Quadrilateral quantum chain hamiltonian cast in positive semidefinite form containing non-linear fermionic contributions

Gyorgy Kovacs, Konstantin Glukhov, Zsolt Gulacsi

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1 Citation (Scopus)


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.

Original languageEnglish
Article number#20
Pages (from-to)187-193
Number of pages7
JournalWSEAS Transactions on Applied and Theoretical Mechanics
Publication statusPublished - Jan 1 2015



  • Exact ground states
  • Hamiltonian in positive semidefinite form
  • Non-integrable many-body systems

ASJC Scopus subject areas

  • Computational Mechanics
  • Civil and Structural Engineering
  • Mechanics of Materials
  • Mechanical Engineering
  • Fluid Flow and Transfer Processes

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