Item – Theses Canada

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OCLC number
46573780
Link(s) to full text
LAC copy
LAC copy
Author
Jin, Beiyan,1961-
Title
Quantum phases for two-body spin-invariant nearest neighbor interactions.
Degree
Ph. D. -- Queen's University, 1998
Publisher
Ottawa : National Library of Canada = Bibliothèque nationale du Canada, [1999]
Description
2 microfiches.
Notes
Includes bibliographical references.
Abstract
We build a family of Hamiltonians which include all two-body spin-invariant nearest neighbor interactions for a class of lattices. We study the phase structure for the pure two-body interactions in the family and label quantum phases with good quantum numbers. Possible quantum phases and phase transitions are investigated in lattices with cubic symmetry. We are especially interested in the superconducting phase and its adjacent quantum phases in these systems. The relationship between the superconducting phase and the antisymmetrized geminal power function, which has a very close relation to the superconducting ground state in the microscopic theory of Bardeen, Cooper and Schrieffer for the conventional superconductivity, is addressed. This is done to gain a better understanding about the physical mechanism of superconducting pairing and thus the physical mechanism of high-temperature superconductivity in the $CuO\sb2$ based superconducting materials. Aiming at a viable alternative to the wave-function approach, we analyze the lower bound method of reduced density matrix theory, a method which obtains a lower bound to the ground state energy of a many-body system as well as an approximation to the corresponding reduced density matrix. Two numerical algorithms based on a main theorem giving necessary and sufficient conditions for the optimum are presented. Numerical procedures for these algorithms are programmed to solve the central optimization program in the lower bound method. We consider their convergence properties which are very crucial for the lower bound method to become a computationally feasible method in large scale. Direct lower bound calculations are carried out for the first time in one-dimensional rings. The entries of both the two-body and the three-body density matrices are used as variational parameters in these computations. The results obtained show that the three-body density matrix is the best choice for the lower bound method in these one-dimensional systems. The lower bound method with the three-body density matrix effectively provides a solution to the n-representability problem. It is predicted that direct lower bound calculations in two-dimensional square lattices and other more complicated systems will be very successful too.
ISBN
061227831X
9780612278318