Exact Ground State of Lieb-Mattis Hamiltonian as a Superposition of N\'eel states

TL;DR

This paper demonstrates that the exact ground state of the Lieb-Mattis Hamiltonian is an equal superposition of all classical Ne9el states, providing an explicit formulation in the spin basis and clarifying the role of symmetrization.

Contribution

It provides an exact superposition formulation of the Lieb-Mattis ground state in the $z$-spin basis for arbitrary spin, using Schwinger bosons, and explains the symmetrization effects on Ne9el states.

Findings

Ground state is an equal superposition of all Ne9el states.

Explicit formulation in the $z$-spin basis for $S=1/2$ and general $S$.

Symmetrization projects onto the singlet component, explaining the vanishing of certain states.

Abstract

We show that the exact ground state of the Lieb-Mattis Hamiltonian is an equal-weight superposition of all possible classical N\'{e}el states, and provide an exact formulation of this superposition in the $z$-spin basis for both $S=1/2$ and general $S$ using Schwinger bosons. In general, a superposition of possible rotations on a general initial state is symmetric if and only if the initial state has a nonzero overlap with a singlet state and is otherwise made up of states that vanish due to the symmetrization. Most notably, $|s, m=0 \rangle$ states will vanish if symmetrized, which explains how a superposition of N\'{e}el states projects onto its singlet component.