Characterization of Reflection Positivity: Majoranas and Spins

TL;DR

This paper characterizes when reflection positivity holds in models with Majoranas and spins, providing necessary and sufficient conditions on coupling constants, and illustrates these with various spin systems.

Contribution

It offers a comprehensive characterization of reflection positivity conditions for Majorana and spin models, enabling easier verification in concrete systems.

Findings

Derived necessary and sufficient conditions for reflection positivity.

Applied conditions to various spin systems with different interactions.

Provided practical criteria for checking reflection positivity in models.

Abstract

We study linear functionals on a Clifford algebra (algebra of Ma- joranas) equipped with a reflection automorphism. For Hamiltonians that are functions of Majoranas or of spins, we find necessary and sufficient conditions on the coupling constants for reflection positivity to hold. One can easily check these conditions in concrete models. We illustrate this by discussing a number of spin systems with nearest-neighbor and long-range interactions.