Immobile and mobile excitations of three-spin interactions on the diamond chain

TL;DR

This paper introduces an exactly solvable 1D spin-1/2 model on a diamond chain with three-spin interactions, revealing both mobile and immobile excitations, and explores their complex interactions and phase transitions.

Contribution

It provides an exact mapping to transverse-field Ising chains, elucidating the nature of immobile excitations and their Casimir-like forces in a fracton-inspired model.

Findings

The model exhibits a second-order phase transition driven by mobile excitations.

It features non-trivial fully immobile excitations with Casimir-like forces.

The exact mapping simplifies analysis of complex excitation behavior.

Abstract

We present a solvable one-dimensional spin-1/2 model on the diamond chain featuring three-spin interactions, which displays both, mobile excitations driving a second-order phase transition between an ordered and a $\mathbb{Z}_2$-symmetry broken phase, as well as non-trivial fully immobile excitations. The model is motivated by the physics of fracton excitations, which only possess mobility in a reduced dimension compared to the full model. We provide an exact mapping of this model to an arbitrary number of independent transverse-field Ising chain segments with open boundary conditions. The number and lengths of these segments correspond directly to the number of immobile excitations and their respective distances from one another. Furthermore, we demonstrate that multiple immobile excitations exhibit Casimir-like forces between them, resulting in a non-trivial spectrum.