Deducing exact ground states for many-body non-integrable systems

Research output: Contribution to journalArticle

Abstract

I describe in details the method which uses positive semidefinite operator properties in deducing non-approximated results for quantum mechanical many-body non-integrable systems. The steps of the procedure, namely i) the transcription of the Hamiltonian in a positive semidefinite form H=O+C, where O is a positive semidefinite operator while C is a scalar, ii) the deduction of the total particle number dependent ground state by constructing the most general solution of the equation O |Ψ> = 0, iii) the demonstration of the uniqueness by concentrating on the kernel of the operator O, and iv) the study of the physical properties of the deduced phase by calculating elevated ground state expectation values and the analysis of the low lying part of the excitation spectrum, are described in extreme details.

Original languageEnglish
Pages (from-to)691-699
Number of pages9
JournalInternational Journal of Mathematical Models and Methods in Applied Sciences
Volume9
Publication statusPublished - 2015

Keywords

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

ASJC Scopus subject areas

  • Applied Mathematics
  • Computational Mathematics
  • Mathematical Physics
  • Modelling and Simulation

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