Topological Quantum Liquids with Long-Range Couplings

TL;DR

This paper extends the Kitaev chain model to include infinite-range couplings, revealing stable topological phases with Majorana modes, and explores their potential relevance to experimental systems with designed interactions.

Contribution

It introduces an analytical framework for topological phases in long-range coupled systems, expanding understanding beyond local interactions.

Findings

Infinite-range couplings support topological Majorana modes.

Topological properties are stable against modifications to long-range couplings.

The work opens new avenues for experimental realization of topological states.

Abstract

Very few topological systems with long-range couplings have been considered so far due to our lack of analytic approaches. Here we extend the Kitaev chain, a 1D quantum liquid, to infinite-range couplings and study its topological properties. We demonstrate that, even though topological phases are intimately linked to the notion of locality, the infinite-range couplings give rise to topological zero and non-zero energy Majorana end modes depending on the boundary conditions of the system. We show that the analytically derived properties are to a large degree stable against modifications to decaying long-range couplings. Our work opens new frontiers for topological states of matter that are relevant to current experiments where suitable interactions can be designed.