WSEAS Transactions on Applied and Theoretical Mechanics
Print ISSN: 1991-8747, E-ISSN: 2224-3429
Volume 10, 2015
Quadrilateral Quantum Chain Hamiltonian Cast in Positive Semidefinite Form Containing Non-Linear Fermionic Contributions
Authors: , ,
Abstract: The transformation of a Hamiltonian (connected to a quantum mechanical many-body system) in positive semidefinite form represents an important procedure in a powerful tool used in deducing exact results for nonintegrable systems. Motivated by this fact, we report in this paper the exact transformation of a Hubbard type of Hamiltonian (describing in the presented case an itinerant fermionic quadrilateral chain) in positive semidefinite form, in a such a way that the kinetic and interaction energy terms of the Hamiltonian are treated similarly together, and are provided by the same positive semidefinite expression. For this reason, non-linear fermionic contributions are used in block operators from which the positive semidefinite forms are constructed. The transformation is possible to be done when a system of nonlinear equations, called matching equations, are satisfied. The procedure of solving the matching equations is also indicated.
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Keywords: Non-integrable many-body systems, Hamiltonian in positive semidefinite form, exact ground states
Pages: 187-193
WSEAS Transactions on Applied and Theoretical Mechanics, ISSN / E-ISSN: 1991-8747 / 2224-3429, Volume 10, 2015, Art. #20