On the ground-state properties of antiferromagnetic half-integer spin chains with long-range interactions

TL;DR

This paper extends the Lieb-Shultz-Mattis theorem to long-range interacting antiferromagnetic chains, proving the absence of an energy gap under certain decay conditions for half-integer spins.

Contribution

It generalizes the theorem to models with long-range interactions, establishing conditions for gapless ground states in one-dimensional systems.

Findings

Half-integer spin chains with interactions decaying faster than 1/r^2 are gapless.

The theorem applies to a broad class of one-dimensional models.

Ground state uniqueness is a key assumption for the results.

Abstract

The Lieb-Shultz-Mattis theorem is extended to Heisenberg chains with long-range interactions. We prove that the half-integer spin chain has no gap, if it possesses unique ground state and the exchange decays faster than the inverse-square of distance between spins. The results can be extended to a wide class of one-dimensional models.