcan be explained by the
theory of d-RVB together with antiferromagnetism.As the number
of doped holes increases, the antiferromagnetic long-range
orderdecreases rapidly and vanishes for doping density $x sim
5%$.In the high density limit, phase separates into a hole-
freeHeisenberg island and a hole-rich region at $J_c/t = 0.6 pm
0.1$.$J_c/t$ increases as the hole density increases. In the
physicalregion of high temperature superconductors, the signal
ofsuperconductivity of this model is too weak to explain the
high$T_c$ of the high temperature superconductors.
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