Non-Linear Methods in Strongly Correlated Electron Systems
May 20, 2014Citations per year
Abstract: (arXiv)
A comprehensive analysis of a scheme for the study of strongly correlated electron systems is presented. We show how the Majorana fermion representation significantly improves the definition and control of non-linear canonical transformations of the degrees of freedom used in the study of a quantum problem. This allows for a more general treatment of quantum Hamiltonians and permits to identify and understand otherwise hidden symmetries of difficult interpretation. In particular, the analysis of strongly correlated electron systems may become more effective in the framework that we suggest, since it permits to define new fermionic degrees of freedom that take into account the correlations of the system. We demonstrate that such (local) non-linear canonical transformations have the structure of a Lie group, providing a representation for the elements of the Lie algebra that is very convenient from both conceptual and practical (computational) reasons: indeed our framework yields as side product an extremely effective tool to handle and work with SU(2n) Lie groups and algebras. Moreover we outline relevant scenarios where the applications of our approach may increase our predictive power, dedicating special attention to the correlated hopping models.Note:
- 22 pages
References(70)
Figures(0)
- [1]
- [2]
- [3]
- [4]
- [5]
- [6]
- [7]
- [8]
- [9]
- [10]
- [11]
- [12]
- [13]
- [14]
- [15]
- [16]
- [17]
- [18]
- [19]
- [20]
- [21]
- [22]
- [23]
- [24]
- [25]