The energy spectrum symmetry of Heisenberg model in Fock space

TL;DR

This paper proves a symmetry in the energy spectrum of the one-dimensional spin 1/2 Heisenberg model between specific subspaces of the Fock space, using quantum operations like spin flip and site reflection.

Contribution

It introduces a rigorous proof of energy spectrum symmetry in the Heisenberg model via novel quantum operations, expanding understanding of its spectral properties.

Findings

Energy spectrum symmetry between subspaces n and L-n

Use of flip and mirror reflection operations in proof

Rigorous mathematical demonstration of spectral symmetry

Abstract

We prove strictly that one dimension spin 1/2 Heisenberg model has a symmetry of energy spectrum between its subspace $n$ and the subspace $L-n$ of the Fock space. Our proof is completed by introducing two general quantum operations. One is a flip operation of spin direction and another is a mirror reflection of spin sites.