Various condensed matter Hamiltonians in terms of U(2/2) operators and their symmetry structures

TL;DR

This paper introduces a unified U(2/2) operator framework to rewrite various condensed matter Hamiltonians, clarifying their symmetry structures and enabling systematic symmetry analysis.

Contribution

The authors develop a novel U(2/2) operator representation that simplifies and unifies the symmetry analysis of multiple lattice Hamiltonians in condensed matter physics.

Findings

Different Hamiltonians reduce to a common form in U(2/2) operators.

The representation clarifies the symmetry structures of the models.

Provides a systematic method for symmetry search.

Abstract

We rewrite various lattice Hamiltonian in condensed matter physics in terms of U(2/2) operators that we introduce. In this representation the symmetry structure of the models becomes clear. Especially, the Heisenberg, the supersymmetric t-J and a newly proposed high-$T_c$ superconducting Hamiltonian reduce to the same form $H=$$-t\sum_{<jk>}\sum_{ac}X^{ac}_j X^{ca}_k (-1)^{F(c)}$. This representation also gives us a systematic way of searching for the symmetries of the system.