The geometric phase of Z$_n$- and T-symmetric nanomagnets as a classification toolkit

TL;DR

This paper derives a general form of a geometric phase influenced by symmetries in nanomagnets, providing a classification scheme that aids in understanding state protection and has implications for quantum computing.

Contribution

It introduces a unified framework to calculate the geometric phase in symmetric nanomagnets, linking symmetry properties to state protection and classification.

Findings

Derived the form of the geometric phase for Z$_n$- and T-symmetric nanomagnets.

Showed how this phase determines eigenstate ordering and quantum numbers.

Highlighted the phase's relevance for topologically protected quantum states.

Abstract

We derive the general form of the non-trivial geometric phase resulting from the unique combination of point group and time reversal symmetries. This phase arises e.g. when a magnetic adatom is adsorbed on a non-magnetic C$_n$ crystal surface, where $n$ denotes the fold of the principal axis. The energetic ordering and the relevant quantum numbers of the eigenstates are entirely determined by this quantity. Moreover, this phase allows to conveniently predict the protection mechanism of any prepared state, shedding light onto a large number of experiments and allowing a classification scheme. Owing to its robustness this geometric phase also has great relevance for a large number of applications in quantum computing, where topologically protected states bearing long relaxation times are highly desired.